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This paper focuses on optimal mismatched disturbance rejection control for linear continuoustime uncontrollable systems. Different from previous studies, by introducing a new quadratic performance index to transform the mismatched disturbance rejection control into a linear quadratic tracking problem, the regulated state can track a reference trajectory and minimize the influence of disturbance. The necessary and sufficient conditions for the solvability and the disturbance rejection controller are obtained by solving a forward-backward differential equation over a finite horizon. A sufficient condition for system stability is obtained over an infinite horizon under detectable condition. This paper details our novel approach for transforming disturbance rejection into a linear quadratic tracking problem. The effectiveness of the proposed method is provided with two examples to demonstrate., Comment: arXiv admin note: substantial text overlap with arXiv:2209.07014

This paper is concerned with mismatched disturbance rejection control for the second-order discrete-time systems.Different from previous work, the controllability of the system is applied to design the disturbance compensation gain, which does not require any coordinate transformations. Via this new idea, it is shown that disturbance in the regulated output is immediately and directly compensated in the case that the disturbance is known. When the disturbance is unknown, an extra generalized extended state observer is applied to design the controller. Two examples are given to show the effectiveness of the proposed methods. Numerical simulation shows that the designed controller has excellent disturbance rejection effect when the disturbance is known. The example with respect to the permanent-magnet direct current motor illustrates that the proposed control method for unknown disturbance rejection is effective.

This paper studies optimal control and stabilization problems for continuous-time mean-field systems with input delay, which are the fundamental development of control and stabilization problems for mean-field systems. There are two main contributions: 1) To the best of our knowledge, the present paper is first to establish the necessary and sufficient solvability condition for this kind of optimal control problem with delay, and to derive an optimal controller through overcoming the obstacle that separation principle no longer holds for multiplicative-noise systems; 2) For the stabilization problem, under the assumption of exact observability, we strictly prove thatthe system is stabilizable if and only if the algebraic Riccati equation has a unique positive definite solution.

This paper is concerned with uniform stabilization and social optimality for general mean field linear quadratic control systems, where subsystems are coupled via individual dynamics and costs, and the state weight is not assumed with the definiteness condition. For the finite-horizon problem, we first obtain a set of forward-backward stochastic differential equations (FBSDEs) from variational analysis, and construct a feedback-type control by decoupling the FBSDEs. For the infinite-horizon problem, by using solutions to two Riccati equations, we design a set of decentralized control laws, which is further proved to be asymptotically social optimal. Some equivalent conditions are given for uniform stabilization of the systems in different cases, respectively. Finally, the proposed decentralized controls are compared to the asymptotic optimal strategies in previous works., Comment: arXiv admin note: substantial text overlap with arXiv:1904.07522

This paper studies uniform stabilization and social optimality for linear quadratic (LQ) mean field control problems with multiplicative noise, where agents are coupled via dynamics and individual costs. The state and control weights in cost functionals are not limited to be positive semi-definite. This leads to an indefinite LQ mean field control problem, which may still be well-posed due to deep nature of multiplicative noise. We first obtain a set of forward-backward stochastic differential equations (FBSDEs) from variational analysis, and construct a feedback control by decoupling the FBSDEs. By using solutions to two Riccati equations, we design a set of decentralized control laws, which is further shown to be asymptotically social optimal. Some equivalent conditions are given for uniform stabilization of the systems with the help of linear matrix inequalities. A numerical example is given to illustrate the effectiveness of the proposed control laws., Comment: arXiv admin note: text overlap with arXiv:1904.07522, arXiv:2009.09864

In this paper, the optimal local and remote linear quadratic (LQ) control problem is studied for a networked control system (NCS) which consists of multiple subsystems and each of which is described by a general multiplicative noise stochastic system with one local controller and one remote controller. Due to the unreliable uplink channels, the remote controller can only access unreliable state information of all subsystems, while the downlink channels from the remote controller to the local controllers are perfect. The difficulties of the LQ control problem for such a system arise from the different information structures of the local controllers and the remote controller. By developing the Pontyagin maximum principle, the necessary and sufficient solvability conditions are derived, which are based on the solution to a group of forward and backward difference equations (G-FBSDEs). Furthermore, by proposing a new method to decouple the G-FBSDEs and introducing new coupled Riccati equations (CREs), the optimal control strategies are derived where we verify that the separation principle holds for the multiplicative noise NCSs with packet dropouts. This paper can be seen as an important contribution to the optimal control problem with asymmetric information structures.

