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This paper proposes a novel reliable model predictive control (MPC) method for active vibration control of structure with nonprobabilistic uncertainties. First, the framework of reliable MPC is established by integrating nonprobabilistic reliability constraints into nominal MPC. Based on the first‐order Taylor expansion and first‐passage theory, an efficient nonprobabilistic reliability analysis method that is suitable for online computation is proposed. A nonprobabilistic Kalman filter is further proposed for determine system states and their uncertain region. Unlike most robust MPC approaches, the proposed reliable MPC focuses on the satisfaction of state constraints in terms of structural reliability and is more suitable for structures with stringent safety requirements. Compared to existing reliability‐based vibration control methods, reliable MPC requires no knowledge of disturbance and exhibits greater adaptability to load environments. The effectiveness and superiority of the proposed reliable MPC are validated through a numerical example and an engineering case study. [ABSTRACT FROM AUTHOR]

In the context of constructing new power systems, the intermittency and volatility of high-penetration renewable generation pose new challenges to the stability and secure operation of power systems. Enhancing the ramping capability of power systems has become a crucial measure for addressing these challenges. Therefore, this paper proposes a bi-level peak regulation optimization model for power systems considering ramping capability and demand response, aiming to mitigate the challenges that the uncertainty and volatility of renewable energy generation impose on power system operations. Firstly, the upper-level model focuses on minimizing the ramping demand caused by the uncertainty, taking into account concerned constraints such as the constraint of price-guided demand response, the constraint of satisfaction with electricity usage patterns, and the constraint of cost satisfaction. By solving the upper-level model, the ramping demand of the power system can be reduced. Secondly, the lower-level model aims to minimize the overall cost of the power system, considering constraints such as power balance constraints, power flow constraints, ramping capability constraints of thermal power units, stepwise ramp rate calculation constraints, and constraints of carbon capture units. Based on the ramping demand obtained by solving the upper-level model, the outputs of the generation units are optimized to reduce operation cost of power systems. Finally, the proposed peak regulation optimization model is verified through simulation based on the IEEE 39-bus system. The results indicate that the proposed model, which incorporates ramping capability and demand response, effectively reduces the comprehensive operational cost of the power system. [ABSTRACT FROM AUTHOR]

Some have defended a Fregean view of perceptual content. On this view, the constituents of perceptual contents are Fregean modes of presentation (MOPs). In this paper, I propose that perceptual MOPs are best understood in terms of object files. Object files are episodic representations that store perceptual information about objects. This information is updated when sensory conditions change. On the proposed view, when a subject perceptually represents some object a under two distinct MOPs, then the subject initiates two object files that both refer to a. My defense of this view appeals to its satisfaction of four constraints that I argue theories of perceptual MOPs should satisfy. Furthermore, I show that some existent accounts of perceptual MOPs fail to satisfy them. The defended constraints also indicate what is unique about perceptual, as opposed to linguistic or cognitive, MOPs. [ABSTRACT FROM AUTHOR]

This paper describes several cases of adjunction in the homomorphism preorder of relational structures. We say that two functors Λ and Γ between thin categories of relational structures are adjoint if for all structures A and B, we have that Λ⁢(A) maps homomorphically to B if and only if A maps homomorphically to Γ⁢(𝐁). If this is the case, Λ is called the left adjoint to Γ and Γ the right adjoint to Λ. In 2015, Foniok and Tardif described some functors on the category of digraphs that allow both left and right adjoints. The main contribution of Foniok and Tardif is a construction of right adjoints to some of the functors identified as right adjoints by Pultr in 1970. We generalise results of Foniok and Tardif to arbitrary relational structures, and coincidently, we also provide more right adjoints on digraphs, and since these constructions are connected to finite duality, we also provide a new construction of duals to trees. Our results are inspired by an application in promise constraint satisfaction -- it has been shown that such functors can be used as efficient reductions between these problems. [ABSTRACT FROM AUTHOR]

The key motivation of this paper lies in the development of a high‐level decision‐making framework for autonomous overtaking maneuvers on two‐lane country roads with dynamic oncoming traffic. To generate an optimal and safe decision sequence for such scenario, an innovative high‐level decision‐making framework that combines model predictive control (MPC) and switching control methodologies is introduced. Specifically, the autonomous vehicle is abstracted and modelled as a switched system. This abstraction allows vehicle to operate in different modes corresponding to different high‐level decisions. It establishes a crucial connection between high‐level decision‐making and low‐level behaviour of the autonomous vehicle. Furthermore, barrier functions and predictive models that account for the relationship between the autonomous vehicle and oncoming traffic are incorporated. This technique enables us to guarantee the satisfaction of constraints, while also assessing performance within a prediction horizon. By repeatedly solving the online constrained optimization problems, we not only generate an optimal decision sequence for overtaking safely and efficiently but also enhance the adaptability and robustness. This adaptability allows the system to respond effectively to potential changes and unexpected events. Finally, the performance of the proposed MPC framework is demonstrated via simulations of four driving scenarios, which shows that it can handle multiple behaviours. [ABSTRACT FROM AUTHOR]

This paper proposes a trajectory-optimization problem for spacecraft close proximity to a noncooperative target, aiming at the generation of a six-degree-of-freedom (DOF) trajectory with the fuel-optimal objective value and considering multiple constraints on the control magnitude, line-of-sight, and glide-slope. The line-of-sight and glide-slope constraints are coupled between translational and rotational motions. The dual quaternion is an effective method for establishing the translationally and rotationally coupled model, because it can represent the translation and rotation in an integrated manner. Therefore, in this study, the trajectory-optimization problem of spacecraft close proximity coupled with position and attitude is established using dual quaternions. Next, the close-proximity trajectory-optimization problem is converted into a nonlinear programming problem, which can be solved efficiently using well-developed algorithms such as convex optimization. However, the zero-order hold used in the discrete method of convex optimization is an equidistant dispersion, which cannot guarantee the satisfaction of constraints between discrete points. Therefore the pseudospectral convex method is proposed using nonequidistant collocation points to mitigate the problem of constraint violation between discrete points and improve the accuracy and computational efficiency of the algorithm. The proposed algorithm can be applied to tasks such as rendezvous and docking with noncooperative targets and close proximity. Finally, the effectiveness of the proposed method was validated via numerical simulation, and the results were compared with those of the existing approach, GPOPS. The results indicate that the proposed algorithm is superior to GPOPS in computational efficiency and objective values. [ABSTRACT FROM AUTHOR]

In recent years, the substantial growth in satellite data transmission tasks and volume, coupled with the limited availability of ground station hardware resources, has exacerbated conflicts among missions and rendered traditional scheduling algorithms inadequate. To address this challenge, this paper introduces an improved tabu genetic hybrid algorithm (ITGA) integrated with heuristic rules for the first time. Firstly, a constraint satisfaction model for satellite data transmission tasks is established, considering multiple factors such as task execution windows, satellite–ground visibility, and ground station capabilities. Leveraging heuristic rules, an initial population of high-fitness chromosomes is selected for iterative refinement. Secondly, the proposed hybrid algorithm iteratively evolves this population towards optimal solutions. Finally, the scheduling plan with the highest fitness value is selected as the best strategy. Comparative simulation experimental results demonstrate that, across four distinct scenarios, our algorithm achieves improvements in the average task success rate ranging from 1.5% to 19.8% compared to alternative methods. Moreover, it reduces the average algorithm execution time by 0.5 s to 28.46 s and enhances algorithm stability by 0.8% to 27.7%. This research contributes a novel approach to the efficient scheduling of satellite data transmission tasks. [ABSTRACT FROM AUTHOR]

