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The widespread adoption of edge computing has revolutionized data processing by decentralizing computational power, resulting in faster response times, decreased network latency, and enhanced privacy. This paradigm shift is crucial due to the increasing demand for real-time analytics and the growth of Internet of Things devices. Optimizing resource allocation and decision-making in on-board computing presents challenges, especially in dynamic and heterogeneous environments. Distributed optimization techniques address these challenges by allowing multiple agents to collaborate and make decisions based on local knowledge. This paper focuses on distributed optimization in multi-agent systems with time-varying communication networks and explores the advantages of considering symmetric group action to reach global optimization. In particular, we focus our study into a class of Integer Linear Programming (ILP) for modeling real-world optimization problems in decentralized environments. The paper introduces a novel approach that leverages group actions and probabilistic selection of initial states to enhance convergence to desirable solutions. The method guarantees feasibility while minimizing computational effort for the agents. Additionally, numerical simulations have been conducted to validate the proposed algorithm, demonstrating its efficacy in optimizing resource allocation for a class of scheduling problems. [ABSTRACT FROM AUTHOR]

This paper introduces a novel dead-zone optimization technique for regulating the initial control input in a flexible manner. Both completely dead-zone optimized and partially dead-zone optimized versions of the conventional fixed-time convergent controller are developed for a single-integrator system. Furthermore, based on the same idea, the dead-zone optimization of a newly proposed nonsingular continuous fixed-time convergent controller is proposed for a double-integrator system. Finally, simulation results are provided to show efficacy of the dead-zone optimized controllers. [ABSTRACT FROM AUTHOR]

This paper proposes a novel multi-step subgradient scheme to solve distributed optimization problem with a balanced digraph. To this end, matrix diameter and radius are first introduced to describe the convergence rate of the adjacency matrix. Then, we propose a hierarchical and recursive observer to estimate the desired optimal solution, and we prove that the proposed strategy can asymptotically obtain an optimal solution, while all networked systems achieve a consensus among estimates in a finite-time. Simulation results verified the effectiveness of the proposed algorithm. [ABSTRACT FROM AUTHOR]

Abstract Nonlinear Auto-Regressive model with eXogenous input (NARX) is one of the most popular black-box model classes that can describe many nonlinear systems. The structure determination is the most challenging and important part during the system identification. NARX can be formulated as a linear-in-the-parameters model, then the identification problem can be solved to obtain a sparse solution from the viewpoint of the weighted l 1 minimization problem. Such an optimization problem not only minimizes the sum squares of model errors but also the sum of reweighted model parameters. In this paper, a novel algorithm named Bayesian Augmented Lagrangian Algorithm (BAL) is proposed to solve the weighted l 1 minimization problem, which is able to obtain a sparse solution and enjoys fast computation. This is achieved by converting the original optimization problem into distributed suboptimization problems solved separately and penalizing the overall complex model to avoid overfitting under the Bayesian framework. The regularization parameter is also iteratively updated to obtain a satisfied solution. In particular, a solver with guaranteed convergence is constructed and the corresponding theoretical proof is given. Two numerical examples have been used to demonstrate the effectiveness of the proposed method in comparison to several popular methods. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, a structured polynomial parameter-dependent approach is proposed for robust filtering of linear uncertain systems. Given a stable system with parameter uncertainties residing in a polytope with vertices, the focus is on designing a robust filter such that the filtering error system is robustly asymptotically stable and has a guaranteed estimation error variance for the entire uncertainty domain. A new polynomial parameter-dependent idea is introduced to solve the robust filtering problem, which is different from the quadratic framework that entails fixed matrices for the entire uncertainty domain, or the linearly parameter-dependent framework that uses linear convex combinations of matrices. This idea is realized by carefully selecting the structure of the matrices involved in the products with system matrices. Linear matrix inequality (LMI) conditions are obtained for the existence of admissible filters and based on these, the filter design is cast into a convex optimization problem, which can be readily solved via standard numerical software. Both continuous and discrete-time cases are considered. The merit of the methods presented in this paper lies in their less conservatism than the existing robust filter design methods, as shown both theoretically and through extensive numerical examples. [Copyright &y& Elsevier]