This paper studies mean field games for multi-agent systems with control-dependent multiplicative noises. For the general systems with nonuniform agents, we obtain a set of decentralized strategies by solving an auxiliary limiting optimal control problem subject to consistent mean field approximations. The set of decentralized strategies is further shown to be an $\varepsilon$-Nash equilibrium. For the integrator multiagent systems, we design a set of $\varepsilon$-Nash strategies by exploiting the convexity property of the limiting problem. It is shown that under the mild conditions all the agents achieve mean-square consensus.

This paper considers the optimal decentralized control for networked control systems (NCSs) with asymmetric partial information sharing between two controllers. In this NCSs model, the controller 2 (C2) shares its observations and part of its historical control inputs with the controller 1 (C1), whereas C2 cannot obtain the information of C1 due to network constraints. We present the optimal estimators for C1 and C2 respectively based on asymmetric observations. Since the information for C1 and C2 are asymmetric, the estimation error covariance (EEC) is coupled with the controller which means that the classical separation principle fails. By applying the Pontryagin's maximum principle, we obtain a solution to the forward and backward stochastic difference equations. Based on this solution, we derive the optimal controllers to minimize a quadratic cost function. Combining the optimal controllers with the EEC, the controller C1 is decoupled from the ECC. It should be emphasized that the control gain is dependent on the estimation gain. What's more, the estimation gain satisfies the forward Riccati equation and the control gain satisfies the backward Riccati equation which makes the problem more challenging. We propose iterative solutions to the Riccati equations and give a suboptimal solution to the optimal decentralized control problem.

The consensus control with optimal cost remains major challenging although consensus control problems have been well studied in recent years. In this paper, we study the consensus control of multi-agent system associated with a given cost function. The main contribution is to present the distributed control protocol while minimizing the given cost function with positive semi-definite weighting matrix of control. The derived controller is composed of two parts: One part is the feedback of the individual state which minimizes the cost function and the other part is the feedback of the relative states between the neighbours which guarantees the consensus. The presented results are new to the best of our knowledge., Comment: 6 pages, 2 figures

In this paper, we mainly investigate an integrated system operating under a software defined network (SDN) protocol. SDN is a new networking paradigm in which network intelligence is centrally administered and data is communicated via channels that are physically separated from those conveying user data. Under the SDN architecture, it is feasible to set up multiple flows for transmitting control signals to an actuator with high priority for each individual application. While each flow may suffer random transmission delay, we focus on the stabilization problem under the joint design of the event-driven strategy in actuator and the control policy in decision-maker. By introducing a predefined application time, the integrated system can be reformulated as the form of stochastic system with input delay and multiplicative noise. For such system, we propose a set of necessary and sufficient stabilization conditions. Specifically, for the scalar system, we derive the allowable sampling period bound that can guarantee stabilization in terms of the probability distributions of the random transmission delays. A simple example is included to show the performance of our theoretic results.

It is well known that stability is the most fundamental nature with regard to a control system, in view of this, the stabilization becomes an inevitable control problem. This article mainly discusses the optimal control and stabilization problem for discrete-time systems involving Markov jump and multiplicative noise. The state and control weighting matrices in the cost function are allowed to be indefinite. By solving the forward-backward stochastic difference equations with Markov jump (FBSDEs-MJ) derived from the maximum principle, we conclude that the necessary and sufficient conditions of the solvability of indefinite optimal control problem in finite-horizon, whose method is different from most previous works [13], etc. Furthermore, necessary and sufficient conditions that stabilize the Markov jump discrete- time systems in the mean square sense with indefinite weighting matrices in the cost are first developed under the basic assumption of exactly observable, which is different from the previous works [12], [14] where an additional assumption of stabilization of systems is made. The key points of this article can be summed up as that an analytic solution to FBSDEs- MJ which makes the optimal controller to be explicitly expressed and the method of trans- formation, i.e., the stabilization problem of indefinite case is boiled down to a definite one whose stabilization is expressed by defining Lyapunov function via the optimal cost subject to a new algebraic Riccati equation involving Markov jump (NGARE-MJ).

