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This article considers the robust consensus problem of the general linear multiagent system (MAS) subject to both heterogeneous additive stable disturbances and input saturation. Distributed low gain feedback-based dynamic output feedback control protocols are proposed, which do not need the controller interaction. Algebraic Riccati equation and unified $H_{∞}$ controller design method are employed to design the output feedback control protocols. It is established that under the assumption that each agent is asymptotically null controllable with bounded controls, semiglobal robust consensus can always be reached under the proposed controller. Furthermore, the design method specialized for leader-following consensus is addressed, under the assumption that the Laplacian matrix is diagonalizable, one can design the control protocol only with the number of follower agents. Finally, several simulations are provided to show the effectiveness of our results.

This work studies the H∞-based minimal energy control with a preset convergence rate (PCR) problem for a class of disturbed linear time-invariant continuous-time systems with matched external disturbance. This problem aims to design an optimal controller so that the energy of the control input satisfies a predetermined requirement. Moreover, the closed-loop system asymptotic stability with PCR is ensured simultaneously. To deal with this problem, a modified game algebraic Riccati equation (MGARE) is proposed, which is different from the game algebraic Riccati equation in the traditional H∞ control problem due to the state cost being lost. Therefore, a unique positive-definite solution of the MGARE is theoretically analyzed with its existing conditions. In addition, based on this formulation, a novel approach is proposed to solve the actuator magnitude saturation problem with the system dynamics being exactly known. To relax the requirement of the knowledge of system dynamics, a model-free policy iteration approach is proposed to compute the solution of this problem. Finally, the effectiveness of the proposed approaches is verified through two simulation examples.

The linear quadratic (LQ) optimal control and stabilization problems for mean-field systems with input delay (MFSID) are investigated in this paper. The necessary and sufficient solvability conditions for LQ control of MFSID are first given in terms of a convexity condition and the solvability of equilibrium conditions. Consequently, by solving the associated mean-field forward and backward stochastic difference equations (MF-FBSDEs), the optimal control is derived in terms of the solution of a modified Riccati equation (MRE). Furthermore, for infinite horizon case, the stabilization problem for MFSID is studied, and the necessary and sufficient stabilizability conditions are obtained. We show that MFSID can be mean square stabilizable if and only if a modified algebraic Riccati equation (MARE) admits a unique positive definite solution.

This article studies the fault-tolerant leader-following consensus problem for multiagent systems with input saturation. The main contribution is to present a modified low-and-high gain feedback approach to deal with multiple actuator faults, including partial loss of effectiveness, outage, and stuck simultaneously. First, without consideration of saturation, a distributed fault-tolerant control scheme is put forward by the adaptive technique, and a practical finite-time stability result is established. Second, by employing the fault-tolerant theory and introducing a novel form of parametric algebraic Riccati equation, a modified low-and-high gain feedback approach is developed for the saturated control strategy. It is proven that the practical finite-time stability can be achieved, and both the steady-state consensus error and the settling time can be well estimated. Finally, numerical simulations are provided to validate the effectiveness of the theoretical results.

This article is concerned with observer-based non-negative edge-consensus (OBNNEC) problems of networked discrete-time systems with or without actuator saturation. An algorithm which only uses actual outputs of neighboring edges is proposed by means of an H∞ control method and modified algebraic Riccati equation (MARE)-based technique. The observer matrix and feedback matrix are constructed by solving the MARE and linear matrix inequality (LMI), respectively. Then, sufficient conditions for guaranteeing bounded inputs and non-negative edge states are derived. In addition, the low-gain characteristic of the MARE-based method is instrumental in guaranteeing non-negative edge states and deriving the feasible observer matrix and feedback matrix. Finally, two examples are shown to demonstrate the obtained theoretical results.