Abstract: The input-constrained LQR problem is addressed in this paper; i.e., the problem of finding the optimal control law for a linear system such that a quadratic cost functional is minimised over a horizon of length N subject to the satisfaction of input constraints. A global solution (i.e., valid in the entire state space) for this problem, and for arbitrary horizon N, is derived analytically by using dynamic programming. The scalar input case is considered in this paper. Solutions to this problem (and to more general problems: state constraints, multiple inputs) have been reported recently in the literature, for example, approaches that use the geometric structure of the underlying quadratic programming problem and approaches that use multi-parametric quadratic programming techniques. The solution by dynamic programming proposed in the present paper coincides with the ones obtained by the aforementioned approaches. However, being derived using a different approach that exploits the dynamic nature of the constrained optimisation problem to obtain an analytical solution, the present result complements the previous methods and reveals additional insights into the intrinsic structure of the optimal solution. [Copyright &y& Elsevier]

In this paper discrete time linear parameter varying (LPV) models with finite impulse response (FIR) dynamic structure are considered. Measurement errors are assumed to be bounded. In such condition optimal input sequences minimizing the worst case parameter uncertainties are derived. The main result of this paper consists in finding optimal worst case input sequences for LPV–FIR models. These are obtained suitably combining the optimal design results for standing alone invariant FIR models and standing alone nonlinear memoryless blocks. The quite relevant improvement obtained using optimal input sequences instead of random sequences is shown by simulation. [Copyright &y& Elsevier]

In this paper, multi-agent dynamic optimization with a coupling constraint is studied. The aim is to minimize a strongly convex social cost function, by considering a linear stochastic dynamics for each agent and also coupling constraints among the agents. In order to handle the coupling constraint and also, to avoid high computational cost imposed by a centralized method for large scale systems, the dual decomposition method is used to decompose the problem into multiple individual sub-problems, while the dual variable is adjusted by a coordinator. Nevertheless, since each sub-problem is not a linear–quadratic (LQ) optimal control problem, and hence its closed-form solution does not exist, approximate dynamic programming (ADP) is utilized to solve the sub-problems. The main contribution of the paper is to propose an algorithm by considering the interrelated iterations of dual variable adjustment and ADP, and to prove the convergence of the algorithm to the global optimal solution of the social cost function. Additionally, the implementation of the proposed algorithm using a neural network is presented. Also, the computational advantage of the proposed algorithm in comparison with other bench-marking methods is discussed in simulation results. [ABSTRACT FROM AUTHOR]

In this paper, we study a resource allocation problem in which a group of agents cooperatively optimize a separable optimization problem with a linear network resource constraint and allocation feasibility constraints, where the global objective function is the sum of agents’ local objective functions. Each agent can only get noisy observations of its local gradient function and its local resource, which cannot be shared by other agents or transmitted to a center. There also exist communication uncertainties such as time-varying topologies (described by random graphs) and additive channel noises. To solve the resource allocation with uncertainties, we propose a stochastic approximation based distributed algorithm, and prove that agents can collaboratively achieve the optimal allocation with probability one by virtue of the ordinary differential equation (ODE) method for stochastic approximation. Finally, simulations related to the demand response management in power systems verify the effectiveness of the proposed algorithm. [ABSTRACT FROM AUTHOR]

We consider a class of nonlinear optimal control problems in which the aim is to minimize control variation subject to an upper bound on the system cost. This idea of sacrificing some cost in exchange for less control volatility—thereby making the control signal easier and safer to implement—is explored in only a handful of papers in the literature, and then mainly for piecewise-constant (discontinuous) controls. Here we consider the case of smooth continuously differentiable controls, which are more suitable in some applications, including robotics and motion control. In general, the control signal's total variation—the objective to be minimized in the optimal control problem—cannot be expressed in closed form. Thus, we introduce a smooth piecewise-quadratic discretization scheme and derive an analytical expression, which turns out to be rational and non-smooth, for computing the total variation of the approximate piecewise-quadratic control. This leads to a non-smooth dynamic optimization problem in which the decision variables are the knot points and shape parameters for the approximate control. We then prove that this non-smooth problem can be transformed into an equivalent smooth problem, which is readily solvable using gradient-based numerical optimization techniques. The paper includes a numerical example to verify the proposed approach. [ABSTRACT FROM AUTHOR]