This paper mainly investigates an integrated control system operating under the software defined network (SDN) protocoI. SDN is a new networking paradigm in which network inteIIigence is centraIIy administered and network controI data and decisions are communicated via channeIs that are physicaIIy separated from those conveying user data. Hence, under the SDN architecture, it is relatively easy to set up multiple flows for transmitting sampled state information to a decision-maker and controI signaIs to an actuator for each individuaI appIication. WhiIe each flow may suffer random transmission deIay, the first arriving control signal is applicable if its transmission delay is within the pre-defined application time. The affiliated integrated controI system can be modeIIed as a stochastic system with transmission deIays and packet dropouts. In this paper, we focus on the stabiIization probIem of such a system and propose a set of necessary and sufficient stabiIizing conditions for it. Moreover, for the scalar case, we derive the maximum sampling period that can guarantee stabilization in terms of the probability distributions of the transmission deIays. ResuIts in this paper find appIication in controIIing autonomous vehicIes over an open access communication network for the purposes of remote site recognition or security controI, such as evader pursuit.

Different from most of the previous works, this paper provides a thorough solution to the fundamental problems of linear-quadratic (LQ) control and stabilization for discrete-time mean-field systems under basic assumptions. Firstly, the sufficient and necessary condition for the solvability of mean-field LQ control problem is firstly presented in analytic expression based on the maximum principle developed in this paper, which is compared with the results obtained in literatures where only operator type solvability conditions were given. The optimal controller is given in terms of a coupled Riccati equation which is derived from the solution to forward and backward stochastic difference equation (FBSDE). Secondly, the sufficient and necessary stabilization conditions are explored. It is shown that, under exactly observability assumption, the mean-field system is stabilizable in mean square sense if and only if a coupled algebraic Riccati equation (ARE) has a unique solution $P$ and $\bar{P}$ satisfying $P>0$ and $P+\bar{P}>0$. Furthermore, under the exactly detectability assumption, which is a weaker assumption than exactly observability, we show that the mean-field system is stabilizable in mean square sense if and only if the coupled ARE has a unique solution $P$ and $\bar{P}$ satisfying $P\geq 0$ and $P+\bar{P}\geq 0$. The key techniques adopted in this paper are the maximum principle and the solution to the FBSDE obtained in this paper. The derived results in this paper forms the basis to solve the mean-field control problem for continuous-time systems and other related problems., 20 pages, 3 figures

This paper studies a dynamic state estimation problem for power systems, which can be seen as the quasi-static systems. The state vector of each subsystem (called node) in power networks is expressed by measurements. Based on a distributed maximum a posteriori (MAP) estimation technique, a fully distributed state estimation method is presented to update the local state at each time instant. Also, the assumption of local observability of every node is no longer needed. Tests on the IEEE 118-bus system are used to show the performance of the proposed approach and compare its results with a centralized state estimation method providing the optimal state estimate for the entire power networks, a local state estimation method using the edge measurements as the local measurements to estimate its local state, and a distributed static state estimation algorithm.

This paper mainly investigates the mean square stabilization problem for discrete-time networked control systems (NCSs). It is assumed that there exists a single network-induced delay between the controller and the plant, while the control signal is sent to the plant over a lossy communication channel whose packet dropout process is modeled as an independent identically distributed (i.i.d.) Bernoulli process. First, a necessary and sufficient condition for stabilization is developed with some new derived coupled algebraic Riccati-type equations (CAREs), where the stabilizing control is designed to be a feedback of the conditional expectation of the state. Second, the maximum packet dropout rate p max is introduced as a measure of stability robustness of the NCSs against the packet dropout. By introducing a proper Lyapunov function, a existence theorem of the maximum packet dropout rate is developed.

