Search

In this paper, we study the team optimal decentralized estimation with partial history sharing information structure. There exist N$$ N $$ agents that have their own observations and share partial history observations to each other. The main contributions include two aspects: One is to give the iterative equations of the common estimation, which is the conditional expectation of state with respect to the common information for all agents and the innovation of the local information for each agent; the other is to provide the structure of the team optimal decentralized estimation, that is, the linear combination of the common estimation and the innovation of the local information. The novelty lies in that the estimation can be obtained at one time by defining an augmented state. In particular, the result is reduced to the well‐known centralized estimation when all the information is sharing for all the agents. [ABSTRACT FROM AUTHOR]

This paper considers a linear‐quadratic mean field control problem involving a major agent and N minor agents. We aim to optimize a social cost as a weighted sum of the individual costs under decentralized information. Firstly, the forward‐backward stochastic difference equations (FBSDEs) are obtained for this problem by variational analysis. Then, by decoupling the FBSDEs, we design the decentralized control laws, which are further shown to be asymptotically optimal. [ABSTRACT FROM AUTHOR]

In this paper, we are concerned with the team optimal decentralized state estimation problem where the state is transmitted to a remote agent with packet dropouts and is observed by N$$ N $$ local agents with additive noises. In particular, the information of the remote agent is available to all local agents with hierarchical relationships, which leads to an asymmetric information structure. The main contribution is to derive the analytical expressions for the team optimal decentralized state estimation. Different from the existing decentralized estimation results, the novelty of the paper is to comprehensively investigate the influence of packet dropouts and additive noises, which occur frequently in networked control systems. [ABSTRACT FROM AUTHOR]

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]

In this article, nominal‐trajectory‐based guidance approach for hypersonic reentry vehicles is considered using the Vinh's equations. The nominal trajectory is generated via pseudo‐spectral method and then tracked by receding horizon control approach. Specially, several strategies are adopted to simplify the practical application. First, we formulate the receding optimal problem discretely using the approximated discrete linear state error dynamics. Thus, the differential matrix Riccati equation is substituted by a difference matrix Riccati equation. Second, we set the terminal state weighting matrix finite which brings flexibility of adjusting the sample period and prediction horizon. Third, the time‐varying state error dynamics is approximated by time invariant system. Lastly, instead of obtaining terminal weighting matrices which satisfy a linear matrix inequality using the LMI toolbox, we set them the same constant matrix. Naturally, numerical simulation is available to verify the validity and efficiency of the proposed approach. [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 article, we are concerned with the Γ‐finite‐time stabilization (Γ‐FTS) with optimal performance for the continuous‐time system. The definition of Γ‐FTS is first proposed. The main contribution is to give the equivalent conditions for the open‐loop solvability and sufficient conditions for the closed‐loop solvability of the Γ‐FTS problem with optimal performance for the finite‐time interval. Moreover, we show that the irregular optimal control problem is solvable under the Γ‐FTS of a specific system. [ABSTRACT FROM AUTHOR]

We consider a distributed convex optimization problem in which a connected network of agents collaboratively seeks to minimize the sum of their local objective functions over a common decision variable. We propose a new distributed optimization method in the Alternating Direction Method of Multipliers (ADMM) framework, But our method combines the celebrated Belief Propagation(BP) algorithm and relaxation iteration method to achieve distributed optimization. Numerical simulation shows that our proposed algorithms have good convergence speed. We also discuss the trade‐off between the convergence rate and the required communication and computational complexities. [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 paper, we consider a distributed convex optimization problem where the objective function is an average combination of individual objective function in multi‐agent systems. We propose a novel Newton Consensus method as a distributed algorithm to address the problem. This method utilises the efficient finite‐time average consensus method as an information fusion tool to construct the exact Newtonian global gradient direction. Under suitable assumptions, this strategy can be regarded as a distributed implementation of the classical standard Newton method and eventually has a quadratic convergence rate. The numerical simulation and comparison experiment show the superiority of the algorithm in convergence speed and performance. [ABSTRACT FROM AUTHOR]

Summary: This paper studies mean‐field games for multiagent 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 ε‐Nash equilibrium. For the integrator multiagent systems, we design a set of ε‐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. [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]

Abstract: This paper studies the consensus problem for a class of general third‐order multi‐agent systems on an undirected connected network. By employing a variables transformation, the consensus control problem can be turned into a asymptotical stability problem. Then we present a necessary and sufficient condition for guaranteeing consensus by using Routh‐Hurwitz stability criterion. And this result can be applied to a special case of third‐order integrator systems. Also we will present a tolerable communication time delay for third‐order integrator systems under the assumption that multi‐agent systems can reach consensus without communication delay. [ABSTRACT FROM AUTHOR]

This paper is concerned with stabilization problem for discrete-time systems with multiple input delay. By defining a new cost function, the stabilization condition is derived based on monotonically nonincreasing of the optimal cost. It is shown that if the 2 weighting matrices in the cost function satisfy the given linear matrix inequality, receding horizon controller can stabilize the input delay systems. Moreover, the explicit stabilization controller with the new cost function is obtained by solving a finite horizon optimal control problem. A numerical example illustrates the effectiveness of the proposed method. [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 note is concerned with the linear estimation problems for discrete-time systems where the measurements are subject to random time delay and packet dropout. Different from most of previous works, the time-stamping is assumed to be unavailable in this paper. In this case, the estimation problems for such systems are very difficult because the information of the received measurements is not exactly known in most cases. To overcome the difficulty caused by the random delay and unavailability of time-stamping, a new observation is introduced by the summation of all the measurements received in the same time. Then, the random time delay measurement system is converted into a constant-delay measurement system with multiplicative noises where the noise is binary distributed random variables with known distributions. Finally, the linear optimal estimator is derived by using the transformation of auto-regressive moving average model to state-space model and the standard Kalman filtering. The convergence and stability of the filter are also analyzed. A simulation example is given to show the effectiveness of the proposed estimator. Copyright © 2016 John Wiley & Sons, Ltd. [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]