The effective exploitation of infeasible solutions plays a crucial role in addressing constrained multiobjective optimization problems (CMOPs). However, existing constrained multiobjective optimization evolutionary algorithms (CMOEAs) encounter challenges in effectively balancing objective optimization and constraint satisfaction, particularly when tackling problems with complex infeasible regions. Subsequent to the prior exploration, this paper proposes a novel tri-stage with reward-switching mechanism framework (TSRSM), including the push, pull, and repush stages. Each stage consists of two coevolutionary populations, namely Pop 1 and Pop 2 . Throughout the three stages, Pop 1 is tasked with converging to the constrained Pareto front (CPF). However, Pop 2 is assigned with distinct tasks: (i) converging to the unconstrained Pareto front (UPF) in the push stage; (ii) utilizing constraint relaxation technique to discover the CPF in the pull stage; and (iii) revisiting the search for the UPF through knowledge transfer in the repush stage. Additionally, a novel reward-switching mechanism (RSM) is employed to transition between different stages, considering the extent of changes in the convergence and diversity of populations. Finally, the experimental results on three benchmark test sets and 30 real-world CMOPs demonstrate that TSRSM achieves competitive performance when compared with nine state-of-the-art CMOEAs. The source code is available at https://github.com/Qu-jq/TSRSM. [ABSTRACT FROM AUTHOR]

Distributed switched large-scale systems are composed by dynamically coupled subsystems, in which interactions among subsystems vary over time according a switching signal. This paper presents a distributed robust switched model-based predictive control (DSwMPC) to control such systems. The proposed method guarantees stabilising the origin of the whole closed-loop system and ensures the constraints satisfaction in the presence of an unknown switching signal. In the distributed model-based predictive control (DMPC) used in this work, by considering the interactions among subsystems as an additive disturbance, the effect of the switch is reflected on the dynamic equation, local, and consistency constraint sets of the nominal subsystems. To compensate the effect of switching signal which creates a time-varying network topology, a robust tube-based switched model-based predictive control (RSwMPC) with switch–robust control invariant set as the target set robust to unknown mode switching is used as local controller. The scheme performance is assessed using three typical examples. The simulation results show that the input and state constraints are satisfied by the proposed DSwMPC at all times. They also validate that the closed-loop system converges to the origin. Also, a comparison of the DSwMPC with a centralised SwMPC (CSwMPC) and a decentralised SwMPC (DeSwMPC) are performed. [ABSTRACT FROM AUTHOR]

Model predictive control is a popular choice for systems that must satisfy prescribed constraints on states and control inputs. Although much progress has been made in distributed model predictive control, existing algorithms tend to be computationally expensive. This limits their use in systems with fast dynamics. In this paper, we propose a new distributed model predictive control algorithm that we term as instant distributed model predictive control (iDMPC). The proposed algorithm employs a realisation of the primal-dual algorithm in the controller dynamics for fast computation. We show that the closed-loop system trajectories with the proposed iDMPC algorithm converge asymptotically to a desired reference. To ensure the satisfaction of the state constraints during the transient, we also include an explicit reference governor in the feedback loop. [ABSTRACT FROM AUTHOR]

In this paper, the trajectory tracking problem of controlling a constrained quadrotor with unmeasurable system states in an environment with stochastic wind‐gust disturbance is considered. The mathematical model of the quadrotor is divided into the translational system and the rotational system, while only the measurement output of the quadrotor can be accessed. A new output‐based control method is developed for solving this problem. In the translational control system, an output feedback stochastic model predictive control (MPC) algorithm is proposed to generate the optimal control sequence with less conservativeness, by taking into account the information on the distribution of the disturbances and the uncertainty resulting from the attitude tracking error. The closed‐loop probabilistic constraints satisfaction, the recursive feasibility and the stability of the algorithm are further proved. In the rotational system, the active disturbance rejection control (ADRC) method to estimate and compensate for external disturbances is leveraged and robust control for attitude tracking is accomplished. The convergence of the disturbance estimator and the stability proof are provided. Finally, the robustness and effectiveness of the proposed control strategy are verified by an illustrative example. [ABSTRACT FROM AUTHOR]

This paper presents a novel approach that facilitates the design of active controllers to mitigate seismically induced damage in structural systems. The proposed method is based on stochastic Modified Black Hole optimization algorithm. Two traditional controllers, namely Proportional-Integral-Derivative (PID) and Linear–Quadratic Gaussian (LQG) controllers were designed, and their performance was demonstrated on a benchmark 20-story steel-framed building. Evaluation criteria were defined to satisfy constraints on various response quantities, including drift, base shear, ductility, residual story drift, and control force. The constraint limits were defined in view of performance-based design requirements for the benchmark structure. The performance of the controllers was contrasted with that of traditional LQG, and significant reductions of all response quantities were achieved for design-level earthquakes. [ABSTRACT FROM AUTHOR]

This paper presents a new approach for designing an event‐triggered predictive sliding mode control (SMC) for discrete‐time systems subject to constraints. The proposed controller is based on an existing reach‐law‐based SMC, and it formulates an optimization control problem (OCP) to generate predictive control actions that satisfy both state and input constraints. An event‐triggered strategy is introduced to reduce the frequency of OCP solving by taking into account the sliding mode controller and unmeasurable states between sampling instants. The paper also analyzes the recursive feasibility of the proposed controller, which ensures the feasibility of each OCP solution. Numerical simulations and comparison studies are performed to validate the theoretical results. The proposed approach offers an effective way to design event‐triggered predictive sliding mode controllers that reduce the computational burden of OCP solving while guaranteeing the satisfaction of system constraints. [ABSTRACT FROM AUTHOR]

Mining frequent sequences (FS) with constraints in a sequence database (SDB) are a critical task in Data Mining, as it forms the basis for discovering meaningful patterns within sequential data. However, traditional algorithms tackling the direct mining of constrained FSs from the SDB often exhibit poor performance, especially when dealing with large SDBs and low support thresholds. Moreover, constraint-based sequence mining algorithms face additional challenges, such as increased runtime and memory usage, particularly when constraints change frequently. To address these issues, this paper introduces an efficient method for generating FSs that include a user-defined sub-sequence. Specifically, the discovered FSs must be super-sequences of the given sub-sequence. Rather than directly discovering these sequences from a sequence database (SDB) in the traditional manner, the proposed method quickly generates constrained FSs from frequent closed sequences (FCS) and frequent generator sequences (FGS). This process involves categorizing constrained FSs into equivalence classes; each represented by FCSs and FGSs. An efficient method is then adapted to swiftly generate constrained FSs within each class based on the representative elements, which are FCSs and FGSs. Additionally, a novel technique called Constraint Satisfaction Technique (CST) is introduced to circumvent computationally expensive checks for the inclusion relation among sequences during the generation process. Furthermore, a novel algorithm named MFS-SubSC is developed based on the proposed theoretical results to generate all constrained FSs efficiently. Experimental results demonstrate that the proposed algorithm surpasses state-of-the-art methods in terms of runtime, memory usage, and scalability. [ABSTRACT FROM AUTHOR]

