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This paper reports the release of PathSum, a new software suite of state-of-the-art path integral methods for studying the dynamics of single or extended systems coupled to harmonic environments. The package includes two modules, suitable for system–bath problems and extended systems comprising many coupled system–bath units, and is offered in C++ and Fortran implementations. The system–bath module offers the recently developed small matrix path integral (SMatPI) and the well-established iterative quasi-adiabatic propagator path integral (i-QuAPI) method for iteration of the reduced density matrix of the system. In the SMatPI module, the dynamics within the entanglement interval can be computed using QuAPI, the blip sum, time evolving matrix product operators, or the quantum–classical path integral method. These methods have distinct convergence characteristics and their combination allows a user to access a variety of regimes. The extended system module provides the user with two algorithms of the modular path integral method, applicable to quantum spin chains or excitonic molecular aggregates. An overview of the methods and code structure is provided, along with guidance on method selection and representative examples. [ABSTRACT FROM AUTHOR]

This paper presents a metrology tool path planning algorithm using an iterative learning-extremum seeking control (ILESC) scheme that combines iterative learning control (ILC) and extremum seeking control (ESC) schemes. In many surface metrology systems, it is inevitable to avoid cosine error that introduces extra uncertainty to the measurement. Cosine error results from the angular misalignment between the measurement probe and the target surface. The proposed ILESC scheme is suitable to address this problem because, unlike the classical control method where the system tracks a given reference signal, ILESC simultaneously compensates for cosine error by simultaneously regenerating the metrology tool path while scanning the target surface, even in case of initial profile unknown. Since no initial geometry profile is given, ESC is deployed to adaptively track the shortest measured distance to the target, which approximately aligns the measurement probe in the perpendicular path to the target. Then, ILC is deployed to each set of measurements to ensure the algorithm converges to an acceptable error threshold given the system's uncertainty. The proposed scheme was implemented to measure the surface profile of a reference cylinder (ϕ25.4 mm) and freeform lens mold, and the effectiveness of ILESC was evaluated by comparing the measurement results and reference data. As a result, the implemented ILESC scheme showed a 0.32% deviation at full scale. [ABSTRACT FROM AUTHOR]

In practical applications, due to the limited communication bandwidth, the network control systems (NCSs) are prone to data dropouts when the load is high. In this paper, the problem of quantized iterative learning control (ILC) based on encoding and decoding mechanism for such communication-constrained systems is studied. By combining the encoding and decoding mechanism with the uniform quantizer, the network burden and the impact of quantization error on the tracking performance of the systems are significantly mitigated. Meanwhile, data dropouts are represented as the Bernoulli random variable model, and an ILC law based on gradient is designed. When data dropouts occur, the signals maintain the value of the previous trial, otherwise the signals are updated. For this kind of learning framework, the asymptotic zero-error tracking performance has been rigorously proven for the uniform quantizer. To validate the proposed design, a joint motion of an industrial robot in the horizontal plane is simulated as an example. [ABSTRACT FROM AUTHOR]

In this paper, we develop an improved data-based integral policy iteration method to address the robust control issue for nonlinear systems. Combining multi-step neural networks with pre-training, the condition of selecting the initial admissible control policy is relaxed even though the information of system dynamics is unknown. Based on adaptive critic learning, the established algorithm is conducted to attain the optimal controller. Then, the robust control strategy is derived by adding the feedback gain. Furthermore, the computing error is considered during the process of implementing matrix inverse operation. Finally, two examples are presented to verify the effectiveness of the constructed algorithm. [ABSTRACT FROM AUTHOR]

This paper applies iterative learning control to point-to-point tracking problems with a general networked structure. The data is quantised and transmitted through restricted communication channels from the controller to the actuator. Combining a logarithmic quantizer with an encoding and decoding mechanism to quantise the input signals reduces the influence of the quantisation error. New design algorithms are developed with conditions for convergence of the tracking error and an extension to fault-tolerant performance under actuator failures. A numerical-based case study demonstrates the application of the new designs, which includes a comparison with another ILC law and the relative merits of the encoding and decoding schemes. [ABSTRACT FROM AUTHOR]

At DLR neural networks, as potential future controller for rocket engines, are studied. A neural network-based chamber pressure controller for a simplified cold gas thruster is presented and analyzed in simulation and experiment. The goal of the controller is twofold: It can track a trajectory with different changes of setpoints and it allows to set and control a wide variety of steady state chamber pressures. The neural network gets feeding line pressure measurement data as input and calculates valve positions as output values. The training phase of the controller is done with a reinforcement learning algorithm in an EcosimPro/ESPSS simulation, that is validated with data from the corresponding experimental set up. To increase the robustness and to allow a transfer from the simulation directly to the test facility domain randomization is applied. The controller is evaluated in simulations and experiment. It was found that – in the range of physically possible operation points – the controller achieves a constantly high reward which corresponds to a low error and a good control performance. In the simulation the controller was able to adjust all required set points with a steady state error of less than 0.1 bar while retaining a small overshoot and an optimal settling time. It is found that the controller is also able to regulate all desired set points in the real experiment. A reference trajectory with different steps, linear and sinus changes in target pressure is tested in simulation and experiment. The controller was in both cases able to successfully follow the given trajectory. • Simulation trained, reinforcement learning based thrust chamber pressure controller. • Experimental and simulative evaluation of control policy. • Steady state error less than 0.1 bar. • Controller follows trajectories successfully. [ABSTRACT FROM AUTHOR]