This paper proposes a fast decentralized algorithm for solving a consensus optimization problem defined in a directed networked multi-agent system, where the local objective functions have the smooth + nonsmooth composite form, and are possibly nonconvex . Examples of such problems include decentralized compressed sensing and constrained quadratic programming problems, as well as many decentralized regularization problems. We extend the existing algorithms PG-EXTRA and ExtraPush to a new algorithm PG-ExtraPush for composite consensus optimization over a directed network. This algorithm takes advantage of the proximity operator like in PG-EXTRA to deal with the nonsmooth term, and employs the push-sum protocol like in ExtraPush to tackle the bias introduced by the directed network. With a proper step size, we show that PG-ExtraPush converges to an optimal solution at a linear rate under some regular assumptions. We conduct a series of numerical experiments to show the effectiveness of the proposed algorithm. Specifically, with a proper step size, PG-ExtraPush performs linear rates in most of cases, even in some nonconvex cases, and is significantly faster than Subgradient-Push, even if the latter uses a hand-optimized step size. The established theoretical results are also verified by the numerical results. [ABSTRACT FROM AUTHOR]

This paper concerns a class of functions, named cost-to-travel functions, which find applications in model-based control. For a given (potentially nonlinear) control system, the cost-to-travel function associates with any given start and end point in the state space and any given travel duration the minimum economic cost of the associated point-to-point motion. Cost-to-travel functions are a generalization of cost-to-go functions, which are often used in the context of dynamic programming as well as model predictive control. We discuss the properties of cost-to-travel functions, their relations to existing concepts in control such as dissipativity, but also a variety of control-theoretic applications of this function class. In particular, we discuss how cost-to-travel functions can be used to analyze the properties of economic model predictive control with return constraints. [ABSTRACT FROM AUTHOR]

This paper studies the global optimal consensus problem for a multi-agent system with bounded controls. Each agent has its own objective function which is known only to itself. We focus on two multi-agent systems, the single integrator multi-agent system and the double-integrator multi-agent system. For each of these two multi-agent systems, we construct, for each agent, a bounded local control protocol that uses the information accessible to it through the communication topology underlying the multi-agent system and information of its own objective function. It is shown that these control protocols together achieve global optimal consensus for the multi-agent system, that is, all agents reaching consensus at a state that minimizes the sum of the objective functions of all agents as long as the communication topology is strongly connected and detailed balanced. Simulation results are given to illustrate the theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, the challenging problem of determining the unknown parameters of an identifiable LTI state-space representation of a stable system is addressed by resorting to a specific H ∞ -norm-based optimization algorithm. More specifically, by assuming the availability of a reliable fully-parameterized representation of the system to identify, the algorithm developed herein consists in restructuring this initial black-box representation of the system dynamics via the optimization of a dedicated maximum eigenvalue-based criterion. This study shows that this H ∞ -norm-based approach can be seen as a good solution for the identification of gray-box LTI state-space representations and, by extension, as an interesting alternative or a reliable initialization step for the standard output-error techniques. [ABSTRACT FROM AUTHOR]

This paper studies the asymptotic convergence properties of the primal–dual dynamics designed for solving constrained concave optimization problems using classical notions from stability analysis. We motivate the need for this study by providing an example that rules out the possibility of employing the invariance principle for hybrid automata to study asymptotic convergence. We understand the solutions of the primal–dual dynamics in the Caratheodory sense and characterize their existence, uniqueness, and continuity with respect to the initial condition. We use the invariance principle for discontinuous Caratheodory systems to establish that the primal–dual optimizers are globally asymptotically stable under the primal–dual dynamics and that each solution of the dynamics converges to an optimizer. [ABSTRACT FROM AUTHOR]

In this paper we first derive a necessary and sufficient condition for a stationary strategy to be the Nash equilibrium of discounted constrained stochastic game under certain assumptions. In this process we also develop a nonlinear (non-convex) optimization problem for a discounted constrained stochastic game. We use the linear best response functions of every player and complementary slackness theorem for linear programs to derive both the optimization problem and the equivalent condition. We then extend this result to average reward constrained stochastic games. Finally, we present a heuristic algorithm motivated by our necessary and sufficient conditions for a discounted cost constrained stochastic game. We numerically observe the convergence of this algorithm to Nash equilibrium. [ABSTRACT FROM AUTHOR]