The paper presents a new Lyapunov-type predefined-time stabilization control algorithm for stochastic high-order nonlinear systems with asymmetric output constraints. In contrast to stochastic finite-time and fixed-time stabilization, the average value of the settling-time function for stochastic predefined-time stabilization control is independent of both the initial value and the control factors. To mitigate the significant uncertainties arising from the asymmetric output constraint, a tan-type barrier Lyapunov function is formulated. Furthermore, by harnessing the previously mentioned barrier Lyapunov function and integrating the power integrator technique, a controller design strategy is formulated based on the backstepping method. The rigorous analysis in this study proves that the designed controller ensures both the attainment of predefined-time convergence of the system states to the origin in probability and the satisfaction of the output constraint. Finally, an example of a roll angle subsystem for quadrotor UAVs and a numerical illustration are presented to corroborate the theoretical analysis. • A novel Lyapunov-type stochastic predefined-time stable control algorithm is presented in Theorem 1. • Controller design based on the backstepping method is formulated through the power integrator technique. • The tan-type barrier Lyapunov function extends the order range and absorbs the inherent properties of the nonlinear terms. [ABSTRACT FROM AUTHOR]

Chance constraints are a valuable tool for the design of safe decisions in uncertain environments; they are used to model satisfaction of a constraint with a target probability. However, because of possible non-convexity and non-smoothness, optimizing over a chance constrained set is challenging. In this paper, we consider chance constrained programs where the objective function and the constraints are convex with respect to the decision parameter. We establish an exact reformulation of such a problem as a bilevel problem with a convex lower-level. Then we leverage this bilevel formulation to propose a tractable penalty approach, in the setting of finitely supported random variables. The penalized objective is a difference-of-convex function that we minimize with a suitable bundle algorithm. We release an easy-to-use open-source python toolbox implementing the approach, with a special emphasis on fast computational subroutines. [ABSTRACT FROM AUTHOR]

This paper proposes an innovative approach for constrained rendezvous trajectory optimization (CRTO) using stochastic optimal feedback control and unscented transform (UT) uncertainty quantification. The method overcomes limitations of traditional deterministic CRTO solutions that suffer from uncontrolled terminal state error growth and severely deteriorated path constraint satisfaction when initial state uncertainty, dynamics uncertainty, and navigation uncertainty are considered. The approach involves constructing a stochastic optimal feedback control (SOFC) problem with chance constraints and introducing linear feedback control to regulate both the mean and variance of terminal state errors. UT is employed to approximately quantify the state errors and their propagation, transforming the SOFC problem into an unconstrained deterministic optimization (UDO) problem. Differential dynamic programming (DDP) is then used to solve the UDO problem. The obtained stochastic optimal solution provides a robust rendezvous trajectory and a corresponding explicit closed-loop guidance law, improving terminal accuracy and path constraint satisfaction in the presence of various considered uncertainties. The influence of different term weights in the objective function on terminal accuracy and path constraint satisfaction is also studied. The effectiveness of the proposed approach is verified through Monte Carlo simulation, demonstrating the robustness of the closed-loop control strategy. The results highlight the potential of the method in enhancing terminal accuracy and path constraint satisfaction in uncertain rendezvous scenarios. • The uncertainty-resilient rendezvous trajectory optimization algorithm provides not only a nominal trajectory but an explicit optimal state-feedback control policy. • Rendezvous trajectory uncertainty caused by initial state errors, dynamics errors, and navigation errors is propagated using an unscented transformation method. • The proposed method considers common input constraints and path constraints in space rendezvous missions. [ABSTRACT FROM AUTHOR]

During the architectural design phase, the decisions made have a crucial impact on developing complex systems. These decisions often limit the performance bounds and steer subsequent research directions. However, the multitude of architectural components and intricate interrelationships cause component combination explosion. Additionally, the diverse requirements of different stakeholders add complexity to determining the weight of indicators, posing challenges to complex system architecture generation and trade-off. This paper proposes a method for exploring the architectural design space in complex systems realisation, which aims to resolve issues related to the formal representation of architectures, selection within the architectural design space, and trade-offs. Firstly, the architectural design space is represented by formulating and mathematically describing a morphological matrix. Then, the construction of the Constraint Satisfaction Problem model aims to achieve a reduction in the scale of the design space. Moreover, through the evolutionary algorithm, the Pareto front is identified. Weight sensitivity analysis and the improved Technique for Order Preference by Similarity to the Ideal Solution method are combined to assist designers in finding a satisfactory architecture from the design space with many combinations. Finally, the proposed method is verified by the design of the launch vehicle's primary and secondary separation system. [ABSTRACT FROM AUTHOR]

Continuous constraint satisfaction is prevalent in many science and engineering fields. When solving continuous constraint satisfaction problems, it is more advantageous for practitioners to derive all feasible regions (i.e., the solution space) rather than a limited number of solution points, since these feasible regions facilitate design concept generation and design tradeoff evaluation. Several central processing unit (CPU)-based branch-and-prune methods and geometric approximation methods have been proposed in prior research to derive feasible regions for continuous constraint satisfaction problems. However, these methods have not been extensively adopted in practice, mainly because of their high computational expense. To overcome the computational bottleneck of extant CPU-based methods, this paper introduces a GPU-based parallel region classification method to derive feasible regions for continuous constraint satisfaction problems in a reasonable computational time. Using interval arithmetic, coupled with the computational power of GPU, this method iteratively partitions the design space into many subregions and classifies these subregions as feasible, infeasible, and indeterminate regions. To visualize these classified regions in the design space, a planar visualization approach that projects all classified regions into one figure is also proposed. The GPU-based parallel region classification method and the planar visualization approach are validated through two case studies about the bird function and the welded beam design. These case studies show that the method and the approach can solve the continuous constraint satisfaction problems and visualize the results effectively and efficiently. A four-step procedure for implementing the method and the approach in practice is also outlined. [ABSTRACT FROM AUTHOR]