We present high-order, finite element–based Second Moment Methods (SMMs) for solving radiation transport problems in two spatial dimensions. We leverage the close connection between the Variable Eddington Factor (VEF) method and SMM to convert existing discretizations of the VEF moment system to discretizations of the SMM moment system. The moment discretizations are coupled to a high-order Discontinuous Galerkin discretization of the SN transport equations. We show that the resulting methods achieve high-order accuracy on high-order (curved) meshes, preserve the thick diffusion limit, and are effective on a challenging multimaterial problem both in outer fixed-point iterations and in inner preconditioned iterative solver iterations for the discrete moment systems. We also present parallel scaling results and provide direct comparisons to the VEF algorithms from which the SMM algorithms were derived. [ABSTRACT FROM AUTHOR]

The present work aims at investigating the adaptive iterative learning control (AILC) design for uncertain high‐order fully actuated nonlinear systems. In order to show the design principles, three types of nonlinear systems are considered, including systems with just parametric uncertainty, systems with both parametric and input distribution uncertainties as well as systems with both parametric uncertainty and an unknown control gain matrix. For different systems, the corresponding AILC schemes are proposed with different techniques in dealing with various system uncertainties, for which the convergence analysis are conducted rigorously based on the composite energy function. The effectiveness of the proposed AILC strategies is verified through numerical simulations. [ABSTRACT FROM AUTHOR]

In this article, a multi‐event‐triggered (MET) near‐optimal tracking control algorithm is developed for a discrete‐time (DT) nonlinear non‐zero‐sum game (NZSG). Firstly, the iterative dual heuristic dynamic programming (DHP) approach is utilized to obtain the optimal tracking control set. Subsequently, distinct independent triggering conditions are formulated for control inputs to improve the utilization efficiency of resources and ensure that the independence between them and the closed‐loop system has an excellent control performance. Meanwhile, input‐to‐state stability (ISS) is proven for the MET tracking plant. Additionally, neural networks (NNs) are designed in the iterative DHP algorithm to construct the model module, the critic module and the action modules, with aims to identify the unknown system, approximate costate function and estimate optimal tracking control strategy set, respectively. Finally, two numerical experimental simulations are conducted to verify the effectiveness of the proposed scheme. [ABSTRACT FROM AUTHOR]

In this paper, the H∞$$ {H}_{\infty } $$ optimal output tracking control problem for Markov jump systems is investigated, where the two cases with known or completely unknown transition probabilities are both considered. Based on game theory and H∞$$ {H}_{\infty } $$ performance, quadratic cost is considered, where a discount parameter is introduced into the quadratic cost in order to track unstable systems and eliminate the assumption that the noise energy is bounded. The game coupled algebraic Riccati equation and the corresponding controller are presented by dynamic programming. The stochastic stability of the tracking error system is further investigated. Moreover, iterative and reinforcement learning‐based algorithms are proposed for solving the H∞$$ {H}_{\infty } $$ optimal tracking controller with known or completely unknown transition probabilities, respectively. Finally, some numerical simulations on a DC motor are performed to validate the effectiveness of the proposed results. [ABSTRACT FROM AUTHOR]

This study investigates the iterative learning control method for discrete‐time systems with data quantization, and it employs a quantizer based on spherical polar coordinates. The quantizer uses spherical polar coordinates to transform an unquantized signal into one with a predetermined quantization level. The quantization capability is dependent on the size of the support sphere, which is dynamically adjustable. In the scenarios of system output quantization, general quantization, and tracking error quantization, the learning control schemes are developed with consideration of the smallest sphere quantization features. The radii of the support spheres are designed independently based on the characteristics of the quantized signals (system output, control input, tracking error). The findings suggest that the system can achieve a bounded error convergence in the scenarios of system output and general quantization. In the context of quantization in tracking error, it is achievable to attain tracking performance with zero error. The example of a permanent magnet synchronous motor is provided to illustrate the findings of the study. [ABSTRACT FROM AUTHOR]

This paper investigates the stabilization of Euler-Bernoulli beam systems modeled by a partial differential equation (PDE) with unknown time-varying disturbance. An iterative learning controller is designed using only boundary state feedback to realize the vibration control subject to unknown boundary disturbance. The well-posedness for the closed-loop system is given by the operator semigroup theory. Furthermore, the exponentially stable for the closed-loop system is proved by the Lyapunov method. The comparisons with existing results are made to demonstrate the effectiveness and advantages of the proposed boundary iterative learning control method. [ABSTRACT FROM AUTHOR]

The fully distributed output leader‐follower event‐triggered resilient control algorithm is proposed for heterogeneous multi‐agent systems (MASs) under communication link faults and constraints. An estimation of the information of the leader is achieved by designing a dynamic event‐triggered observer with resilience to link faults without using the eigenvalues of the global matrix. Zeno behavior is also excluded under the dynamic triggering mechanism. Considering that the state information of the follower is not available, a distributed output leader‐follower control law is further designed to achieve asymptotically convergence of the leader‐follower consensus error, and only the output information of followers is required. Finally, the availability of the theoretical results is shown in two numerical examples. [ABSTRACT FROM AUTHOR]