This paper focus on the consensusability of high-order multi-agent systems (MASs) with uniform constant communication delay in an undirected network. We show that N agents achieve consensus if and only if N − 1 time-delay subsystems associated with the eigenvalues of the Laplacian matrix are simultaneously asymptotically stable. By employing a linear matrix inequality (LMI) method, we present a sufficient condition for MASs to reach consensus. Also we consider the consensus condition of first-order integrator system by using frequency domain analysis.

This paper considers the consensus for the first-order multi-agent systems with communication delay. Under the assumptions that the undirected network topology is connected and the constant communication delay is exactly detectable, agent's own historical input information is used in the protocol design. By investigating the relations among agent dynamic, network topology and communication, delay-dependent conditions are obtained. Finally, the results are illustrated by numerical simulations.

Stochastic linear-quadratic Gaussian nonzero-sum Nash games with constrained state information is proposed for joint control of power and rate in wireless networks. When each player(node) is constrained to use a linear Kalman-like state estimator to solve onepsilas optimal strategy, state estimators of two players are investigated according to information structure: the current output and a one-step delayed control input of the player. To model the loop delay in distributed wireless networks, an optimal power and rate control scheme that minimizes the energy of the difference between the actual and desired Signal-to-Interference-plus-Noise-Ratio (SNR) levels and the two playerspsila control sequence is obtained for the congestion levels and the information structure. Algorithms for computing Nash-optimal feedback gains are given. The optimal controllers of two players for the closed-loop Nash equilibrium solution are interrelated and cannot be determined separately. The fact exactly demonstrates a cooperative and influential relationship between players.

This paper investigates the linear minimum mean square error estimation for discrete-time linear systems with Markov jump delays. In order to solve the optimal estimation problem, the single Markov delayed measurement is firstly rewritten as an equivalent measurement with multiple constant delays, and then a delay-free Markov jump linear system is obtained via state augmentation. The estimator is derived on the basis of the geometric arguments in the Hilbert space, and a recursive equation of the filter is obtained by solving the Riccati equations.

This paper considers the stochastic LQR problem for systems with input delay and stochastic parameter uncertainties in the state and input matrices. The key to our approach is to covert the LQR control problem into an optimization problem in a Hilbert space for an associated backward stochastic model and give the optimal solution by exploiting the dynamic programming approach. Our solution is given in terms of two generalized Riccati difference equations (RDEs) of the same dimension as that of the plant.

This paper is concerned with the linear quadratic regulation (LQR) problem for linear continuous-time systems with distributed input delay. In this paper, we address the LQR problem by first establishing a duality between it and a smoothing problem for an associated stochastic backward system with output delay. An analytical solution to the LQR control is then derived by solving the smoothing problem and is given in terms of the solution of Riccati type partial differential equation of the same dimension as the plant (ignoring the delays). The infinite horizon LQR problem is also considered in this paper and the convergence and stability analysis of the LQR controller is provided based on infinite dimensional system theory.

The system identification problem is researched when the input and output signal are both corrupted by noise. The robust least square (RLS) method and its application to parameter estimation problem, in which the perturbations are unknown but bounded (UBB), are introduced. The method can be interpreted as Tikhonov regularization procedure, with the advantage that it provides an exact bound on the robustness of solution and a rigorous way to compute the regularization parameter. Simulation results verify that the estimation precision and the robustness anti-noise of RLS are remarkably higher than other method when the input and output signal are both corrupted by noise.

This paper is concerned with the optimal filter problems for networked systems with random transmission delays, while the delay process is modeled as a multi-state Markov chain which incorporates the data losses naturally. By defining a delay-free observation sequence, the optimal filter problems are transformed into the ones of the standard Markov jumping parameter measurement system. We first present an optimal Kalman filter, which is with time-varying, path-dependent filter gains, and the number of the paths grows exponentially in time delay. Thus an alternative optimal Markov jump linear filter is presented, in which the filter gains just depend on the present value of the Markov chain, and as a result, the obtained filter is again a Markov jump linear system. It can be shown that the proposed Markov jump linear filter converges to the constant-gain filter under appropriate assumptions.