The ArtGallery problem is a fundamental visibility problem in Computational Geometry. The input consists of a simple polygon P, (possibly infinite) sets G and C of points within P, and an integer k; the task is to decide if at most k guards can be placed on points in G so that every point in C is visible to at least one guard. In the classic formulation of ArtGallery, G and C consist of all the points within P. Other well-known variants restrict G and C to consist either of all the points on the boundary of P or of all the vertices of P. Recently, three new important discoveries were made: the above mentioned variants of ArtGallery are all W[1]-hard with respect to k [Bonnet and Miltzow in 24th Annual European Symposium on Algorithms (Aarhus 2016)], the classic variant has an O (log k) -approximation algorithm [Bonnet and Miltzow in 33rd International Symposium on Computational Geometry (Brisbane 2017)], and it may require irrational guards [Abrahamsen et al. in 33rd International Symposium on Computational Geometry (Brisbane 2017)]. Building upon the third result, the classic variant and the case where G consists only of all the points on the boundary of P were both shown to be ∃ R -complete [Abrahamsen et al. in 50th Annual ACM SIGACT Symposium on Theory of Computing (Los Angeles 2018)]. Even when both G and C consist only of all the points on the boundary of P, the problem is not known to be in NP. Given the first discovery, the following question was posed by Giannopoulos [Lorentz Workshop on Fixed-Parameter Computational Geometry (Leiden 2016)]: Is ArtGallery FPT with respect to r, the number of reflex vertices? In light of the developments above, we focus on the variant where G and C consist of all the vertices of P, called Vertex-Vertex Art Gallery. Apart from being a variant of ArtGallery, this case can also be viewed as the classic DominatingSet problem in the visibility graph of a polygon. In this article, we show that the answer to the question by Giannopoulos is positive: Vertex-VertexArtGallery is solvable in time r O (r 2) · n O (1) . Furthermore, our approach extends to assert that Vertex-BoundaryArtGallery and Boundary-VertexArtGallery are both FPT as well. To this end, we utilize structural properties of "almost convex polygons" to present a two-stage reduction from Vertex-VertexArtGallery to a new constraint satisfaction problem (whose solution is also provided in this paper) where constraints have arity 2 and involve monotone functions. [ABSTRACT FROM AUTHOR]

The current study investigates to characterize the Complex Programming Problem (CPP) solution in a fuzzy environment. The paper is divided into two parts: 1) the first presents a Fuzzy Complex Programming Problem (FCPP) with fuzzy complex constraints, and 2) the second presents the optimality criteria using the fuzzy complex cone. The CPP is suggested by involving fuzzy numbers in the constraints in parts. Using the α -cut set concepts, the problem is converted into the α -complex programming. A number of basic theorems with proofs are established concerning the basic results for the fuzzy complex set of solutions for the F-CPP, and the optimality criteria of the saddle point for F-CPP with fuzzy cones is derived. [ABSTRACT FROM AUTHOR]

Model‐based methods in autonomous driving and advanced driving assistance gain importance in research and development due to their potential to contribute to higher road safety. Parameters of vehicle models, however, are hard to identify precisely or they can change quickly depending on the driving conditions. In this paper, we address the problem of safe trajectory planning under parametric model uncertainties motivated by automotive applications. We use the generalized polynomial chaos expansions for efficient nonlinear uncertainty propagation and distributionally robust inequalities for chance constraints approximation. Inspired by the tube‐based model predictive control, an ancillary feedback controller is used to control the deviations of stochastic modes from the nominal solution, and therefore, decrease the variance. Our approach allows reducing conservatism related to nonlinear uncertainty propagation while guaranteeing constraints satisfaction with a high probability. The performance is demonstrated on the example of a trajectory optimization problem for a simplified vehicle model with uncertain parameters. [ABSTRACT FROM AUTHOR]

In this paper, the problem of adaptive fuzzy tracking control for a class of uncertain switched nonlinear systems with unknown control direction is studied. Aiming at the problem, an adaptive control scheme with Nussbaum gain technology is constructed by using the average dwell time (ADT) method and the backstepping method to overcome the unknown control direction, and time‐varying asymmetric barrier Lyapunov functions (ABLFs) are adopted to ensure the full‐state constraints satisfaction. The proposed control scheme guarantees that all closed‐loop signals remain bounded under a class of switching signals with ADT, while the output tracking error converges to a small neighborhood of the zero. An important innovation of this design method is that the unknown control direction, asymmetric time‐varying full state constraints, and predefined time‐varying output requirements are simultaneously considered in uncertain switched nonlinear systems for the first time. We set a moment in advance, and make the systems comply with the constraint conditions before running the moment by the shift function nested in the first time‐varying ABLF. Finally, a simulation example verifies the effectiveness of the proposed scheme. [ABSTRACT FROM AUTHOR]

This paper investigates the distributed model predictive control (DMPC) problem for multiple dynamically-decoupled heterogeneous linear systems subject to both local state and input constraints and coupled non-convex constraints (e.g., collision avoidance constraints). To solve the resulting non-convex optimal control problem (OCP) at each time step, successive convex approximation (SCA) technique is a promising convexification approach. However, an algorithm that is fully distributed, computationally efficient, and recursively feasible for both local and coupled non-convex constraints remains an open problem. In this paper, we propose an inner–outer layer framework that integrates three important modifications into the SCA scheme for solving each OCP. Specifically, (i) in the inner layer, we utilize a distributed dual fast gradient approach to enable the distributed execution, (ii) as for the outer layer, instead of requiring the optimal solution at each iteration by classical SCA scheme, we improve computational efficiency by relying solely on a suboptimal solution achieved through flexible termination, and (iii) an adaptive tightening strategy imposing on the convexified coupled constraints is developed which permits both the inner and outer layers to terminate in advance with the guarantee of the closed-loop non-convex coupled constraints satisfaction. Under some reasonable assumptions, convergence of the proposed inner–outer layer framework, recursive feasibility of the proposed DMPC algorithm and stability of the resulting whole closed-loop system are ensured. Simulation results on multi-agent control with non-convex coupled collision avoidance constraints and comparisons against some benchmark solutions using the centralized method are carried out to verify the performance of the proposed DMPC method. [ABSTRACT FROM AUTHOR]

A trigraph is a graph where each pair of vertices is labelled either 0 (a non-arc), 1 (an arc) or ⋆ (both an arc and a non-arc). In a series of papers, Hell and co-authors (see for instance [P. Hell, 2014 [21] ]) proposed to study the complexity of homomorphisms from graphs to trigraphs, called Matrix Partition Problems , where arcs and non-arcs can be both mapped to ⋆-arcs, while a non-arc cannot be mapped to an arc, and vice-versa. Even though Matrix Partition Problems are generalisations of Constraint Satisfaction Problems (CSPs) , they share with them the property of being "intrinsically" combinatorial. So, the question of a possible P-time vs NP-complete dichotomy is a very natural one and was raised in Hell et al.'s papers. We propose a generalisation of Matrix Partition Problems to relational structures and study them with respect to the question of a dichotomy. We first show that trigraph homomorphisms and Matrix Partition Problems are P-time equivalent, and then prove that one can also restrict (with respect to having a dichotomy) to relational structures with a single relation. Failing in proving that Matrix Partition Problems on directed graphs are not P-time equivalent to Matrix Partitions on relational structures, we give some evidence that it might be unlikely by formalising the reductions used in the case of CSPs and by showing that such reductions cannot work for the case of Matrix Partition Problems. We then turn our attention to Matrix Partition problems that can be described by finite sets of (induced-subgraph) obstructions. We show, in particular, that any such problem has finitely many minimal obstructions if and only if it has finite duality. We conclude by showing that on trees (seen as trigraphs) it is NP-complete to decide whether a given tree has a homomorphism to another input trigraph. The latter shows a notable difference on tractability between CSP and Matrix Partition Problems as it is well-known that CSP is tractable on the class of trees. [ABSTRACT FROM AUTHOR]