Magnetized plasma columns and extended magnetic structures with both footpoints anchored to a surface layer are an important building block of astrophysical dissipation models. Current loops shining in X-rays during the growth of plasma instabilities are observed in the corona of the Sun and are expected to exist in highly magnetized neutron star magnetospheres and accretion disk coronae. For varying twist and system sizes, we investigate the stability of line-tied force-free flux tubes and the dissipation of twist energy during instabilities using linear analysis and time-dependent force-free electrodynamics simulations. Kink modes (m = 1) and efficient magnetic energy dissipation develop for plasma safety factors q ≲ 1, where q is the inverse of the number of magnetic field line windings per column length. Higher-order fluting modes (m > 1) can distort equilibrium flux tubes for q > 1 but induce significantly less dissipation. In our analysis, the characteristic pitch μ ˜ 0 of flux-tube field lines determines the growth rate ( ∝ μ ˜ 0 3 ) and minimum wavelength of the kink instability ( ∝ μ ˜ 0 − 1 ). We use these scalings to determine a minimum flux tube length for the growth of the kink instability for any given μ ˜ 0 . By drawing analogies to idealized magnetar magnetospheres with varying regimes of boundary shearing rates, we discuss the expected impact of the pitch-dependent growth rates for magnetospheric dissipation in magnetar conditions. [ABSTRACT FROM AUTHOR]

In this paper, the framework of dissipativity-based iterative learning control for singular systems (SSs) is established for the first time. Firstly, under the P-type learning algorithm, it has been demonstrated that the dissipative SSs can achieve the accurate tracking for the desired trajectory in a finite time interval. Secondly, a sufficient condition for the SSs to satisfy dissipativity is given by using the linear matrix inequality (LMI) method, and the solvability criterion of the LMI is further presented. Moreover, the relationship between dissipativity and positive realness is revealed. Finally, two examples are given to verify the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

We present a novel approach for achieving high-precision trajectory tracking control in an unmanned surface vehicle (USV) through utilization of receding horizon reinforcement learning (RHRL). The control architecture for the USV involves a composite of feedforward and feedback components. The feedforward control component is derived directly from the curvature of the reference path and the dynamic model. Feedback control is acquired through application of the RHRL algorithm, effectively addressing the problem of achieving optimal tracking control. The methodology introduced in this paper synergizes with the rolling time domain optimization mechanism, converting the perpetual time domain optimal control predicament into a succession of finite time domain control problems amenable to resolution. In contrast to Lyapunov model predictive control (LMPC) and sliding mode control (SMC), our proposed method employs the RHRL controller, which yields an explicit state feedback control law. This characteristic endows the controller with the dual capabilities of direct offline and online learning deployment. Within each prediction time domain, we employ a time-independent executive–evaluator network structure to glean insights into the optimal value function and control strategy. Furthermore, we substantiate the convergence of the RHRL algorithm in each prediction time domain through rigorous theoretical proof, with concurrent analysis to verify the stability of the closed-loop system. To conclude, USV trajectory control tests are carried out within a simulated environment. [ABSTRACT FROM AUTHOR]

Many complex engineering systems can be represented in a topological form, such as graphs. This paper utilizes a machine learning technique called Geometric Deep Learning (GDL) to aid designers with challenging, graph-centric design problems. The strategy presented here is to take the graph data and apply GDL to seek the best realizable performing solution effectively and efficiently with lower computational costs. This case study used here is the synthesis of analog electrical circuits that attempt to match a specific frequency response within a particular frequency range. Previous studies utilized an enumeration technique to generate 43,249 unique undirected graphs presenting valid potential circuits. Unfortunately, determining the sizing and performance of many circuits can be too expensive. To reduce computational costs with a quantified trade-off in accuracy, the fraction of the circuit graphs and their performance are used as input data to a classification-focused GDL model. Then, the GDL model can be used to predict the remainder cheaply, thus, aiding decision-makers in the search for the best graph solutions. The results discussed in this paper show that additional graph-based features are useful, favorable total set classification accuracy of 80% in using only 10% of the graphs, and iteratively built GDL models can further subdivide the graphs into targeted groups with medians significantly closer to the best and containing 88.2 of the top 100 best-performing graphs on average using 25% of the graphs. [ABSTRACT FROM AUTHOR]

Summary: Data losses and noises in both forward and feedback channels significantly impact the convergence of networked iterative learning control (ILC) systems. To address this issue, this article considers a class of linear time‐invariant objects controlled by proportional ILC controllers, an optimal state filter is then designed at the ILC controller side that aims to guarantee the convergence of the input transmitted by ILC controllers. First, two data transmission processes are introduced to account for the effects of data losses and noises. Second, a filtering model is established utilizing only the object information and the aforementioned data transmission processes. Third, the optimal state filter is designed on the basis of the orthogonal projection principle. This filtered state facilitates the acquisition of actual output errors, thus improving the convergence of the input transmitted by ILC controllers. Simulation results demonstrate the effectiveness of the proposed state filters. [ABSTRACT FROM AUTHOR]

Before starting stability analysis of the multivirtual synchronous machine (n‐VISMA) power system, it is necessary to obtain the steady‐state operating points (SSOPs) of all dynamic nodes in the network. Modified traditional iterative schemes using the concept of droop bus technique in an islanded microgrid are not feasible for load flow analysis of VISMA microgrid incorporating non‐control dynamics. This paper proposes closed‐form steady‐state, fundamental‐frequency models for islanded VISMA microgrids using the concept of virtual swing buses. In this technique, the virtual internal buses of all VISMAs in the network are governed by the swing equation. The voltage at all buses is variable except the virtual buses in which the pole wheel voltages are prespecified. The algorithm was extended by a droop control localized to each VISMA. The suitability of the proposed algorithm to obtaining SSOPs of VISMA was tested on IEEE‐9 bus system with VISMA replacing electromechanical synchronous machines and also on a low‐voltage distribution system. To validate the applicability of the proposed algorithm and prove its accuracy, the case study systems were also modeled in the SIMULINK environment for detailed time domain analysis. The algorithm was found to be computationally effective for a load flow analysis of the VISMA microgrid. The results also reveal that the addition of external droop control improves the frequency stability of the system. [ABSTRACT FROM AUTHOR]

