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This paper considers the incentive feedback Stackelberg game with multi‐hierarchy players under a H∞$H_\infty$ constraint, with the proposed solution involving nested hierarchies A and B. In hierarchy A, P0 represents the leader (the leader's control input corresponding to i‐th follower, i=1,2,...,n$i=1,2,\ldots ,n$), and P1,...,Pn$P_1,\ldots ,P_n$ are the followers, with non‐cooperative followers induced to virtually cooperate in achieving team‐optimal solution and the Nash equilibrium. In hierarchy B, the external disturbance represents the follower, and hierarchy A represents the leader. The main contributions of this work are three‐fold. First, an incentive Stackelberg strategy set under the H∞$H_\infty$ constraint through observation information is obtained for the first time. Second, a novel iterative algorithm to solve the coupled backward and forward Riccati equations is introduced and thus obtaining an explicit expression of a team‐optimal feedback Stackelberg strategy set with an H∞$H_\infty$ constraint. Finally, the necessary and sufficient conditions for the existence and uniqueness of the hierarchical game's optimal solutions using the Lyapunov equation and the induction algorithm are presented. [ABSTRACT FROM AUTHOR]

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 the authors' knowledge, the present paper is the first to establish the necessary and sufficient solvability condition for this kind of optimal control problem with input delay, and to derive the analytical form of 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, it is strictly proven that the system is stabilizable if and only if the algebraic Riccati equation has a unique positive definite solution. [ABSTRACT FROM AUTHOR]

In this study, the authors are concerned with the long‐standing mixed H2/H∞ problem for discrete linear systems. The main contribution is to derive the standard solution of the mixed H2/H∞ problem by a regular Riccati equation. Firstly, in H∞‐optimisation procedure, the optimal strategy (u,w) is explicitly given where the H∞‐norm is maximised by w and H2‐norm is minimised by u at the same time. It is noted that there exists an arbitrary item in the optimal strategy for the positive semi‐definite weighting matrices. Secondly, the H2‐optimisation problem is explicitly solved with respect to the arbitrary item. Finally, the standard solution of the mixed H2/H∞ problem is explicitly given in terms of regular Riccati equations by combining the optimal strategy (u,w) in H∞ optimisation procedure and the optimal solution of H2 optimisation procedure. Examples are presented to show the effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]

In this study, a sampled‐data networked control system over a multipath routing‐enabled network is investigated, where each delivered signal in a path suffers a random delay. For such a system, the mean square stabilisation problem is considered under the joint design of the event‐driven strategy on the actuator side and the control policy on the decision‐maker side. The contributions of this study are twofold. First, by pre‐defining an application time as an event‐triggering parameter, the sampled‐data system is transformed into a stochastic form with input delay and packet dropout. When the probability distribution F(⋅) of random delay is known a priori, the close form of packet dropout rate is proposed and a set of necessary and sufficient stabilisation conditions are developed simultaneously. When F(⋅) is unknown, the reduced system is an uncertain dynamic system. Utilising matrix polynomials, a verifiable criterion is derived for stabilising the uncertain system, which is also necessary and sufficient. Second, for the scalar system, the close form of allowable sampling period bound is developed in terms of F(⋅) and system parameters. [ABSTRACT FROM AUTHOR]

This study mainly concerns the linear quadratic optimal control and stabilisation problems for large‐scale systems with constraint, the constraint is imposed on the weighted control and state, which arises from coordination problem for multi‐agent systems. The main contributions of this study are: first, the optimal controller is developed via using the maximum principle and decoupling the forward and backward difference equations (FBDEs); secondly, by defining the Lyapunov function with the optimal cost function, the necessary and sufficient stabilisation conditions for the large‐scale systems are derived. The main techniques adopted in this study are the maximum principle and the solution to the FBDEs. It is noted that the optimal control strategy involves the centralised information of the weighted state average, but this can be easily accessed for the large‐scale‐system network. [ABSTRACT FROM AUTHOR]

In this study, the authors derive a new type of maximum principle for both stochastic evolution and parabolic type stochastic partial differential systems. The systems only require the Hamiltonian functional to be concave in the state variable rather than in both state and control variables. They also show a connection between these two types of systems. Finally, examples are given to illustrate the authors' theoretical results. [ABSTRACT FROM AUTHOR]

This study is concerned with the mixed H2/H∞ control problem under an open‐loop information pattern with input delay. Compared with the delay‐free case, one of the main difficulties is the non‐causality caused by the time delay in the control input. The mixed H2/H∞ control problem is reformulated as a leader–follower game and the Stackelberg strategy based on the maximum principle is introduced to deal with this. By introducing two co‐states to capture the future information and one new state to capture the past effects, the problem can be addressed. The controllers are designed by solving the symmetric and decoupled Riccati equations. Necessary and sufficient conditions that guarantee the existence and uniqueness of the solution are proposed in this study. [ABSTRACT FROM AUTHOR]

This study presents a study on delay‐dependent algebraic Riccati equations (DAREs) derived from linear quadratic optimisation and stabilisation problems of networked control systems (NCSs) that endure both transmission delay and packet dropout. By applying the operator spectrum theory, two sets of fundamental results are obtained for such DARE: first, it is shown that the stabilising solution to a DARE, if it exists, is unique and coincides with a maximal solution. Moreover, under the assumption of detectability or observability, it is shown that the unique stabilising solution exists if and only if the associated NCS is stabilisable. Second, an iterative algorithm for computing the stabilising solution is proposed. The proof of convergence of the algorithm is presented. To confirm the validity of our theoretic results, two illustrative examples are included in this study. One of the example is motivated by a pursuit–evasion problem. [ABSTRACT FROM AUTHOR]

This study investigates robust consensus problem for multi‐agent systems (MASs) with both system and communication noises. The agent state is estimated based on the noisy measurement information by applying Kalman‐filtering theory, and then the estimated state is sent to the neighbour agents through a noisy communication environment. A consensus protocol is proposed based on the relative estimated state, under which the consensus error of the MASs can be characterised precisely via the unique solution of a Lyapunov equation. In addition, the consensusability via dynamic output feedback control of the MASs without noises is studied. Finally, simulation examples are given to show the correctness of the proposed results. [ABSTRACT FROM AUTHOR]

A globally optimal real‐time distributed fusion algorithm is discussed for multi‐channel observation systems. The performance of the fusion is equal to that of centralised Kalman filtering. Different from the existing one based on information filters, the algorithm uses the projection theorem in Hilbert space according to First‐Come‐First‐Serve principle. Local estimates are instantly fused with arrival of local information at fusion centre. Meantime, a real‐time strategy is presented to balance the performance and the speed of fusion. Therefore the algorithm is flexible and has the practical benefits. [ABSTRACT FROM AUTHOR]