A constraint satisfaction problem (CSP), \(\textsf {Max-CSP}(\mathcal {F})\) , is specified by a finite set of constraints \(\mathcal {F}\subseteq \lbrace [q]^k \rightarrow \lbrace 0,1\rbrace \rbrace\) for positive integers q and k. An instance of the problem on n variables is given by m applications of constraints from \(\mathcal {F}\) to subsequences of the n variables, and the goal is to find an assignment to the variables that satisfies the maximum number of constraints. In the (γ ,β)-approximation version of the problem for parameters 0 ≤ β ≤ γ ≤ 1, the goal is to distinguish instances where at least γ fraction of the constraints can be satisfied from instances where at most β fraction of the constraints can be satisfied. In this work, we consider the approximability of this problem in the context of sketching algorithms and give a dichotomy result. Specifically, for every family \(\mathcal {F}\) and every β < γ, we show that either a linear sketching algorithm solves the problem in polylogarithmic space or the problem is not solvable by any sketching algorithm in \(o(\sqrt {n})\) space. In particular, we give non-trivial approximation algorithms using polylogarithmic space for infinitely many constraint satisfaction problems. We also extend previously known lower bounds for general streaming algorithms to a wide variety of problems, and in particular the case of q=k=2, where we get a dichotomy, and the case when the satisfying assignments of the constraints of \(\mathcal {F}\) support a distribution on \([q]^k\) with uniform marginals. Prior to this work, other than sporadic examples, the only systematic classes of CSPs that were analyzed considered the setting of Boolean variables q = 2, binary constraints k =2, and singleton families \(|\mathcal {F}|=1\) and only considered the setting where constraints are placed on literals rather than variables. Our positive results show wide applicability of bias-based algorithms used previously by [47] and [41], which we extend to include richer norm estimation algorithms, by giving a systematic way to discover biases. Our negative results combine the Fourier analytic methods of [56], which we extend to a wider class of CSPs, with a rich collection of reductions among communication complexity problems that lie at the heart of the negative results. In particular, previous works used Fourier analysis over the Boolean cube to initiate their results and the results seemed particularly tailored to functions on Boolean literals (i.e., with negations). Our techniques surprisingly allow us to get to general q-ary CSPs without negations by appealing to the same Fourier analytic starting point over Boolean hypercubes. [ABSTRACT FROM AUTHOR]

Tree search algorithms, such as branch-and-bound, are the most widely used tools for solving combinatorial and non-convex problems. For example, they are the foremost method for solving (mixed) integer programs and constraint satisfaction problems. Tree search algorithms come with a variety of tunable parameters that are notoriously challenging to tune by hand. A growing body of research has demonstrated the power of using a data-driven approach to automatically optimize the parameters of tree search algorithms. These techniques use a training set of integer programs sampled from an application-specific instance distribution to find a parameter setting that has strong average performance over the training set. However, with too few samples, a parameter setting may have strong average performance on the training set but poor expected performance on future integer programs from the same application. Our main contribution is to provide the first sample complexity guarantees for tree search parameter tuning. These guarantees bound the number of samples sufficient to ensure that the average performance of tree search over the samples nearly matches its future expected performance on the unknown instance distribution. In particular, the parameters we analyze weight scoring rules used for variable selection. Proving these guarantees is challenging because tree size is a volatile function of these parameters: we prove that, for any discretization (uniform or not) of the parameter space, there exists a distribution over integer programs such that every parameter setting in the discretization results in a tree with exponential expected size, yet there exist parameter settings between the discretized points that result in trees of constant size. In addition, we provide data-dependent guarantees that depend on the volatility of these tree-size functions: our guarantees improve if the tree-size functions can be well approximated by simpler functions. Finally, via experiments, we illustrate that learning an optimal weighting of scoring rules reduces tree size. [ABSTRACT FROM AUTHOR]

Ship-mounted heave compensation offshore cranes are indispensable for isolating connected payloads from the support vessel during lifting operations under harsh sea conditions. In this paper, an innovative adaptive robust control strategy is presented for the electric-driven active heave compensation (EDAHC) system, combining an equivalent model predictive control (EMPC) method with a bias proportional integral derivative (BPID) framework to effectively mitigate the adverse effects of wave-induced heave motions from the support vessel on the suspended payload. Building upon the inherent field-oriented control in the permanent magnet synchronous motor (PMSM), the BPID-based control structure is introduced, motivated by its prompt responsiveness and robust resistance against model discrepancies and irregular disturbances. Facilitated by a torque compensation mechanism, the EMPC-based control scheme, synthesized with an autoregressive integrated moving average (ARIMA)-based heave motion prediction algorithm, is subsequently developed to achieve nonlinear friction deadzone correction and adaptive regulation of BPID parameters, thereby ensuring optimal performance of the EDAHC system within specified state and input constraints. Comparative experimental tests conducted on a scaled EDAHC testbed validate the superior capabilities of the proposal in station-keeping, position tracking, constraint satisfaction, and robustness against parametric uncertainties. • A novel adaptive robust control strategy is proposed for the electric-driven active heave compensation system. • A scaled active heave compensation testbed is established for experimental validation and practical feasibility analysis. • A compensation mechanism is designed to synergize with EMPC for deadzone correction and computational complexity reduction. • EMPC is introduced to BPID controller for optimal parameter regulation and constraint satisfaction. • The compensation efficiency and robustness performance of EMPC is improved by the BPID component. [ABSTRACT FROM AUTHOR]

Explicit reference governor (ERG) is an add-on unit that provides constraint handling capability to pre-stabilized systems. The main idea behind ERG is to manipulate the derivative of the applied reference in continuous time such that the satisfaction of state and input constraints is guaranteed at all times. However, ERG should be practically implemented in discrete-time. This paper studies the discrete-time implementation of ERG, and provides conditions under which the feasibility and convergence properties of the ERG framework are maintained when the updates of the applied reference are performed in discrete time. Specifically, using Zero-Order Hold (ZOH) discretization method, we develop an adaptive algorithm to adjust the gain of the discretized term based on actual measurements to maintain all properties of ERG when implemented in discrete-time. The proposed approach is validated via extensive simulation and experimental studies. [ABSTRACT FROM AUTHOR]

This paper proposes a novel guidance law for hypersonic entry vehicles, considering no-fly zones with height limits. Traditional planar assumptions restrict the flexibility of trajectory design for scenarios like radar avoidance. Besides, the numerical integration proves inefficient for long-term prediction and avoidance. Therefore, a model-based reinforcement learning policy is designed. It offline learns entry dynamics in advance and onboard plans a feasible trajectory. The planner's state includes flight status and no-fly zones; action presents waypoints; and reward ensures constraint while maximizing terminal precision. Then, analytical prediction converts spatial no-fly zone constraints to flight-path angle constraints, improving precision compared to traditional one-step estimates. Finally, the two parts are assembled into the predictor-corrector framework, which gives the augmented guidance commands. While retaining its robustness to bias, our method reduces online optimization calculations and outperforms constraint satisfaction. Experiments show that the model-based method reduces 60% training in offline training compared with proximal policy optimization. Besides, our method is 80% faster than conventional predictor-corrector guidance regarding online computation speed. • Develops an entry guidance law for spatial no-fly zones • Proposes intelligent waypoint planning and guidance algorithm within each segment. • Integrates model-based reinforcement learning to ensure efficient offline training. • Reduces 60% training steps in offline training compared with proximal policy optimization. • Online computation speed is 80% faster than conventional predictor-corrector guidance. [ABSTRACT FROM AUTHOR]