A new ray tracing algorithm based on the shortest path method was designed and optimized to model seismic rays. The workflow is based on Dijkstra's algorithm to find the shortest path iteratively on self-adapting random grids. These random grids adapt from one iteration to the next, storing in memory those nodes that minimize the traveltime in each iteration, consequently automatically densifying the grid in areas with significant velocity variations. Different data structures and grid geometries were studied, and it was confirmed that using a combination of a binary heap and random grids prevents systematic errors generated by using regular grids while keeping the computational times low. Since the nodes that minimize the traveltime are stored in each iteration, the memory requirements increase logarithmically, with the initial iterations having the most significant impact on the error minimization but plateauing afterwards. It was found that, albeit this increase in memory requirements, by focusing the densification of nodes in areas close to the actual trajectory of the rays, the error minimization requires fewer iterations than other implementations based on multiple realizations of random grids (requiring less than a tenth of the number of iteration of other methods). A function to handle extreme topographic variations was also designed, which uses a boolean test to reject rays crossing the topography, making the algorithm suitable for first arrival modelling in complex topography areas, such as the required for tomographic inversion of first arrivals in thrust-belt land seismic. [ABSTRACT FROM AUTHOR]

Shaking tables are widely used across numerous engineering research and industrial sectors, including mechanical (e.g. automotive and aerospace testing), electrical (e.g. instrumentation testing) and civil (e.g. structural and geotechnical testing) engineering. It is commonly required to replicate the shake table motions accurately and precisely. Iterative learning control algorithms can be used to complement traditional proportional–integral–differential feedback control algorithms to optimize drive signals using a test payload prior to the real experiment. Historically, the design of these test payloads has focused on matching the mass of the actual payload and neglected its dynamic response. In this study, experimental results from shake table tests using multiple geotechnical containers with dry and saturated beds that exhibit a range of stiffnesses and material damping when shaken are presented. Errors between the demanded and achieved motions are explored and compared to the changing secant stiffness abstracted from the dynamic shear stress–strain loops of the payload. A clear trend emerges that demonstrates increased errors as the payload stiffness deviates from the constant stiffness test payload originally used with the open loop iterative learning control, and further the errors are not necessarily bounded by test payloads significantly softer or stiffer than the actual specimen. The findings support that in cases where repeatable, accurate and precise shake table motions are required for payloads that exhibit a complex material response that is not readily modelled mathematically, it may be necessary to reproduce the specimen's overall dynamic response during the iterative learning control process. [ABSTRACT FROM AUTHOR]

To solve the problem of trajectory tracking lateral control in autonomous driving technology, a model predictive control (MPC) controller trajectory tracking lateral control method combined with a deep deterministic policy gradient algorithm (DDPG) is proposed in this paper. This method inputs the real-time state of the vehicle into DDPG to achieve real-time automatic optimization of the prediction time domain and control time domain parameters of the MPC controller, and then affects the specific performance of the MPC controller in trajectory tracking lateral control. Specifically, the state space, action space, and reward function of DDPG are defined, and the automatic driving trajectory tracking lateral controller is designed in combination with the vehicle dynamics model. To reduce the exploration space of DDPG and improve the training efficiency of the entire model, the technique of advantage-disadvantage experience separation and extraction is introduced. Finally, the proposed method was trained and verified in various scenarios, and compared with two other lateral control methods for autonomous driving. The results showed that the learning and training time of the trajectory tracking lateral control method based on DDPG-MPC was shorter than that of the DDPG-based method, and the evaluation indicators in the trajectory tracking control process were better than those of the DDPG-based method and original MPC-based method. [ABSTRACT FROM AUTHOR]

Some cognitive abilities are suggested to be the result of a complex social life, allowing individuals to achieve higher fitness through advanced strategies. However, most evidence is correlative. Here, we provide an experimental investigation of how group size and composition affect brain and cognitive development in the guppy (Poecilia reticulata). For 6 months, we reared sexually mature females in one of 3 social treatments: a small conspecific group of 3 guppies, a large heterospecific group of 3 guppies and 3 splash tetras (Copella arnoldi)—a species that co-occurs with the guppy in the wild, and a large conspecific group of 6 guppies. We then tested the guppies' performance in self-control (inhibitory control), operant conditioning (associative learning), and cognitive flexibility (reversal learning) tasks. Using X-ray imaging, we measured their brain size and major brain regions. Larger groups of 6 individuals, both conspecific and heterospecific groups, showed better cognitive flexibility than smaller groups but no difference in self-control and operant conditioning tests. Interestingly, while social manipulation had no significant effect on brain morphology, relatively larger telencephalons were associated with better cognitive flexibility. This suggests alternative mechanisms beyond brain region size enabled greater cognitive flexibility in individuals from larger groups. Although there is no clear evidence for the impact on brain morphology, our research shows that living in larger social groups can enhance cognitive flexibility. This indicates that the social environment plays a role in the cognitive development of guppies. [ABSTRACT FROM AUTHOR]

