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Irregular linear quadratic control (LQ, was called Singular LQ) has been a long-standing problem since 1970s. This paper will show that an irregular LQ control (deterministic) is solvable (for arbitrary initial value) if and only if the quadratic cost functional can be rewritten as a regular one by changing the terminal cost x′(T)Hx(T) to x′(T)[H + P1(T)]x(T), while the optimal controller can achieve P1(T)x(T) = 0 at the same time. In other words, the irregular controller (if exists) needs to do two things at the same time, one thing is to minimize the cost and the other is to achieve the terminal constraint P1(T)x(T) = 0, which clarifies the essential difference of irregular LQ from the standard LQ control where the controller is to minimize the cost only. With this breakthrough, we further study the irregular LQ control for stochastic systems with multiplicative noise. A sufficient solving condition and the optimal controller is presented based on Riccati equations. [ABSTRACT FROM AUTHOR]

This paper is concerned with the linear delayed forward–backward stochastic differential equations (D-FBSDEs). The existence of time delay leads to the infinite-dimensional problem which makes the explicit solvability more challenging. The main contribution is to propose a discretisation approach which gives the explicit solution of the D-FBSDEs and consists of the following three steps: first, we transform the continuous-time D-FBSDEs into the discrete-time form with the aid of interval partition. Second, we derive the solution of the discrete-time D-FBSDEs by applying backward iterative induction. Finally the explicit solution of the continuous-time D-FBSDEs is obtained by taking the limit to the solution of discrete-time form which is also strictly proved under continuous-time framework. The proposed approach is applicable for more general FBSDEs with delay, which would provide a complete solution to the stochastic LQ control with time delay. [ABSTRACT FROM AUTHOR]

In this paper, we study the cooperative output consensus problem of discrete-time heterogeneous multi-agent systems over nonidentical channel fading networks. Different from the traditional output consensus problem, the communication channels among agents are perturbed by stochastic multiplicative noises, which can also describe the packet loss phenomenon. The perturbed channels can result in a significant challenge for consensus analysis since their effect cannot be separated linearly from the communication topology. Based on the distributed feedforward control method, a novel distributed dynamic output feedback controller is developed to ensure output synchronization for each agent in the mean-square sense. To facilitate the consensus analysis, we utilize the relationship between the graph Laplacian matrix and the incidence matrix and matrix transformation technique, and find sufficient solvability conditions relying on each agent's dynamics, the maximum eigenvalue of communication graph and the packet loss probability for the scenarios of undirected graph and directed graph, respectively. Finally, simulation results are given to verify the theoretical analysis. [ABSTRACT FROM AUTHOR]

Irregular linear quadratic control (LQ, was called Singular LQ) has been a long-standing problem since 1970s. This paper will show that an irregular LQ control (deterministic) is solvable (for arbitrary initial value) if and only if the quadratic cost functional can be rewritten as a regular one by changing the terminal cost x′(T)Hx(T) to x′(T)[H + P1(T)]x(T), while the optimal controller can achieve P1(T)x(T) = 0 at the same time. In other words, the irregular controller (if exists) needs to do two things at the same time, one thing is to minimize the cost and the other is to achieve the terminal constraint P1(T)x(T) = 0, which clarifies the essential difference of irregular LQ from the standard LQ control where the controller is to minimize the cost only. With this breakthrough, we further study the irregular LQ control for stochastic systems with multiplicative noise. A sufficient solving condition and the optimal controller is presented based on Riccati equations. [ABSTRACT FROM AUTHOR]

In this paper, we consider a class of general linear forward and , backward stochastic difference equations (FBSDEs) which are fully coupled. The necessary and sufficient conditions for the existence of a (unique) solution to FBSDEs are given in terms of a Riccati equation. Two kinds of stochastic LQ optimal control problem are then studied as applications. First, we derive the optimal solution to the classic stochastic LQ problem by applying the solution to the associated FBSDEs. Secondly, we study a new type of LQ problem governed by a forward–backward stochastic system (FBSS). By applying the maximum principle and the solution to FBSDEs, an explicit solution is given in terms of a Riccati equation. Finally, by exploring the asymptotic behavior of the Riccati equation, we derive an equivalent condition for the mean-square stabilizability of FBSS. [ABSTRACT FROM AUTHOR]