This paper is concerned with the problem of the disturbance observer based control for a class of continuous-time uncertain systems subject to input saturation and nonlinearity. The input of the system includes two parts, the control input and the disturbance input. The nonlinearity of the system, which satisfies a global Lipschitz condition, is considered as two cases of known nonlinearity and unknown nonlinearity. By virtue of the technique of the disturbance observer based controller, the anti-disturbance controllers are designed respectively with both the polytopic and dead-zone representations of the saturation function, which ensure that the resulting closed-loop systems are asymptotically stable with an estimation of the domain of attraction described by the level set of the Lyapunov function. Further, an iterative optimization method is used to obtain the maximum estimation of the domain of the set of initial states. An example of application design for a flight control system illustrates the effectiveness of the proposed results. [ABSTRACT FROM AUTHOR]

This paper considers the problem of designing accelerated gradient-based algorithms for optimization and saddle-point problems. The class of objective functions is defined by a generalized sector condition. This class of functions contains strongly convex functions with Lipschitz gradients but also non-convex functions, which allows not only to address optimization problems but also saddle-point problems. The proposed design procedure relies on a suitable class of Lyapunov functions and, for a fixed convergence rate, is a convex semi-definite program in all but one scalar parameter. The proposed synthesis allows the design of algorithms that reach the performance of state-of-the-art accelerated gradient methods and beyond. [ABSTRACT FROM AUTHOR]

In the literature, there exist strong results on the qualitative dynamical properties of chemical reaction networks (also called kinetic systems) governed by the mass action law and having zero deficiency. However, it is known that different network structures with different deficiencies may correspond to the same kinetic differential equations. In this paper, an optimization-based approach is presented for the computation of deficiency zero reaction network structures that are linearly conjugate to a given kinetic dynamics. Through establishing an equivalent condition for zero deficiency, the problem is traced back to the solution of an appropriately constructed mixed integer linear programming problem. Furthermore, it is shown that weakly reversible deficiency zero realizations can be determined in polynomial time using standard linear programming. Two examples are given for the illustration of the proposed methods. [ABSTRACT FROM AUTHOR]

This paper addresses the discretisation problem for sparse linear systems. Classical methods usually destroy sparsity patterns of continuous-time systems. We develop an optimisation procedure that yields the best approximation to the discrete-time dynamical matrix with a prescribed sparsity pattern and subject to stability and other constraints. By formulating this problem in an adequate manner, tools from convex optimisation can be then applied. Error bounds for the approximation are provided for special classes of matrices. Numerical examples are included. [ABSTRACT FROM AUTHOR]

From the recent literature, we know that some consecutive measurements of the consensus protocol can be used to compute the exact average of the initial condition. In this paper, we show that these measurements can also be used for estimating the Laplacian eigenvalues of the graph representing the network. As recently shown in the literature, by solving the factorization of the averaging matrix, the Laplacian eigenvalues can be inferred. Herein, the problem is posed as a constrained consensus problem formulated two-fold. The first formulation (direct approach) yields a non-convex optimization problem solved in a distributed way by means of the method of Lagrange multipliers. The second formulation (indirect approach) is obtained after an adequate re-parameterization. The problem is then convex and is solved by using the distributed subgradient algorithm and the alternating direction method of multipliers (ADMM). The proposed algorithms allow estimating the actual Laplacian eigenvalues with high accuracy. [ABSTRACT FROM AUTHOR]

We investigate the identification of a class of block-oriented nonlinear systems which is represented by a common model in this paper. Then identifying the common model is formulated as a biconvex optimization problem. Based on this, a normalized alterative convex search (NACS) algorithm is proposed under a given arbitrary nonzero initial condition. It is shown that we only need to find the unique partial optimum point of a biconvex cost function in order to obtain its global minimum point. Thus, the convergence property of the proposed algorithm is established under arbitrary nonzero initial conditions. By applying the results to Hammerstein–Wiener systems with an invertible nonlinear function, the long-standing problem on the convergence of iteratively identifying such systems under arbitrary nonzero initial conditions is also now solved. [ABSTRACT FROM AUTHOR]