• A dynamic task mechanism is designed to improve the generality of the algorithm. • The main task processes constraints with higher constraint priority in turn. • Auxiliary task P 2 stops the evolution adaptively after converging to UPF. • The entire solution process is divided into exploration and exploitation stages. Compared with common multi-objective optimization problems, constrained multi-objective optimization problems demand additional consideration of the treatment of constraints. Recently, many constrained multi-objective evolutionary algorithms have been presented to reconcile the relationship between constraint satisfaction and objective optimization. Notably, evolutionary multi-task mechanisms have also been exploited in solving constrained multi-objective problems frequently with remarkable outcomes. However, previous methods are not fully applicable to solving problems possessing all types of constraint landscapes and are only superior for a certain type of problem. Thus, in this paper, a novel dynamic-multi-task-assisted constrained multi-objective optimization algorithm, termed DTCMO, is proposed, and three dynamic tasks are involved. The main task approaches the constrained Pareto front by adding new constraints dynamically. Two auxiliary tasks are devoted to exploring the unconstrained Pareto front and the constrained Pareto front with dynamically changing constraint boundaries, respectively. In addition, the first auxiliary task stops the evolution automatically after reaching the unconstrained Pareto front, avoiding the waste of subsequent computational resources. A series of experiments are conducted with eight mainstream algorithms on five benchmark problems, and the results confirm the generality and superiority of DTCMO. [ABSTRACT FROM AUTHOR]

Using infeasible information to balance objective optimization and constraint satisfaction is a very promising research direction to address constrained multi-objective problems (CMOPs) via evolutionary algorithms (EAs). The existing constrained multi-objective evolutionary algorithms (CMOEAs) still face the issue of striking a good balance when solving CMOPs with diverse characteristics. To alleviate this issue, in this paper we develop a two-stage different evolution with a dynamic population assignment strategy for CMOPs. In this approach, two cooperative populations are used to provide feasible driving forces and infeasible guiding knowledge. To adequately utilize the infeasibility information, a dynamic population assignment model is employed to determine the primary population, which is used as the parents to generate offspring. The entire search process is divided into two stages, in which the two populations work in weak and strong cooperative ways, respectively. Furthermore, multistrategy-based differential evolution operators are adopted to create aggressive offspring. The superior exploration and exploitation ability of the proposed algorithm is validated via some state-of-the-art CMOEAs over artificial benchmarks and real-world problems. The experimental results show that our proposed algorithm gained a better, or more competitive, performance than the other competitors, and it is an effective approach to balancing objective optimization and constraint satisfaction. [ABSTRACT FROM AUTHOR]

We present a novel data-driven Model Predictive Control (MPC) algorithm for nonlinear systems. The method is based on recent extensions of behavioural theory and Willem's Fundamental Lemma for nonlinear systems by the means of adequate Input–Output (IO) quasi-Linear Parameter-Varying (qLPV) embeddings. Thus, the MPC is formulated to ensure regulation and IO constraints satisfaction, based only on measured datasets of sufficient length (and under persistent excitation). The main innovation is to consider the knowledge of the function that maps the qLPV realisation, and apply an extrapolation procedure in order to generate the corresponding future scheduling trajectories, at each sample. Accordingly, we briefly discuss the issues of closed-loop IO stability and recursive feasibility certificates of the method. The algorithm is tested and discussed with the aid of a numerical application. [ABSTRACT FROM AUTHOR]

The task of localizing distinct anatomical structures in medical image data is an essential prerequisite for several medical applications, such as treatment planning in orthodontics, bone-age estimation, or initialization of segmentation methods in automated image analysis tools. Currently, Anatomical Landmark Localization (ALL) is mainly solved by deep-learning methods, which cannot guarantee robust ALL predictions; there may always be outlier predictions that are far from their ground truth locations due to out-of-distribution inputs. However, these localization outliers are detrimental to the performance of subsequent medical applications that rely on ALL results. The current ALL literature relies heavily on implicit anatomical constraints built into the loss function and network architecture to reduce the risk of anatomically infeasible predictions. However, we argue that in medical imaging, where images are generally acquired in a controlled environment, we should use stronger explicit anatomical constraints to reduce the number of outliers as much as possible. Therefore, we propose the end-to-end trainable Global Anatomical Feasibility Filter and Analysis (GAFFA) method, which uses prior anatomical knowledge estimated from data to explicitly enforce anatomical constraints. GAFFA refines the initial localization results of a U-Net by approximately solving a Markov Random Field (MRF) with a single iteration of the sum-product algorithm in a differentiable manner. Our experiments demonstrate that GAFFA outperforms all other landmark refinement methods investigated in our framework. Moreover, we show that GAFFA is more robust to large outliers than state-of-the-art methods on the studied X-ray hand dataset. We further motivate this claim by visualizing the anatomical constraints used in GAFFA as spatial energy heatmaps, which allowed us to find an annotation error in the hand dataset not previously discussed in the literature. [ABSTRACT FROM AUTHOR]

This paper presents a novel data-driven approach that leverages reinforcement learning to enhance the efficiency and safety of existing energy flexibility controllers, addressing challenges posed by the dynamic and uncertain nature of modern energy landscapes. With the increasing integration of renewable energy sources, conventional controllers struggle to maintain both safety and optimality. Our proposed approach introduces two significant contributions to standard RL approaches: a data-driven predictive safety filter and an online changepoint detection and policy updating module. Through continuous constraint satisfaction, the predictive safety filter guarantees absolute safety of the proposed controller. Meanwhile, the changepoint detection and policy updating module, inspired by the concept of continual learning, enhances the controller's adaptivity to non-stationary environments. By identifying changes in the environment, it triggers relearning of the agent, making the controller resilient to evolving conditions. Validation of our approach is conducted on a grid-connected PV-battery-load system, demonstrating its effectiveness in simultaneously improving safety and performance over traditional learning methods. More specifically, the proposed solution was able to increase the energy flexibility by reducing energy costs with 9.3%. • Proposed an innovative control framework employing reinforcement learning to enhance energy flexibility. • Incorporated a changepoint detection and policy updating mechanism to address the challenge of dynamic environments. • Introduced a predictive safety filter to enhance the safety of current reinforcement learning methods. • Validated effectiveness in a case study, demonstrating improved energy flexibility and safety. [ABSTRACT FROM AUTHOR]

This paper proposes a novel safe Gaussian process model predictive control scheme for discrete-time nonlinear systems subject to additive uncertainties. The scheme is implemented using an online learning framework that provides safety guarantees based on a nominal model, and employs Gaussian process regression (GPR) to learn the uncertainties to improve the control performance. The advantage of this framework lies in the ability to decouple safety and performance in the robust controller design. Furthermore, the inaccuracy measure given by GPR can be used to adaptively tighten the constraints, leading to the less conservative behaviors. A rigorous analysis of the constraint satisfaction, recursive feasibility and closed-loop stability is also presented. Two simulation examples, including a regulation problem of a nominally linear system and a tracking problem of a car whose model is nonlinear, are performed to verify the effectiveness of the proposed scheme. [ABSTRACT FROM AUTHOR]