The secure consensus problem of multiagent systems with input saturation and denial-of-service (DoS) attacks constraints is an interesting research problem. To solve this problem, the assumptions that all the agents own the same saturation level and suffer the same DoS attacks from a single adversary are usually made. This paper removes the above assumptions and investigates the secure consensus problem of multiagent systems with different saturation levels and multiple DoS attacks. The studied multiagent systems have different layers, in which different saturation levels are studied for different layers. Moreover, the DoS attacks are launched from different adversaries and will cause different effects for different agents. To achieve the desired objective, two different consensus protocols for agents in different levels are first designed using the low-gain technique. Then, the investigated dynamic system under DoS attacks is modeled by a switched system by categorizing the DoS attacks into several types. The controller is proposed by solving parametric algebraic Riccati equation (ARE). Sufficient conditions for the DoS attack duration on each channel are derived.

This brief studies the optimal control problem of linear singularly perturbed systems (SPSs) via reinforcement learning (RL). We first present an offline model-based algorithm on the basis of Kleinman algorithm to solve the underlying algebraic Riccati equation with singular perturbation parameter and its convergence is proven. This revised version of Kleinman algorithm is the key to develop the subsequent learning algorithm. Then, by means of two time-scale characteristics of SPSs, we present a novel model-free learning algorithm relating to the online measurement of state and input to design the optimal controller. Compared with the existing learning approaches, the obtained RL algorithm is free of ill-conditioned numerical issues caused by the co-existence of fast and slow modes in SPSs and thus is more robust with respect to the computation and measurement errors. Finally, we verify the effectiveness of the developed results by a simulation example.

This paper investigates the time varying formation problem of Lipschitz-type nonlinear multi-agent systems. An event-triggered adaptive controller is proposed. Comparing to existing related results, in this brief, both the neighbors!/ states information and formation configurations are transmitted via an event-triggered mechanism, which reduce the frequency of communications. Besides, based on state-dependent-gain designs, the proposed protocol can ensure the Lipschitz-type agents achieving the desired final configuration by only solving algebraic Riccati equation (ARE) but linear matrix inequality (LMI), which is not only more practical in engineering scenarios, but also feasible if the system is stabilizable. Also, it follows from continuous adaptive modification, some global information, such as the eigenvalue of the Laplacian matrix and the Lipschitz constant, is not required here.

This brief studies the event-triggered cooperative tracking problem for multiple autonomous agents described by Lipschitz-type nonlinear dynamics. A new kind of event-triggered cooperative tracking strategy is developed by using model-based local sampled state information and the state-dependent gain approach. Compared with some event-triggered cooperative tracking strategies in existing works, the dynamics of agents is extended to Lipschitz-type nonlinearity in this brief, which can better meet the practical engineering needs. Besides, the cooperative tracking algorithms overcome the infeasibility of linear matrix inequality (LMI) conditions, and the cooperative tracking problem can be addressed by only solving an algebraic Riccati equation (ARE), which is feasible if the system is stabilizable. Finally, a simulation example of is presented to verify the theoretical analysis and the effectiveness of the control strategy.

This article presents an event-triggered output-feedback adaptive optimal control method for continuous-time linear systems. First, it is shown that the unmeasurable states can be reconstructed by using the measured input and output data. An event-based feedback strategy is then proposed to reduce the number of controller updates and save communication resources. The discrete-time algebraic Riccati equation is iteratively solved through event-triggered adaptive dynamic programming based on both policy iteration (PI) and value iteration (VI) methods. The convergence of the proposed algorithm and the closed-loop stability is carried out by using the Lyapunov techniques. Two numerical examples are employed to verify the effectiveness of the design methodology.