This paper considers a class of optimal control problems for general nonlinear time-delay systems with free terminal time. We first show that for this class of problems, the well-known time-scaling transformation for mapping the free time horizon into a fixed time interval yields a new time-delay system in which the time delays are variable. Then, we introduce a control parameterization scheme to approximate the control variables in the new system by piecewise-constant functions. This yields an approximate finite-dimensional optimization problem with three types of decision variables: the control heights, the control switching times, and the terminal time in the original system (which influences the variable time delays in the new system). We develop a gradient-based optimization approach for solving this approximate problem. Simulation results are also provided to demonstrate the effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we consider a team of spacecraft which requires changing its orientation to a common attitude using a decentralized control scheme under a connected communication topology, while satisfying cone avoidance constraints due to blind celestial objects, plume impingement and so on. For this purpose, we first combine consensus theory and optimization theory to develop a quaternion-based attitude consensus protocol. Based on the communication graph at each time step, each spacecraft generates a guidance command or reference attitude trajectory by synthesizing a series of Laplacian-like matrix , using semidefinite programming (SDP) which involves linear matrix inequalities (LMIs). It is analytically shown that this series of matrices is capable of collectively driving the initial attitudes to a common consensus attitude. For satisfying cone avoidance constraints, exclusion zones are then identified and expressed as LMIs. This identification of the exclusion zones gives rise to selecting safe waypoints from the reference attitude trajectory and then to passing through the selected waypoints while avoiding the exclusion zones via proper control inputs. This solution procedure is demonstrated via numerical simulations of coordinated attitude rendezvous and attitude formation acquisition of multiple spacecraft with cone avoidance manoeuvres. [Copyright &y& Elsevier]

Abstract: In this paper, we discuss some optimality results for the approximation of large-scale matrix equations. In particular, this includes the special case of Lyapunov and Sylvester equations, respectively. We show a relation between the iterative rational Krylov algorithm and a Riemannian optimization method which recently has been shown to locally minimize a certain energy norm of the underlying Lyapunov operator. Moreover, we extend the results for a more general setting leading to a slight modification of IRKA. By means of some numerical test examples, we show the efficiency of the proposed methods. [Copyright &y& Elsevier]

Abstract: We propose a method for model reduction on a given frequency range, without the use of input and output filter weights. The method uses a nonlinear optimization approach to minimize a frequency limited like cost function. An important contribution of the paper is the derivation of the gradient of the proposed cost function. The fact that we have a closed form expression for the gradient and that considerations have been taken to make the gradient computationally efficient to compute enables us to efficiently use off-the-shelf optimization software to solve the optimization problem. [Copyright &y& Elsevier]

Abstract: This paper studies the problems of stability analysis and controller synthesis of switched systems with time-varying delay based on an input–output approach. The attention is focused on developing a new method to further reduce the conservatism of the existing results. The system under consideration is transformed into an interconnection system, and the scaled small gain condition for the interconnection systems is introduced. Based on the system transformation and the scaled small gain theorem, an improved delay-dependent stability criterion is proposed such that the interconnection system is asymptotically stable, which is also proved to guarantee the asymptotic stability of the system based on the direct Lyapunov method in another perspective. The proposed stability condition is demonstrated to be less conservative than most existing results. Moreover, an admissible controller, which solves the problem of controller synthesis, is formulated into a convex optimization problem. Illustrative examples are provided to show the advantage and the effectiveness of the proposed method. [Copyright &y& Elsevier]

Abstract: In this paper Infinitesimal Perturbation Analysis (IPA) is used to derive the gradient estimators for loss volume and queue workload in a multi-stage tandem of stochastic fluid queues with instantaneous additive loss-feedback for overall congestion control. These gradient estimators are then used to drive a standard stochastic approximation algorithm to optimize, with respect to the buffer limits of the individual queues, an objective function which is the weighted sum of loss volume and queue workload of the queues that make up the tandem. [Copyright &y& Elsevier]