This paper introduces the manta ray foraging optimization algorithm (MRFO) and its enhanced version, the oppositional-based manta ray foraging optimization algorithm (OMRFO), as effective meta-heuristic approaches for solving challenging economic dispatch (ED) problems in power systems. Specifically tailored for economic power dispatch (EPD), combined economic emission dispatch (CEED), and combined heat and power economic dispatch (CHPED) problems, considering factors like valve-point loading effects (VPL), transmission power losses, and prohibited operating zones (POZs) inherent in real-world power systems. To address MRFO's limitations, including slow convergence, susceptibility to local optima, and limited exploration capacity due to foraging behavior, this study integrates oppositional-based learning (OBL) with MRFO to enhance solution quality, speed up convergence, and improve exploration of the search space. Extensive testing is conducted on benchmark functions and ED problems of four standard test systems with non-convex solution spaces. The comprehensive comparative assessment shows that both MRFO and OMRFO outperform other algorithms in terms of solution quality and system constraint satisfaction. Additionally, OMRFO exhibits significant improvements over MRFO, especially for more complex problems. For instance, for small test systems like the 6-unit test system, both algorithms achieve a cost of 15,441.84 $/h. However, for larger systems with higher complexity, such as the 40-unit test system, OMRFO significantly outperforms MRFO with a cost of 119,733.27 $/h compared to 120,221.34 $/h. Similarly, for a 24-unit test system with VPL only and with VPL and POZs, OMRFO achieves costs of 58,054.78 $/h and 58,191.69 $/h, respectively, surpassing MRFO's costs of 58,125.803 $/h and 58,223.578 $/h. [ABSTRACT FROM AUTHOR]

Striking a balance between diverse constraints and conflicting objectives is one of the most crucial issues in solving constrained multi-objective optimization problems (CMOPs). However, it remains challenging to existing methods, due to the reduced search space caused by the constraints. For this issue, this paper proposes a Pareto fronts relationship identification-based two-stage constrained evolutionary algorithm called RITEA, which balances objective optimization and constraint satisfaction by identifying and utilizing the relationship between the unconstrained Pareto front (UPF) and the constrained Pareto front (CPF). Specifically, the evolutionary process is divided into two collaborative stages: training stage and reinforcement stage. In the training stage, a relationship identification method is developed to estimate the relationship between UPF and CPF, which guides the population search direction. In the reinforcement stage, the corresponding evolutionary strategies are designed based on the identified relationship to enhance the accurate search on the CPF. Furthermore, a dynamic preference fitness function (termed DPF) is designed to adaptively maintain the balance of search preference between convergence and diversity. Compared to seven state-of-the-art algorithms on 36 benchmark CMOPs in three popular test suites, RITEA obtains 77.8% of the best IGD values and 66.7% of the best HV values. The experimental results show that RITEA exhibits highly competitively when dealing with CMOPs. [Display omitted] • RITEA, a two-stage constrained evolutionary algorithm for CMOPs. • Identify and utilize the relationship between UPF and CPF to balance optimization and constraint satisfaction. • Utilizes collaborative training stage and reinforcement stage to guide population search accurately. • Introduction of a dynamic preference fitness function to adaptively balance the search preferences between convergence and diversity. [ABSTRACT FROM AUTHOR]

• Communication-free protection of MGs/SGs, using non-standard relay characteristics. • Considering N-1 contingency configurations and different operation modes. • Facilitating coordination constraints satisfaction and speed up the protection system. • Linearizing and solving the proposed COP using GA-PSO-LP and WCA-MFO-LP algorithm. • Around a 36 % improvement in the speed of the proposed scheme compared to the available ones. Smart grids (SGs), meshed active distribution networks (ADNs), and microgrids (MGs) frequently experience reconfigurations and changes in their operation modes (grid-connected and islanded), which leads to protection miscoordination and speed challenges. Several research works have studied the protection of MGs/SGs, considering different configurations. On the other hand, non-standard relay characteristics provide some flexibility in protection design. However, the literature review shows that less attention has been paid to the optimal protection of MGs/SGs, incorporating non-standard relay curves and consideration of N-1 contingency configurations and operation modes. This paper aims to respond to this research gap. Also, the slow tripping of backup relays, a common drawback of recent works, is concerned with a modified objective function (OF). The presented coordination optimization problem (COP) is formulated in a mixed-integer nonlinear programming-linear programming (MINLP-LP) form and solved using hybrid heuristic-linear programming algorithms: Genetic algorithm-particle swarm optimization-linear programming (GA-PSO-LP) and water cycle algorithm-moth flame optimization-linear programming (WCA-MFO-LP). The introduced research is applied to the distribution portion of the IEEE-14 test system. The analysis and discussions emphasize that the proposed protection scheme speed is improved by over 36 % compared to available ones. Also, there is no coordination violation under different system configurations. [ABSTRACT FROM AUTHOR]

In this paper, the problem associated with active heave motion compensation during heavy-lift operations performed by ship-mounted offshore cranes beneath rough marine environment is investigated. To effectively decouple the correlated motion of the suspended payload from the support vessel via the secondary regulated active heave compensation (SRAHC) system, a novel hierarchical control strategy is proposed by integrating a cascade control structure with an adaptive robust control scheme that incorporates a vertical motion forecast algorithm based on autoregressive integrated moving average (ARIMA) model, a conventional proportional-integral-derivative (PID) framework, and a nonlinear model predictive control (NMPC) method. The introduction of the cascade structure is motivated by its prompt error response against control lag and efficient system order reduction for computational burden alleviation, which forms a crucial foundation for the NMPC-based real-time regulation of PID gains, ensuring optimal evolution of the SRAHC system while improving its practical feasibility. Furthermore, the enhancements in heave compensation and trajectory tracking performance, noise resistance, constraint satisfaction, and engineering application potential of the proposal are demonstrated through a thorough comparative analysis conducted in a practical co-simulation research system. • A novel hierarchical control strategy is proposed for the secondary regulated active heave compensation system. • A joint mechanical-electrical-hydraulic research system is employed for practical heave compensation analysis. • NMPC-PID is retained to ensure superior compensation accuracy, accounting for system nonlinearities and model constraints. • The response speed and computational efficiency of NMPC-PID are enhanced through the introduction of a cascade control structure. • The noise resistance performance of cascade PID controller is improved by the NMPC-based regulation mechanism, synthesized with an ARIMA-based heave motion prediction. [ABSTRACT FROM AUTHOR]

The Cognitive Radio Network, incorporating Device-to-Device communication and a heterogeneous network, has garnered significant attention due to its ability to address spectrum shortage issues and optimize the efficient utilization of spectrum resources. However, resource allocation considering stochastic behavior has not been considered in existing studies. In this paper, our work aimed to maximize the throughput of the overall network considering multiple users under the umbrella of the Cognitive radio network assisted by amplify and forward relay. The constraints are treated as chance constraints with a probability of satisfaction in them, which leads to a non-convex mixed integer nonlinear problem which is an NP-Hard problem. To solve this problem an exhaustive search solution for optimal results is required. However, the computational burden always increases with the user equipment. Therefore, to obtain an optimal solution with having low computational burden, the Outer Approximation Algorithm is utilized in this research. To evaluate the desired results, extensive simulations have been carried out. The effectiveness of the proposed algorithm is verified by results in terms of throughput maximization under the impact of chance constraint formulation in the cognitive radio networks. [ABSTRACT FROM AUTHOR]