The article proposes a nonlinear optimal (H-infinity) control approach for a type of underactuated power-line inspection robots. To implement this control scheme, the state-space model of the power-line inspection robots undergoes first approximate linearization around a temporary operating point, through first-order Taylor series expansion and through the computation of the associated Jacobian matrices. To select the feedback gains of the controller an algebraic Riccati equation is solved at each time step of the control method. The global stability properties of the control loop are proven through Lyapunov analysis. The significance of the article’s results is outlined in the following: (i) the proposed control method is suitable for treating underactuated robotic systems and in general nonlinear dynamical systems with control inputs gain matrices which are in a nonquadratic form, (ii) by achieving stabilization of the power-line inspection robots in underactuation conditions the proposed control method ensures the reliable functioning of these robotic systems in the case of actuators’ failures or enables the complete removal of certain actuators and the reduction of the weight of these robotic systems, (iii) the proposed control method offers a solution to the nonlinear optimal control problem which is of proven global stability while also remaining computationally tractable, (iv) the proposed nonlinear optimal control method retains the advantages of linear optimal control that is fast and accurate tracking of reference setpoints under moderate variations of the control inputs, and (v) by minimizing the amount of energy that is dispersed by the actuators of the power-line inspection robots the proposed control method improves the autonomy and operational capacity of such robotic systems.

In the present paper, we consider the semilocal convergence issue of two-step Newton method for solving nonlinear operator equation in Banach spaces. Under the assumption that the first derivative of the operator satisfies a generalized Lipschitz condition, a new semilocal convergence analysis for the two-step Newton method is presented. The Q-cubic convergence is obtained by an additional condition. This analysis also allows us to obtain three important spacial cases about the convergence results based on the premises of Kantorovich, Smale and Nesterov-Nemirovskii types. As applications of our convergence results, a nonsymmetric algebraic Riccati equation arising from transport theory and a two-dimensional nonlinear convection-diffusion equation are provided.

The paper investigates the state estimation problem of general continuous-time linear systems with the consideration of time-varying communication delay. A solution is proposed in terms of the networked distributed observer, which consists of multiple local observers. Each local observer relies on only part of the system output and exchanges information with neighbors through undirected links modeled by a prespecified communication graph. A simple approach for computing observer parameters is presented by solving a parametric algebraic Riccati equation. Furthermore, by the Lyapunov–Krasovskii stability theorem, an upper bound of the delay could be calculated explicitly and together with the conditions of joint observability and connectivity of the communication graph; the resulting distributed observers work coordinately to achieve an asymptotic estimate of the full plant state. An illustrative example is provided to confirm the analytical results.

This paper is concerned with the secure consensus problem of multiagent systems under switching topologies. The studied multiagent systems are affected by both denial-of-service (DoS) attacks and external disturbances . To solve the secure H ∞ consensus problems, some modified definitions are presented. Some graph-based Lyapunov functions , which are based on the solutions of some Lyapunov equations and the graph information , are also designed for the H ∞ performance analysis. Moreover, graph-based frequency and durations have also been presented for attaining the expected system performance. The stabilization controllers are also developed based on the solutions to some Lyapunov equations and an algebraic Riccati equation (ARE), which are easy to acquire. Some simulations are provided to validate the feasibility of the proposed scheme.

In this article, by using the linear graph theory, modified algebraic Riccati equation (MARE)-based method and duality principle, two interaction protocols are proposed to achieve the scaled edge-consensus of networked discrete-time systems with unmeasurable edge-sates. Meanwhile, drawing support from MARE-based low-gain feedback technique and positive system theory, sufficient conditions are derived to ensure the bounded control inputs and positive edge-states. Moreover, feedback matrices and observer matrices are, respectively, constructed by utilizing the solutions of MARE and modified algebraic dual Riccati equation (MADRE). Remarkably, the theoretical results only use the edge number and vertex number of network rather than the global information of network. Finally, five examples are shown to demonstrate the feasibility of the interaction protocols.

Although robust control has been studied for decades, the output-feedback robust control design is still challenging in the control field. This article proposes a new approach to address the output-feedback robust control for continuous-time uncertain systems. First, we transform the robust control problem into an optimal control problem of the nominal linear system with a constructive cost function, which allows simplifying the control design. Then, a modified algebraic Riccati equation (MARE) is constructed by further investigating the corresponding relationship with the state-feedback optimal control. To solve the derived MARE online, the vectorization operation and Kronecker's product are applied to reformulate the output Lyapunov function, and then, a new online data-driven learning method is suggested to learn its solution. Consequently, only the measurable system input and output are used to derive the solution of the MARE. In this case, the output-feedback robust control gain can be obtained without using the unknown system states. The control system stability and convergence of the derived solution are rigorously proved. Two simulation examples are provided to demonstrate the efficacy of the suggested methods.