Abstract: This paper derives a differential contraction condition for the existence of an orbitally-stable limit cycle in an autonomous system. This transverse contraction condition can be represented as a pointwise linear matrix inequality (LMI), thus allowing convex optimisation tools such as sum-of-squares programming to be used to search for certificates of the existence of a stable limit cycle. Many desirable properties of contracting dynamics are extended to this context, including the preservation of contraction under a broad class of interconnections. In addition, by introducing the concepts of differential dissipativity and transverse differential dissipativity, contraction and transverse contraction can be established for interconnected systems via LMI conditions on component subsystems. [Copyright &y& Elsevier]

Abstract: The problem of identifying a fixed-order FIR approximation of linear systems with unknown structure, assuming that both input and output measurements are subjected to quantization, is dealt with in this paper. A fixed-order FIR model providing the best approximation of the input–output relationship is sought by minimizing the worst-case distance between the output of the true system and the modeled output, for all possible values of the input and output data consistent with their quantized measurements. The considered problem is firstly formulated in terms of robust optimization. Then, two different algorithms to compute the optimum of the formulated problem by means of linear programming techniques are presented. The effectiveness of the proposed approach is illustrated by means of a simulation example. [Copyright &y& Elsevier]

Abstract: If imposing general structural constraints on controllers, it is unknown how to design optimal -controllers by convex optimization. Under the so-called quadratic invariance condition on the generalized plant, the Youla parametrization allows to translate the structured synthesis problem into an infinite dimensional convex program. Nested interconnections that are characterized by a block-triangular structure of the standard plant’s control channel and of the controller fall into this class. Recently it has been shown how to design optimal -controllers for such nested structures in the state-space by solving algebraic Riccati equations. In the present paper we provide a state-space solution of the corresponding output-feedback -synthesis problem without any counterpart in the literature. We argue that a solution based on Riccati equations is–even for state-feedback synthesis–not feasible and we illustrate our results by means of a simple numerical example. [Copyright &y& Elsevier]

Abstract: In many applications, it is of interest to derive information about the topology and the internal connections of multiple dynamical systems interacting together. Examples can be found in fields as diverse as Economics, Neuroscience and Biochemistry. The paper deals with the problem of deriving a descriptive model of a network with no a-priori knowledge on its topology. It is assumed that the network nodes are passively observed and data are collected in the form of time series. The underlying structure is then determined by the non-zero entries of a “sparse Wiener filter”. We cast the problem as the optimization of a quadratic cost function, where a set of parameters are used to operate a trade-off between accuracy and complexity in the final model. [Copyright &y& Elsevier]

Abstract: This paper considers the problem of finding the optimal network topology and consensus gain for the fastest second-order consensus with time delay. By using the root locus method in the frequency domain, the problem can be decomposed into two convex optimization problems. In the case that the network topology is fixed, a multi-hop relay scheme is introduced for fast consensus seeking. Each agent can receive information from its multi-hop neighbors with a certain delay. The optimal number of hops for the fastest convergence speed can be derived from the largest generalized eigenvalue of a pair of extension matrices. Finally, some examples are supplied to verify the theoretical results. [Copyright &y& Elsevier]

Abstract: The paper presents a tube model predictive control (MPC) scheme of continuous-time nonlinear systems based on robust control invariant sets with respect to unknown but bounded disturbances. The cost functional of the optimization problem is not necessarily quadratic. The scheme has the same online computational burden as the standard MPC with guaranteed nominal stability. Robust stability, as well as recursive feasibility, is guaranteed if the optimization problem is feasible at the initial time instant. In particular, we consider a scheme to obtain robust control invariant sets for a class of Lipschitz nonlinear systems, and to show the effectiveness of the proposed schemes by a simple example. [Copyright &y& Elsevier]

Abstract: In this paper we propose a distributed dual averaging method for solving the constrained multi-agent optimization problem, in which multiple agents try to cooperatively optimize the sum of their local convex objective functions subject to a global convex constraint set over a network. We consider two cases: (i) The communications among agents are perfect, and (ii) The communications among agents are deterministically or probabilistically quantized. In the first case, we provide a way to control the convergence performance of the proposed method through adjusting the number of consensus iterations we run in the subgradient step. In the second case, we consider two kinds of quantizers, and provide bounds on their convergence rates to highlight the dependence on the quantization resolutions respectively. Finally, we provide a numerical example to show the effectiveness of the proposed methods. [Copyright &y& Elsevier]