This paper studies the consensusability of a continuous-time linear time-invariant multi-agent system (MAS) with time delay in an undirected network with N nodes. We show that the MAS can achieve consensus if and only if N -- 1 time-delay subsystems associated with the eigenvalues of the Laplacian matrix of the network are simultaneously asymptotically stable. By employing a linear matrix inequality (LMI) method, we present a controller design method for a MAS to reach consensus. We also obtain a bound on the maximum time delay for consensusability for a MAS with first-order integrator dynamics by using frequency-domain analysis. [ABSTRACT FROM AUTHOR]

In this paper, the design of the distributed suboptimal controller for discrete-time multi-agent systems is considered. The distributed controllers, which only use the state information of itself and the relative states of its neighbors, are designed based on the topological structure of the system. The suboptimal feedback gain matrices of the distributed controllers are presented by using the 'averaged' optimization approach. It is showed that the distributed suboptimal controller is existent and unique. The design method of the distributed controller is obtained by the iteration procedure step by step. An example is given as an illustration of the proposed results. Copyright © 2014 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In this paper, we consider the problem of quantized quadratic performance control for a class of stochastic systems, which are subject to multiplicative noises in the measurement. A dynamic output feedback controller is designed to guarantee a given level of performance. By using the sector bound approach to characterize the quantization error, the existence of a solution for the quantized quadratic performance control problem is found by solving the so-called guaranteed cost control problem of the associated system with a sector bounded uncertainty. We show that the latter problem can be solved using LMIs. Copyright © 2014 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper studies the optimal distributed control design problem for both continuous-time and discrete-time systems. We consider an identical decoupled dynamical system and a coupled performance index which is described through the Laplacian matrix. It is showed that the optimal feedback gain matrix corresponds to a complete undirected graph for the Laplacian matrix in the cost function. We aim to get the distributed controllers that only use the information of its state and the states of its neighbors. The existence conditions of the optimal distributed control for special cost function are given and the asymptotic stability of the system is discussed. Examples are given to show the efficiency of the proposed results. [ABSTRACT FROM AUTHOR]

SUMMARY This paper studies an optimal state estimation (Kalman filtering) problem under the assumption that output measurements are subject to random time delays caused by network transmissions without time stamping. We first propose a random time delay model which mimics many practical digital network systems. We then study the so-called unbiased, uniformly bounded linear state estimators and show that the estimator structure is given based on the average of all received measurements at each time for different maximum time delays. The estimator gains can be derived by solving a set of recursive discrete-time Riccati equations. The estimator is guaranteed to be optimal in the sense that it is unbiased with uniformly bounded estimation error covariance. A simulation example shows the effectiveness of the proposed algorithm. Copyright © 2013 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

SUMMARY This paper studies the containment control problem for multi-agent systems consisting of multiple leaders and followers connected as a network. The objective is to design control protocols so that the leaders will converge to a certain desired formation while the followers converge to the convex hull of the leaders. A novel protocol is proposed by exploiting the control input information of neighbors. Both continuous-time and discrete-time systems are considered. For continuous-time systems, it is proved that the protocol is robust to any constant delays of the neighbors' control inputs. For discrete-time systems, a sufficient condition on the feedback gain for the containment control is given in terms of the time delay and graph information. Some numerical examples are given to demonstrate the results. Copyright © 2013 John Wiley & Sons, Ltd. [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]

SUMMARY A kind of real-time Kalman filtering problem is discussed for systems with distributed multichannel measurements. Recursive filters are presented for two cases with correlated and uncorrelated measurement noises. An optimal algorithm is constructed using projection theory in Hilbert space according to a first-come-first-served scheme. An update is generated whenever a new measurement arrives at a central unit. Therefore, the algorithm has the practical advantages of flexibility and the easiness for real-time implementation. Copyright © 2012 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

SUMMARY This paper considers the problem of quadratic mean-square stabilization of a class of stochastic linear systems using quantized state feedback. Different from the previous works where the system is restricted to be deterministic, we focus on stochastic systems with multiplicative noises in both the system matrix and the control input. A static quantizer is used in the feedback channel. It is shown that the coarsest quantization density that permits stabilization of a stochastic system with multiplicative noises in the sense of quadratic mean-square stability is achieved with the use of a logarithmic quantizer, and the coarsest quantization density is determined by an algebraic Riccati equation, which is also the solution to a special stochastic linear control problem. Our work is then extended to exponential quadratic mean-square stabilization of the same class of stochastic systems. Copyright © 2011 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

SUMMARY This paper is concerned with the linear minimum mean square error estimation for Itô-type differential equation systems with random delays, where the delay process is modeled as a finite-state Markov chain. By first introducing a set of equivalent delay-free observations and then defining two reorganized Markov chains, the estimation problem of random delayed systems is reduced to the one of delay-free Markov jump linear systems. The estimator is derived by using the innovation analysis method based on the Itô differential formula. And the analytical solution to this estimator is given in terms of two Riccati differential equations that are of finite dimensions. Conditions for existence, uniqueness, and stability of the steady-state optimal estimator are studied for time-invariant cases. In this case, the obtained estimator is very easy to implement, and all calculation can be performed off line, leading to a linear time-invariant estimator. Copyright © 2011 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]