This work examines a class of distributed linear systems that fit a tree type of hierarchical structure. Therefore, unidirectional information flow from a subsystem higher in the hierarchy impacts subsystems lower in the hierarchy. While prior efforts at control focused on feedback solutions to these systems, this effort introduces Iterative Learning Control as a feedforward controller. This is termed hierarchical iterative learning control (HILC). This HILC can be implemented in parallel with feedback algorithms or can be used in a series feedforward manner assuming stable, or stabilized, subsystems. An augmentation of the standard learning update operators provides stability and monotonic convergence for the proposed approach. A simulation case study highlights the performance of the proposed design approach. [ABSTRACT FROM AUTHOR]

The precision of workpiece machining is critically influenced by the geometric errors in the kinematics of grind robots, which directly affect their absolute positioning accuracy. To tackle this challenge, this paper introduces a logistic-tent chaotic mapping Levenberg Marquardt algorithm designed to accurately identify and compensate for this geometric error. the approach begins with the construction of a forward kinematic model and an error model specific to the robot. Then the algorithm is adopted to identify and compensate for the geometric error. The method establishes a mapping interval around the initial candidate solutions derived from iterative applications of the Levenberg Marquardt algorithm. Within this interval, the logistic-tent chaotic mapping method generates a diverse set of candidate solutions. These candidates are evaluated based on their fitness values, with the optimal solution selected for subsequent iterations. Empirical compensation experiments have validated the proposed method's precision and effectiveness, demonstrating a 6% increase in compensation accuracy and a 47.68% improvement in efficiency compared to existing state-of-the-art approaches. This process not only minimizes the truncation error inherent in the Levenberg Marquardt algorithm but also significantly enhances solution efficiency. Moreover, simulation experiments on grind processes further validate the method's ability to significantly improve the quality of workpiece machining. [ABSTRACT FROM AUTHOR]

Efficient control of cardiac pacing is a very important aspect as it provides lifesaving regulated cardiac rhythm in this dynamic hostile environment. The foremost control objective is set to design a highly reliable and advanced control strategy to ensure the utmost accuracy in the control effort. A modified artificial neural network (ANN)–based modelling and pace tracking using finite dimension repetitive controller (FDRC) design based on internal model principle (IMP) has been presented here. This controller will not only provide accurate tracking but also minimize the control action time due to less amount of data handling through the deployment of discrete wavelet transform (DWT) in the loop of repetitive controller (RC). Finally, a case study has been propounded considering ANN model using available data sets and software to validate the control strategy and justify the control objective for optimizing the pace tracking in a pacemaker. Result of the experiment showed good accuracy as well as very low error in terms of mean-squared error (MSE), integral absolute error (IAE), integral time absolute error (ITAE) and integral time square error (ITSE). Along with that, it is observed that DWT not only benefits the handling of very less memory but also acts as an additional filter while reconstructing the signal, which serves as an added advantage of this model. [ABSTRACT FROM AUTHOR]

Robust model predictive control (RMPC) is an effective technology for controlling uncertain systems while robustly handling constraints, and its closed-loop performance heavily relies on the selection of objective functions. However, the objective functions are typically chosen to be close to the real control objectives, despite an objective function that leads to less conservative constraints often provides better closed-loop performance. In this paper, we propose an automatic tuning framework for RMPC in iterative tasks. In particular, we parameterize RMPC and develop a Bayesian optimization (BO) method to tune it by solving a black-box optimization problem. We then introduce an efficient transfer learning framework within BO, which speeds up the searching process and enhances the controller performance. The effectiveness of the proposed tuning framework is illustrated on numerical examples. [ABSTRACT FROM AUTHOR]

This paper investigates the design of a model‐free adaptive iterative learning controller(MFAILC) based on sampled‐data under the presence of denial‐of‐service(DoS) attacks in nonlinear networked control systems. First, the MFAILC is presented only using I/O data, where a compensation mechanism for DoS attacks is proposed. With dynamic linearization techniques, the nonlinear system is transformed into a linear system in the iteration domain. Then an improved MFAILC is designed to actively compensate the lost data caused by DoS attacks, where the estimation of pseudo‐partial derivative (PPD) is improved by establishing the AR model. The proposed algorithm can weaken the adverse effects of the DoS attacks and ensure the excellent tracking performance of the system. Finally, the stability of the method is proved, and the effectiveness of the proposed algorithm is demonstrated by a numerical example. [ABSTRACT FROM AUTHOR]

Iterative learning control (ILC) algorithms appeared in connection with the problems of increasing the accuracy of performing repetitive operations by robots. They use information from previous repetitions to adjust the control signal on the current repetition. Most often, information from the previous repetition only is used. ILC algorithms that use information from several previous iterations are called higher-order algorithms. Recently, interest in these algorithms has increased in the literature in connection with robotic additive manufacturing problems. However, in addition to the fact that these algorithms have been little studied, there are conflicting estimates regarding their properties. This paper proposes new higher-order ILC algorithms for linear discrete and differential systems. The idea of these algorithms is based on an analogy with multi-step methods in optimization theory, in particular, with the heavy ball method. An example is given that confirms the possibility to accelerate convergence of the learning error when using such algorithms. [ABSTRACT FROM AUTHOR]

In order to meet the increasing demand for high‐speed joining processes, laser beam micro welding is used to reproducibly weld metallic joining partners such as steel. Long weld seams or high cycle speeds, however, remain a challenge to achieve a constant welding depth throughout the entire welding process without major fluctuations. This paper shows the development and evaluation of a weld penetration depth control system based on interferometric measurement of the depth of the vapor capillary. High path speeds and small weld depths are challenging for real‐time depth control. Therefore, the offline data of the interferometric measurements are used to implement an iterative learning control of the weld penetration depth. The quality of the control is verified by welding with and without spatial power modulation on 1.4301 steel while following a linear and sinusoidal trajectory. [ABSTRACT FROM AUTHOR]