Abstract: In this paper we consider a class of optimal control problems that have continuous-time nonlinear dynamics and nonconvex control constraints. We propose a convex relaxation of the nonconvex control constraints, and prove that the optimal solution to the relaxed problem is the globally optimal solution to the original problem with nonconvex control constraints. This lossless convexification enables a computationally simpler problem to be solved instead of the original problem. We demonstrate the approach in simulation with a planetary soft landing problem involving a nonlinear gravity field. [Copyright &y& Elsevier]

Abstract: We consider the use of linear multivariable feedback control to achieve a nonovershooting and nonundershooting step response. Recently, Schmid and Ntogramatzidis (2010)  introduced a linear state feedback controller design method to avoid overshoot. In this paper, we describe conditions under which the design method may be modified to avoid undershoot. The method is applicable to square and nonsquare systems, minimum and nonminimum phase systems, and also strictly proper and bi-proper systems. [Copyright &y& Elsevier]

Abstract: In this paper, we study an abstract constrained optimization problem which subsumes a common model for the optimal control of linear partial differential equations. Our emphasis is the case when the ordering cone for the optimization problem has an empty interior. To circumvent this difficulty, we propose a new regularization approach which is based on the decoupling of the ordering cone by using certain half-spaces. The approach results in a family of regular optimization problems having a simpler structure than the original optimization problem. Existence theorems, convergence analysis, and optimality conditions are given for the regularized problems. We present two numerical examples and the results are quite encouraging, showing the potential of the proposed approach. [Copyright &y& Elsevier]

Abstract: In this paper, the problem of estimating signals from a dynamic system at regular periods from scarce, delayed and possibly time disordered measurements acquired through a network is addressed. A model based predictor that takes into account the delayed and irregularly gathered measurements from different devices is used. Robustness of the predictor to the time-delays and scarce data availability as well as disturbance and noise attenuation is dealt with via performance optimization. The result is a time variant estimator gain that depends on the measurement characteristics, but belonging to an offline precalculated finite set, and hence, the online needed computer resources are low. An alternative to reduce the number of gains to be stored has been proposed, based on defining the gain as a function of the sampling parameters. The idea allows reaching a compromise between online computer cost and performance. [Copyright &y& Elsevier]

Abstract: In this paper, we consider a control synthesis problem for a class of polynomial dynamical systems subject to bounded disturbances and with input constraints. More precisely, we aim at synthesizing at the same time a controller and an invariant set for the controlled system under all admissible disturbances. We propose a computational method to solve this problem. Given a candidate polyhedral invariant, we show that controller synthesis can be formulated as an optimization problem involving polynomial cost functions over bounded polytopes for which effective linear programming relaxations can be obtained. Then, we propose an iterative approach to compute the controller and the polyhedral invariant jointly. Each iteration of the approach mainly consists in solving two linear programs (one for the controller and one for the invariant) and is thus computationally tractable. Finally, we show with several examples the usefulness of our method in applications. [Copyright &y& Elsevier]

Abstract: In this paper, we propose a new design strategy for nonlinear systems with input saturation. The resulting nonlinear controllers are locally asymptotically stabilizing the origin. The proposed methodology is based on exact feedback linearization which is used to reformulate the nonlinear system as a linear system having state-dependent input saturation. Linear saturating state feedback controllers and soft variable-structure controllers are developed based on this system formulation. The resulting convex optimization problems can be written in terms of linear matrix inequalities and sum of squares conditions for which efficient solvers exist. Polynomial approximation based on Legendre polynomials is used to extend the methodology to a more general class of nonlinear systems. To demonstrate the benefit of this design method, a stabilizing controller for a single link manipulator with flexible joint is developed. [Copyright &y& Elsevier]