This paper addresses the distributed optimal decoupling synchronous control of multiple autonomous unmanned linear systems (MAUS) subject to complex network dynamic coupling. The leader–follower mechanism based on neighborhood error dynamics is established and the network coupling term is regarded as the external disturbance to realize the decoupling cooperative control of each agent. The Bounded L2-Gain problem for the network coupling term is formulated into a multi-player zero-sum differential game. It is shown that the solution to the multi-player zero-sum differential game requires the solution to coupled Hamilton–Jacobi (HJ) equations. The coupled HJ equations are transformed into an algebraic Riccati equation (ARE), which can be solved to obtain the Nash equilibrium of a multi-player zero-sum game. It is shown that the bounded L2-Gain for coupling attenuation can be realized by applying the zero-sum game solution as the control protocol and the ultimately uniform boundedness (UUB) of a local neighborhood error vector under conservative conditions is proved. A simulation example is provided to show the effectiveness of the proposed method.

In the present study, the flutter performance of a composite thin-walled beam wing–engine system is optimized by implementing two different control approaches: 1) passive open-loop and 2) active cl...

To achieve control and synchronization of chaotic electronic circuits, a nonlinear optimal (H-infinity) control method is developed and is tested on Chua’s circuit. Although this electronic circuit is deterministic, for specific values of its parameters its phase diagrams may change in a random-like manner, thus exhibiting a chaotic behavior. In the article’s control approach, an approximate linearization procedure is applied first to the dynamic model of the circuit. The linearization takes place around a temporary operating point which is recomputed at each iteration of the control method. It actually uses Taylor series expansion and the computation of the system’s Jacobian matrices. At a next stage, an H-infinity feedback controller is developed for the approximately linearized model of the circuit. This controller is obtained after solving an algebraic Riccati equation at each time step of the control method. To prove the stability properties of the control scheme and the elimination of the synchronization error, Lyapunov analysis is used. The proposed control scheme is demonstrated to satisfy the H-infinity tracking performance condition, and this indicates elevated robustness against model uncertainty and external perturbations. Moreover, the global asymptotic properties of the control method are proven. Finally, under the proposed nonlinear optimal control approach, it is shown that different Chua’s circuits can get synchronized and that chaotic behavior can be replicated by them.

This paper is concerned with the optimal output synchronization control problem for a class of heterogeneous complex dynamical networks (CDNs) with partially unknown system dynamics. By defining a new quadratic performance index including the information of state couplings, an optimal controller consisting of a feedback control and a compensated feedforward control is then designed. A necessary and sufficient condition for the optimal control minimizing the quadratic performance index is established. Especially, an algebraic Riccati equation (ARE) associated with a discount factor is obtained, and a novel online iteration algorithm by iteratively solving the ARE is proposed to compute the optimal controller gain for the case that the CDNs are with partially unknown system dynamics. Moreover, it is proved that the output synchronization errors converge to zero asymptotically by applying the optimal control laws. Finally, two simulation examples are provided to verify the effectiveness of the proposed control method.

This paper studies optimal input port selection for simple undirected graphs with an objective to control the graph externally with least amount of supplied energy. Given a graph with n-nodes, we address the problem of selecting k out of these for external input with this minimization objective. We formulate a resistive-capacitive (RC) network analogy of such single integrator multiagent networks, allowing us to consider the given problem as that of optimal selection of the input ports w.r.t. the energy required for charging/discharging of the RC circuit. We set up a link between these optimal port locations and values in the Fiedler vector of the corresponding graph Laplacian matrix L and other eigenvectors of L. This paper contains new results involving passivity, Hamiltonian matrix and the Algebraic Riccati equation in the context of RC networks associated with such graphs. We link this formulation to optimal node(s) identification for optimal external communication with a multi-agent network of single integrator systems.