Component failures can lead to performance degradation or even failure in multi-agent systems, thus necessitating the development of fault diagnosis methods. Addressing the distributed fault diagnosis problem in a class of partial differential multi-agent systems with actuators, a fault estimator is designed under the introduction of virtual faults to the agents. A P-type iterative learning control protocol is formulated based on the residual signals, aiming to adjust the introduced virtual faults. Through rigorous mathematical analysis utilizing contraction mapping and the Bellman–Gronwall lemma, sufficient conditions for the convergence of this protocol are derived. The results indicate that the learning protocol ensures the tracking of virtual faults to actual faults, thereby facilitating fault diagnosis for the systems. Finally, the effectiveness of the learning protocol is validated through numerical simulation. [ABSTRACT FROM AUTHOR]

This paper presents a comprehensive study on the implementation and analysis of PID controllers in an automated voltage regulator (AVR) system. A novel tuning technique, Virtual Time response-based iterative gain evaluation and re-design (V-Tiger), is introduced to iteratively adjust PID gains for optimal control performance. The study begins with the development of a mathematical model for the AVR system and initialization of PID gains using the Pessen Integral Rule. Virtual time-response analysis is then conducted to evaluate system performance, followed by iterative gain adjustments using Particle Swarm Optimization (PSO) within the V-Tiger framework. MATLAB simulations are employed to implement various controllers, including the V-Tiger PID controller, and their performance is compared in terms of transient response, stability, and control signal generation. Robustness analysis is conducted to assess the system's stability under uncertainties, and worst-case gain analysis is performed to quantify robustness. The transient response of the AVR with the proposed PID controller is compared with other heuristic controllers such as the Flower Pollination Algorithm, Teaching–Learning-based Optimization, Pessen Integral Rule, and Zeigler-Nichols methods. By measuring the peak closed-loop gain of the AVR with the controller and adding uncertainty to the AVR's field exciter and amplifier, the robustness of proposed controller is determined. Plotting the performance degradation curves yields robust stability margins and the accompanying maximum uncertainty that the AVR can withstand without compromising its stability or performance. Based on the degradation curves, robust stability margin of the V-Tiger PID controller is estimated at 3.5. The worst-case peak gains are also estimated using the performance degradation curves. Future research directions include exploring novel optimization techniques for further enhancing control performance in various industrial applications. [ABSTRACT FROM AUTHOR]

This paper develops a novel hierarchical control strategy for improving the trajectory tracking capability of aerial robots under parameter uncertainties. The hierarchical control strategy is composed of an adaptive sliding mode controller and a model-free iterative sliding mode controller (MFISMC). A position controller is designed based on adaptive sliding mode control (SMC) to safely drive the aerial robot and ensure fast state convergence under external disturbances. Additionally, the MFISMC acts as an attitude controller to estimate the unmodeled dynamics without detailed knowledge of aerial robots. Then, the adaption laws are derived with the Lyapunov theory to guarantee the asymptotic tracking of the system state. Finally, to demonstrate the performance and robustness of the proposed control strategy, numerical simulations are carried out, which are also compared with other conventional strategies, such as proportional-integralderivative (PID), backstepping (BS), and SMC. The simulation results indicate that the proposed hierarchical control strategy can fulfill zero steady-state error and achieve faster convergence compared with conventional strategies. [ABSTRACT FROM AUTHOR]

Summary: In this article, the decentralized repetitive tracking controller design for fractional‐order large‐scale Takagi–Sugeno fuzzy system with time delays is developed. We mainly focus on the design of a decentralized repetitive tracking controller based on the Lyapunov stability theory, by which the addressed large‐scale system asymptotically stabilized with H∞$$ {H}_{\infty } $$ performance index. Further, the repetitive control with quantized signal is developed to ensure the good tracking performance with the presence of interconnected model and external disturbances. Specifically, a logarithmic quantizer is used to quantify the control signal which can reduce the data transmission rate in the network. Finally, a numerical example is presented to verify the effectiveness of the proposed controller design technique. [ABSTRACT FROM AUTHOR]

The lack of a central controller, severe resource constraints, and multi-path data routing have turned data exchanges into one of the fundamental challenges of the Internet of Things. Despite numerous research efforts on various aspects of routing and data exchanges, some fundamental challenges such as the instant negative impacts of selecting the best possible path and the absence of measures to observe the dynamic conditions of nodes still exist. This study introduces a method called RI-RPL, based on the development of the RPL routing protocol, along with the use of reinforcement learning to address these challenges effectively. To achieve this, RI-RPL is designed in three general stages. In the first stage, routers are aligned with optimizing the RPL protocol with a focus on the Q-learning algorithm. In the second stage, based on learning and convergence, changes in the parents' learning in different network conditions are supported. In the third stage, control and management changes are coordinated. The reason for choosing this algorithm is its ability to address the desired challenges effectively without wasting network resources for calculations. Simulation results using the Cooja software show that the proposed RI-RPL method, compared to similar recent methods such as ELBRP, RLQRPL, and RPL, has improved successful delivery rates by 4.03%, 13.26%, and 28.87%, respectively, for end-to-end delay by 3.04%, 9.82%, and 13.12%, respectively, for energy consumption optimization by 10.43%, 28.91%, and 36.35%, respectively, for throughput by 10.23%, 28.45%, and 46.88%, respectively, and for network data loss rate by 15.06%, 34.95%, and 49.66%, respectively. [ABSTRACT FROM AUTHOR]