For a class of full‐states constraints nonlinear system with actuator failure, an adaptive fuzzy disturbance observer tracking design is carried out by using Lyapunov function and the dynamic surface method. The integral explosion problem is avoided by using the dynamic surface design method. Because the disturbance of the system is unknown, a nonlinear fuzzy disturbance observer is designed to estimate the unknown disturbance. And the unknown nonlinear function is approximated fuzzy logic systems. Based on the Lyapunov function method and backstepping approach, the stability of considered systems are analysed. And the proposed method can guarantee that all the signals in the closed‐loop system are bounded and the system output can track the desired signal to the small neighbourhood range. In addition, the fuzzy disturbance observer can estimate the unknown disturbance state well. Finally, several sets of simulation examples are given and compared with other method, and the experimental results are quantitatively analysed. Then, the robustness and superiority of the proposed control scheme are verified and demonstrated. [ABSTRACT FROM AUTHOR]

We study the complexity of the Distributed Constraint Satisfaction Problem (DCSP) on a synchronous, anonymous network from a theoretical standpoint. In this setting, variables and constraints are controlled by agents which communicate with each other by sending messages through fixed communication channels. Our results endorse the well-known fact from classical CSPs that the complexity of fixed-template computational problems depends on the template's invariance under certain operations. Specifically, we show that DCSP(Γ) is polynomial-time tractable if and only if Γ is invariant under symmetric polymorphisms of all arities. Otherwise, there are no algorithms that solve DCSP(Γ) in finite time. We also show that the same condition holds for the search variant of DCSP. Collaterally, our results unveil a feature of the processes' neighbourhood in a distributed network, its iterated degree, which plays a major role in the analysis. We explore this notion establishing a tight connection with the basic linear programming relaxation of a CSP. [ABSTRACT FROM AUTHOR]

In the Determinant Maximization problem, given an n × n positive semi-definite matrix A in Q n × n and an integer k, we are required to find a k × k principal submatrix of A having the maximum determinant. This problem is known to be NP-hard and further proven to be W[1]-hard with respect to k by Koutis (Inf Process Lett 100:8–13, 2006); i.e., a f (k) n O (1) -time algorithm is unlikely to exist for any computable function f. However, there is still room to explore its parameterized complexity in the restricted case, in the hope of overcoming the general-case parameterized intractability. In this study, we rule out the fixed-parameter tractability of Determinant Maximization even if an input matrix is extremely sparse or low rank, or an approximate solution is acceptable. We first prove that Determinant Maximization is NP-hard and W[1]-hard even if an input matrix is an arrowhead matrix; i.e., the underlying graph formed by nonzero entries is a star, implying that the structural sparsity is not helpful. By contrast, Determinant Maximization is known to be solvable in polynomial time on tridiagonal matrices (Al-Thani and Lee, in: LAGOS, 2021). Thereafter, we demonstrate the W[1]-hardness with respect to the rankr of an input matrix. Our result is stronger than Koutis' result in the sense that any k × k principal submatrix is singular whenever k > r . We finally give evidence that it is W[1]-hard to approximate Determinant Maximization parameterized by k within a factor of 2 - c k for some universal constant c > 0 . Our hardness result is conditional on the Parameterized Inapproximability Hypothesis posed by Lokshtanov et al. (in: SODA, 2020), which asserts that a gap version of Binary Constraint Satisfaction Problem is W[1]-hard. To complement this result, we develop an ε -additive approximation algorithm that runs in ε - r 2 · r O (r 3) · n O (1) time for the rank r of an input matrix, provided that the diagonal entries are bounded. [ABSTRACT FROM AUTHOR]

The constraint satisfaction problem (CSP) on a finite relational structure B is to decide, given a set of constraints on variables where the relations come from B, whether or not there is an assignment to the variables satisfying all of the constraints; the surjective CSP is the variant where one decides the existence of a surjective satisfying assignment onto the universe of B. We present an algebraic framework for proving hardness results on surjective CSPs; essentially, this framework computes global gadgetry that permits one to present a reduction from a classical CSP to a surjective CSP. We show how to derive a number of hardness results for surjective CSP in this framework, including the hardness of the disconnected cut problem, of the no-rainbow three-coloring problem, and of the surjective CSP on all two-element structures known to be intractable (in this setting). Our framework thus allows us to unify these hardness results and reveal common structure among them; we believe that our hardness proof for the disconnected cut problem is more succinct than the original. In our view, the framework also makes very transparent a way in which classical CSPs can be reduced to surjective CSPs. [ABSTRACT FROM AUTHOR]

Virtual coupling (VC) is an emerging technology to improve the flexibility and capacity of railway services. To adjust the formation of a virtually coupled train set (VCTS) on-the-fly, dynamic coupling control is essential to couple multiple trains (units) stably and efficiently. However, it is still hard to be achieved in real-time, since safety constraints are complex but have to be satisfied for collision avoidance. Thus, this paper proposes a computation-efficient distributed model predictive control (DMPC) approach to solve this problem. First, the movement of VCTS is captured by a three-order dynamics model, while the safety constraints are unspecified and can be defined by arbitrary functions. Then, the DMPC approach is designed which consists of reference planning and tracking. Specifically, we design a prediction-based control scheme to plan reference trajectory for each unit, where the future satisfaction of safety constraints is addressed. Resorting to this design, the reference tracking in DMPC is achieved by solving a computation-efficient quadratic programming problem. The shifting principle is employed in the closed-loop implementation of DMPC to guarantee stability. Finally, experiments are conducted to verify the performance of the proposed approach. Dynamic coupling of a real VCTS is the first time achieved in field tests, where two units are coupled stably and efficiently while satisfying a numerically-evaluated safety constraint. It is a breakthrough in the development of VC technology. • Dynamic coupling of virtually coupled train set in field tests. • Computation-efficient distributed MPC for engineering. • Addressing complex safety constraints in virtual coupling. [ABSTRACT FROM AUTHOR]

How to balance the satisfaction of constraints and the optimization of objective functions is one of the key issues to solve constrained multi-objective optimization problems (CMOPs), especially when the constraints are complex. Although many algorithms have been designed to handle this, most of them are still unable to effectively handle CMOPs with complex constraints. Based on the above issue, this paper proposes a framework for bi-directional search, which evolves two populations (P 1 and P 2). P 1 aims to search the constrained Pareto front (CPF) from the infeasible side of the objective space, and P 2 from the feasible side, aiming to achieve a more efficient and comprehensive bi-directional search for the CPF. To ensure the diversity, we adopt a preferred weight vector selection strategy to choose potential mating parents, which improves the search capability for the marginal CPF. Furthermore, to coordinate the interaction between the two populations, we propose an environmental selection strategy to select the offspring generated by P 1 and P 2 under the same weight vector with the better fitness to update the populations respectively, and the fitness is evaluated based on the different constraint relaxations of the two populations, to update them respectively. Extensive experiments indicate that our proposed algorithm has significantly better results or was at least competitive when compared to eight state-of-the-art methods. [ABSTRACT FROM AUTHOR]