An optimal ergodic control problem (EC problem, for short) is investigated for a linear stochastic differential equation with quadratic cost functional. Constant nonhomogeneous terms, not all zero, appear in the state equation, which lead to the asymptotic limit of the state non-zero. Under the stabilizability condition, for any (admissible) closed-loop strategy, an invariant measure is proved to exist, which makes the ergodic cost functional well-defined and the EC problem well-formulated. Sufficient conditions, including those allowing the weighting matrices of cost functional to be indefinite, are introduced for finiteness and solvability for the EC problem. Some comparisons are made between the solvability of EC problem and the closed-loop solvability of stochastic linear quadratic optimal control problem in the infinite horizon. Regularized EC problem is introduced to be used to obtain the optimal value of the EC problem.

We present a robust recursive framework for the regulation of discrete-time linear systems subject to polytopic uncertainties. Based on regularized least-squares with a penalty parameter, we formulate a convex optimization problem and weight the polytope vertices altogether. In this sense, the main contribution of this paper consists of a robust recursive framework for the computation of stabilizing feedback gains. The solution does not require numerical optimization packages and relies ultimately on a single penalty parameter which is easily tuned. Moreover, the gains are obtained recursively through algebraic expressions, as opposed to related works which employ linear matrix inequalities. Under observability and controllability conditions, we demonstrate convergence and stability of the closed-loop system in terms of an algebraic Riccati equation. We provide numerical and real-world examples to validate the proposed approach and for comparison with a robust $H_{\infty }$ controller.

This brief investigates the fully distributed optimal control of linear multi-agent systems on generally directed topologies. Considering the existence of disturbances, a dynamical sliding-mode control protocol is designed. The optimization of energy-cost performance is achieved by solving a topology-free algebraic Riccati equation. The presented control protocol is independent with the global information of topologies, and each agent can manage its protocol in a fully distributed way. A numerical example is finally reported to show the efficiency of presented protocol.

A modified discrete-time algebraic Riccati equation (MARE) is a discrete-time algebraic Riccati equation (DARE) for which the quadratic term is weighted by a modifying parameter $\alpha $ . The MARE is known to arise for example when conducting estimation or stabilization of single-input single-output (SISO) systems subject to packet losses in networked control systems (NCSs). In the present paper we characterize the solution to the MARE in closed form that, to the best of the author’s knowledge, is a completely novel result. We then verify the already known critical value of the modifying parameter $\alpha _{c}$ for which the MARE is solvable and propose closed-form expressions for the optimal state feedback gain matrix. We finally present examples to illustrate the obtained contributions.

Cooperation of multiple connected vehicles has the potential to benefit the road traffic greatly. In this paper, we consider analysis and synthesis problems of the cooperative control of a platoon of heterogeneous connected vehicles with directed acyclic interactions (characterized by directed acyclic graphs). In contrast to previous works that view heterogeneity as a type of uncertainty, this paper directly takes heterogeneity into account in the problem formulation, allowing us to develop a deeper understanding of the influence of heterogeneity on the collective behavior of a platoon of connected vehicles. Our major strategies include an application of the celebrated internal model principle and an exploitation of lower-triangular structures for platoons with directed acyclic interactions. The major findings include: 1) we explicitly highlight the tracking ability of heterogeneous platoons, showing that the followers can only track the leader's spacing and velocity; 2) we analytically derive a stability region of feedback gains for platoons with directed acyclic interactions; 3) and consequently we propose a synthesis method based on the solution to an algebraic Riccati equation that shares the dimension of single vehicle dynamics. Numerical experiments are carried out to validate the effectiveness of our results., 12 pages, 8 figures. To appear at IEEE ITSM