An each step time-limited iterative learning control model was developed for a cushion robot with velocity constraints. A predictive modeling method was proposed to solve the velocity mutation problem by employing a kinematic model to constrain the velocity inputs, which can then constrain the robot's actual velocity. Furthermore, a tracking error system was established that used constrained motion velocity and a dynamic model. A new iterative controller with each step time-limited learning was built to reduce the transient adjustment time. Simulation results and comparative analyses revealed that the proposed control method quickly stabilizes the system and ensures that the human–robot system operates at a safe velocity. [ABSTRACT FROM AUTHOR]

This paper studies a secure iterative interval estimation approach for cyber-physical systems subject to stealthy deception attacks. Under the hypothesis that the system is accessed by a stealthy attack, an iteration scheme integrating the T-N-L observer framework is employed to reconstruct the system state. With the help of a structure separation method, a sufficient condition in terms of linear matrix inequality is provided to obtain convergent observation errors under deception attacks. Resorting to the reachability analysis, a secure state interval is built by means of the analyzed attack bounds and the observation error interval. Simulation studies verify the effectiveness of the proposed method for attack and attack-free cases. [ABSTRACT FROM AUTHOR]

This paper develops a novel guaranteed cost control (GCC) approach under the event-triggered mechanism for completely unknown systems using integral reinforcement learning (IRL) algorithm. First, based on the adaptive dynamic programming (ADP) method, the GCC problem is addressed by transforming it into the optimal control problem. Second, without using the accurate information of system dynamics, a model-free data-based GCC approach is designed via IRL algorithm. Moreover, for the purpose of reducing the waste of communication resources, a GCC algorithm is presented under the event-triggered mechanism for completely unknown system by utilizing the explorized IRL algorithm. The critic–actor–disturbance neural networks (NNs) are applied to approximate near optimal solution. In addition, the weight estimations of NNs are tuned synchronously according to the designed novel triggering condition. Furthermore, the stability analysis of the controlled system is given by utilizing the Lyapunov principle. Finally, the simulation results are presented to verify the feasibility of the designed approach. [ABSTRACT FROM AUTHOR]

This paper presents a model predictive control (MPC) approach based on the extended disturbance observer (EDOB) for trajectory tracking of a coaxial octorotor unmanned aerial vehicle (UAV). First, the system dynamic model is derived using Newton–Euler relations in the presence of time‐varying centre of gravity (COG); then, a two‐loop cascade structure is presented to perform the trajectory tracking task. Both loops are controlled using MPC with feedforward compensation based on the EDOB to improve disturbance rejection abilities. When the mass changes, the moment of inertia and COG are affected. The EDOB simultaneously estimates the effects of time‐varying mass, external disturbances, and parametric uncertainties in six degrees of freedom. After obtaining virtual control inputs using designed controllers, constrained control allocation is used to obtain rotors speed in a valid range. The proposed control scheme is evaluated using simulation. The simulation results show the ability of the developed control strategy in accurate trajectory tracking and stable flight in different conditions and being robust to uncertainty and disturbance. [ABSTRACT FROM AUTHOR]

In this paper, we intend to utilize the generalized scalar auxiliary variable (GSAV) approach proposed in recent paper (Ju et al., SIAM J. Numer. Anal., 60 (2022), 1905–1931) for the nonlocal coupled sine-Gordon equation to construct a class of fully decoupled, linear, and second-order accurate energy-preserving scheme. The unconditional unique solvability and discrete energy conservation law of the proposed scheme are rigorously discussed, and the unconditional convergence is then proved by the mathematical induction. Particularly, the convergence analysis covers the proposed scheme in multiple dimensions due to the corresponding nonlinear terms satisfy the global Lipschitz continuity straightforwardly. Finally, time evolution of dynamical behavior of the governing equation with different nonlocal parameters are observed, and ample numerical comparisons demonstrate that the proposed scheme manifests high efficiency in long-time computations. [ABSTRACT FROM AUTHOR]

This study employs a two-dimensional and incompressible flow of Herschel–Bulkley visco-plastic materials in order to investigate the hydrodynamic forces that are acting on a barrier that is located close to the inlet of a channel. As the benchmark configuration, the flow domain that has been selected is a channel that still contains the impediment. The two important parameters of the Herschel–Bulkley Model (HBM) are the yield stress τ y and power law index n. Obtaining special situations within the HBM, such as Newtonian, power-law, and Bingham fluids, can be accomplished by assigning certain values to these parameters at the appropriate times. Utilizing a numerical strategy grounded in the Finite Element Method (FEM), we tackle the nonlinearity of the governing equations as well as the viscosity models. As a result of this nonlinearity, FEM becomes an essential tool. The generation of a refined hybrid mesh is done in order to guarantee accuracy in the computations. The stable finite element pair ( ℙ 2 ∕ ℙ 1 ) has been selected for discretization purposes. The discretized nonlinear system is linearized with Newton's method and subsequently, a direct linear solver PARDISO has been employed in the inner iterations. The pressure, velocity, and viscosity profiles are plotted for various values of n and Bingham number (Bn). In addition, the velocity behavior is observed along the y-direction in a channel through line graphs. Code validation is done as a special case Bn = 0 and a good agreement is found with the results available in the literature. Finally, a correlation analysis has been performed for the drag coefficient C d and lift coefficient C l . [ABSTRACT FROM AUTHOR]