This paper is concerned with the multiplicative-noise rational expectations (MRE) problem. By resorting to a linear quadratic optimal control (LQOC) problem, the approximate solution to the MRE problem can be obtained. It is worth highlighting that this approximate solution can be highly close to the exact solution by adjusting weighted matrices in the cost function of the LQOC problem. Since the conditional expectation of the state is involved in the cost function, the LQOC problem is an optimization control with an additional measurability restriction, which is very involved. The orthogonal decomposition technique is used to deal with this measurability restriction. The solvability condition and the optimal decision are given by developing generalized Riccati-type equations. Numerical experiments are provided to illustrate the effectiveness of the achieved results. [ABSTRACT FROM AUTHOR]

This paper is concerned with a new class of mean-field games which involve a finite number of agents. Necessary and sufficient conditions are obtained for the existence of the decentralized open-loop Nash equilibrium in terms of non-standard forward–backward stochastic differential equations (FBSDEs). By solving the FBSDEs, we design a set of decentralized strategies by virtue of two differential Riccati equations. Instead of the ɛ -Nash equilibrium in classical mean-field games, the set of decentralized strategies is shown to be a Nash equilibrium. For the infinite-horizon problem, a simple condition is given for the solvability of the algebraic Riccati equation arising from consensus. Furthermore, the social optimal control problem is studied. Under a mild condition, the decentralized social optimal control and the corresponding social cost are given. [ABSTRACT FROM AUTHOR]

This paper is concerned with mean field linear quadratic social control with common noise, where the weight matrices of individual costs are indefinite We first obtain a set of forward–backward stochastic differential equations (FBSDEs) from variational analysis, and then construct a centralized feedback representation by decoupling the FBSDEs. By using solutions of two Riccati equations, we design a set of decentralized control laws, which is further shown to be asymptotically social optimal. The necessary and sufficient conditions are given for uniform stabilization of the systems by exploiting the relation between population state average and aggregate effect. An explicit expression of the optimal social cost is given in terms of two Riccati equations. Besides, the decentralized optimal solution is provided for mean field social control problem with finite agents. [ABSTRACT FROM AUTHOR]

This study deals with the problem of consensus error calculation for linear multi-agent systems (MASs) with system noises and measurement noises. It is supposed that there exist communication noises when the information exchanges among distinct agents. The agents cannot reach consensus due to the existence of the system noises. We aim to design proper distributed control protocol to calculate the consensus error for the MASs. The states of each agent and its neighbors are estimated by applying Kalman-filtering theory. The distributed control protocol is designed by employing the estimated state information. Then the consensus error is calculated via the unique solution of a Lyapunov equation. Finally, a simulation example is presented to verify the correctness of the proposed results. [ABSTRACT FROM AUTHOR]

This paper considers the recovery of sparse initial state for deterministic discrete-time linear time-invariant systems based on the compressed sensing theory. A class of deterministic linear systems with the global observation matrices satisfying the restricted isometry property (RIP) is characterized. Sufficient conditions on the measurement time instants that guarantee the global observation matrix to be a RIP matrix are obtained. With respect to the recovery of the sparse initial state of a high-dimensional linear system, it is worth mentioning that the number of measurements can be significantly decreased in terms of compressed sensing theory. [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]

Abstract: This paper considers the linear quadratic (LQ) control problem for the Itô-type stochastic system with input delays. Due to simultaneous appearances of diffusion terms (dependent on the state and the control) as well as delays in the dynamic system, the problem is very involved and remains to be solved. We not only provide the solvable condition of the problem but also the explicit expression of the causal and adapted controller for a kind of LQ problems. All of these are based on a stochastic Riccati equation. The key technique is to pursue the explicit cost value of the LQ problem by FBSDE and derive the analytical controller via the interplay between the original problem and its equivalent abstract description. [Copyright &y& Elsevier]

Abstract: This paper is concerned with optimal filter problems for networked systems with random transmission delays, while the delay process is modeled as a multi-state Markov chain. By defining a delay-free observation sequence, the optimal filter problems are transformed into ones of the Markov jumping parameter 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. Further, an optimal filter with constant-gains is developed, the existence condition for the stabilizing solutions to the filter is given, and it can be shown that the proposed Markov jump linear filter converges to the constant-gain filter under appropriate assumptions. [Copyright &y& Elsevier]

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]