Abstract: This paper presents a new technique to design switching gain-scheduling controllers for plants with measurable time-varying parameters. By dividing the parameter set into a sufficient number of subsets, and by designing a robust controller to each subset, the designed switching gain-scheduling controllers achieve a desired -gain performance for each subset, while ensuring stability whenever a controller switching occurs due to the crossing of the time-varying parameters between any two adjacent subsets. Based on integral quadratic constraints theory and Lyapunov stability theory, a switching gain-scheduling controllers design problem amounts to solving optimization problems. Each optimization problem is to be solved by a combination of the bisection search and the numerical nonsmooth optimization method. The main advantage of the proposed technique is that the division of the parameter region is determined automatically, without any prespecified parameter set division which is required in most of previously developed switching gain-scheduling controllers design methods. A numerical example illustrates the validity of the proposed technique. [Copyright &y& Elsevier]

Abstract: In this paper, an economic parameterization for positive parahermitian matrix functions is introduced and applied to the -analysis framework wherein we propose a new state-space optimization problem for finding the required -scales. Among the four state-space matrices to be used to realize the optimal -scale, and are chosen via a Laguerre parameterization whereas the other two state-space matrices, and are obtained by spectral factorization after solving a convex optimization problem formulated in an LMI framework. The obtained -scale satisfies the commuting property with the uncertainty structure. The proposed economic parameterization yields advantages in terms of less computational time and less number of decision variables and also, the proposed state-space optimization framework gives a frequency independent solution algorithm in state-space variables for the required -scales. Two numerical examples are used to demonstrate the effectiveness of the proposed algorithm. [Copyright &y& Elsevier]

Abstract: We address the inherent robustness properties of nonlinear systems controlled by suboptimal model predictive control (MPC), i.e., when a suboptimal solution of the (generally nonconvex) optimization problem, rather than an element of the optimal solution set, is used for the control. The suboptimal control law is then a set-valued map, and consequently, the closed-loop system is described by a difference inclusion. Under mild assumptions on the system and cost functions, we establish nominal exponential stability of the equilibrium, and with a continuity assumption on the feasible input set, we prove robust exponential stability with respect to small, but otherwise arbitrary, additive process disturbances and state measurement/estimation errors. These results are obtained by showing that the suboptimal cost is a continuous exponential Lyapunov function for an appropriately augmented closed-loop system, written as a difference inclusion, and that recursive feasibility is implied by such (nominal) exponential cost decay. These novel robustness properties for suboptimal MPC are inherited also by optimal nonlinear MPC. We conclude the paper by showing that, in the absence of state constraints, we can replace the terminal constraint with an appropriate terminal cost, and the robustness properties are established on a set that approaches the nominal feasibility set for small disturbances. The somewhat surprising and satisfying conclusion of this study is that suboptimal MPC has the same inherent robustness properties as optimal MPC. [Copyright &y& Elsevier]

Abstract: In this paper, we develop a new semistability theory for linear dynamical systems. Specifically, necessary and sufficient conditions based on the new notion of weak semiobservability for the existence of solutions to the semistable Lyapunov equation are derived. Unlike the standard optimal control problem, a complicating feature of the optimal semistable control problem is that the semistable Lyapunov equation can admit multiple solutions. We characterize all the solutions using matrix analysis tools. With this theory, we present a new framework to design optimal semistable controllers for linear coupled systems by converting the original optimal control problem into a convex optimization problem. [Copyright &y& Elsevier]

Abstract: It is well documented (e.g. Zhou (1998) ) that the near-optimal controls, as the alternative to the “exact” optimal controls, are of great importance for both the theoretical analysis and practical application purposes due to its nice structure and broad-range availability, feasibility as well as flexibility. However, the study of near-optimality on the stochastic recursive problems, to the best of our knowledge, is a totally unexplored area. Thus we aim to fill this gap in this paper. As the theoretical result, a necessary condition as well as a sufficient condition of near-optimality for stochastic recursive problems is derived by using Ekeland’s principle. Moreover, we work out an -optimal control example to shed light on the application of the theoretical result. Our work develops that of but in a rather different backward stochastic differential equation (BSDE) context. [Copyright &y& Elsevier]

Abstract: In this paper the sampled-data stabilization of linear time-invariant systems with feedback delay is considered. We assume that the delay is time-varying and that its value is approximatively known. We investigate how to use the available information about the evolution of delays for adapting the control law in real time. Numerical methods for the design of a delay-dependent controller are presented. This allows for providing a control for some cases in which the stabilization cannot be ensured using a controller with a fixed structure. [ABSTRACT FROM AUTHOR]