This paper proposes a distributed model predictive control (DMPC) algorithm for dynamic decoupled discrete‐time nonlinear systems subject to nonlinear (maybe non‐convex) coupled constraints and costs. Solving the resulting nonlinear optimal control problem (OCP) using a DMPC algorithm that is fully distributed, termination‐flexible, and recursively feasible for nonlinear systems with coupled constraints and costs remains an open problem. To address this, we propose a fully distributed and globally convergence‐guaranteed framework called inexact distributed sequential quadratic programming (IDSQP) for solving the OCP at each time step. Specifically, the proposed IDSQP framework has the following advantages: (i) it uses a distributed dual fast gradient approach for solving inner quadratic programming problems, enabling fully distributed execution; (ii) it can handle the adverse effects of inexact (insufficient) calculation of each internal quadratic programming problem caused by early termination of iterations, thereby saving computational time; and (iii) it employs distributed globalization techniques to eliminate the need for an initial guess of the solution. Under reasonable assumptions, the proposed DMPC algorithm ensures the recursive feasibility and stability of the entire closed‐loop system. We conduct simulation experiments on multi‐agent formation control with non‐convex collision avoidance constraints and compare the results against several benchmarks to verify the performance of the proposed DMPC method. [ABSTRACT FROM AUTHOR]

This article studies the control barrier function (CBF) guided tracking performance optimization for switched systems under iterative learning control (ILC). CBF is an effective method for handling control system state safety. If the safe set is designed as expected performance, and the unsafe set is not expected, then this may be a good choice for optimizing control system performance. We propose a tracking performance optimization method based on CBF to speed up the convergence of the tracking error. A safe set is used to describe the expected tracking performance, by utilizing CBF, safety is further transformed into a set of inequality conditions that constrain ILC controller gains, which ensures that the tracking error is always within the safe set. In addition, an event‐triggering mechanism (ETM) is considered to reduce unnecessary data transmission, and sufficient conditions for exponential stability of the tracking error of switched systems and ILC controllers design are obtained. Finally, a simulation example is given to verify the feasibility of the proposed method. [ABSTRACT FROM AUTHOR]

This article studies the model‐free learning‐based distributed cooperative tracking control of human‐in‐the‐loop multi‐agent systems in the presence of an active leader. The core role of human‐in‐the‐loop is to use the ground station to send control commands to the non‐zero control input of the leader, and then directly or indirectly control a group of agents to complete complex tasks. Meanwhile, three essential demands including the completely unknown system model, the control objective obtained optimally, as well as no initial admissible control strategy requirement, are satisfied simultaneously. It is worth emphasizing that the relevant results only satisfy one or two demands at most, which are essentially not applicable to this problem. In this article, a model‐based human‐in‐the‐loop learning algorithm is first presented to achieve the optimal tracking control, as well as the convergence of the proposed learning algorithm is proved. Then, a bias‐based data‐driven learning algorithm is proposed, which provides the potential opportunities to overcome the difficulties caused by the above‐mentioned three demands. Finally, the validity of theoretical results is testified by a numerical example. [ABSTRACT FROM AUTHOR]

This paper investigates the secure optimal tracking control problem for cyber-physical systems, in which the controller-actuator channel is jammed by denial-of-service attacks. Without leveraging model knowledge, learning-based tracking control algorithms are proposed by utilizing the measured input-output data. The impact of malicious attacks on tracking performance is discussed. More specifically, an augmented system consisted of the system model and the reference model is derived. Then the states of the augmented system are rewritten by utilizing the input, output, and reference trajectory, following which both the Bellman equation and algebraic Riccati equation are given. The conditions of existence and uniqueness of the solution to the algebraic Riccati equation are derived. Furthermore, both policy iteration and value iteration learning-based tracking control algorithms are provided for cyber-physical systems against denial-of-service attacks, and the convergence of the algorithms is also proved. Finally, a DC motor system and a numerical example are given to illustrate the effectiveness of the proposed control algorithms. [ABSTRACT FROM AUTHOR]

To solve the control problem of time-varying state-scale nonlinear systems whose initial state is not affected by settling time, fixed-time convergence algorithms are proposed for first-order systems and higher-order systems in this paper. First, a scalar model is used to illustrate how the time-varying feedback parameter can guarantee that the system achieves asymptotic stability while achieving finite-time convergence, and it is proved that the settling time obtained in this paper is only related to the prescribed boundary. This allows us to design the settling time with an appropriate parameter based on the prescribed boundary. To exhibit the effectiveness and extensibility of the proposed algorithm for first-order scalar systems, the results are subsequently extended to general higher-order systems based on the backstepping method. By introducing numerical simulation results, this paper verifies that the proposed algorithm will make the system achieve asymptotic stability and its output can converge to a given boundary, regardless of the system's initial states. [ABSTRACT FROM AUTHOR]

This paper proposes a data-driven predictive iterative learning control (DDPILC) for nonlinear nonaffine systems. First, we develop an iterative predictive model (IPM) where an iterative dynamic linearisation technique is introduced for addressing the strong nonlinearities and nonaffine structure. Then, an auto-regressive model is employed to estimate the unavailable parameter of IPM along with the iteration direction. Next, the outputs in the future iterations are predicted pointwisely over the finite operation interval that are further incorporated into the optimal objective function to obtain the optimal control input sequence. In addition, a constrained-DDPILC is extended for systems with I/O constraints which are reformulated as a linear matrix inequality (LMI). The two proposed methods do not have model requirement except for I/O data. Simulation study verifies the results. [ABSTRACT FROM AUTHOR]