Abstract: In this paper, we are concerned with the consensus of multi-agent systems with input delay. Among all standard static protocols that achieve the consensus for the multi-agent system under no input delay, we aim to find the maximum input delay such that the system remains consensusable under the same protocols. In the case of continuous-time systems, in view of the continuity of stability with respect to the time delay, the maximum delay margin for consensusability is given for scalar systems and vector systems with a single unstable open-loop pole. For scalar discrete-time systems, we show that the maximum delay margin for consensusability is strictly greater than zero if and only if the open-loop pole of the system is located in a specified interval. [Copyright &y& Elsevier]

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]

In this paper, we are concerned with the stabilization problem of the game-based control system. In particular, two players are involved in the system where one is to minimize the related cost function and the other is to stabilize the system. Different from the previous works, the new contribution is to derive the necessary and sufficient condition for the stabilization of the game-based control system by applying Stackelberg game method. The key technique is to explicitly solve the forward and backward difference equations (FBDEs) from the Stackelberg game and give the optimal feedback gain matrix of the leader by using the matrix maximum principle. [ABSTRACT FROM AUTHOR]

We consider scheduling two Gauss–Markov systems. Two sensors, each measuring the state of one of the two systems, compute and report their local state estimates to a central remote estimator, respectively. Due to the bandwidth constraint, at each time, only one of the sensors is allowed to communicate its estimate with the remote estimator. Upon receiving the data from the sensors, the remote estimator computes the minimum mean squared error estimate of each system's state. We provide an explicit construction of an optimal schedule, which is periodic (hence allows simple and efficient practical implementation) and minimizes the sum of the average estimation error covariance of each system. [ABSTRACT FROM PUBLISHER]

Abstract: This paper is concerned with the linear estimation problems for discrete-time systems with random delayed observations. When the random delay is known online, i.e., time-stamped, the random delayed system is reconstructed as an equivalent delay-free one by using measurement reorganization technique, and then an optimal linear filter is presented based on the Kalman filtering technique. However, the optimal filter is time-varying, stochastic, and does not converge to a steady state in general. Then an alternative suboptimal filter with deterministic gains is developed under a new criteria. The estimator performance in terms of their error covariances is provided, and its mean square stability is established. Finally, a numerical example is presented to illustrate the efficiency of proposed estimators. [Copyright &y& Elsevier]

Abstract: This paper considers the stochastic LQR problem for systems with input delay and stochastic parameter uncertainties in the state and input matrices. The problem is known to be difficult due to the presence of interactions among the delayed input channels and the stochastic parameter uncertainties in the channels. The key to our approach is to convert the LQR control problem into an optimization one in a Hilbert space for an associated backward stochastic model and then obtain the optimal solution to the stochastic LQR problem 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. [Copyright &y& Elsevier]

Abstract: This paper is concerned with the dynamic Markov jump filters for discrete-time system with random delays in the observations. It is assumed that the delay process is modeled as a finite state Markov chain. To overcome the difficulty of estimation caused by the random delays, the single random delayed measurement system is firstly rewritten as the multiplicative noise constant-delay system. Then, by applying the measurement reorganization approach, the system is further transformed into the delay-free one with Markov jump parameters. Finally, the estimator is derived by using the standard Markov jump filter theories. It is interesting to show that the presented filter for the system with random jump delays can be designed by performing two sets of standard Riccati equations with the same dimension as that of the original system. A simulation example is given to illustrate the effectiveness of the proposed result. [Copyright &y& Elsevier]

Abstract: This paper studies the shunting cellular neural networks with variable coefficients and time-varying delays. By applying Dini derivative and introducing many real parameters, a series of new and useful criteria on the existence and local exponential stability for general shunting inhibitory cellular neural networks have been derived. Those results obtained in this paper extend and generalize the corresponding results existing in the previous literature. [Copyright &y& Elsevier]

Abstract: The paper is to investigate the white noise fixed-lag smoothing problem in an setting for continuous-time systems. Although white noise fixed-lag smoothing and filtering have been well studied, the white noise smoothing under index remains difficult since the latter is equivalent to a time delay problem. Actually, by introducing a Krein-space state space model, it will be shown that the white noise central smoother is an fixed-lag smoothing with delayed measurements. To overcome the time delay, the re-organized innovation analysis approach is adopted in this paper. The derived fixed-lag smoother is given in terms of two differential Riccati equations (DREs) with the same order as that of the original system. [Copyright &y& Elsevier]

This paper presents a new sufficient condition for the existence, uniqueness and global exponential stability of the equilibrium point for bidirectional associative memory (BAM) neural networks with constant delays. The results are also compared with the previous results in the literature, implying that the results obtained in this paper provide one more set of criteria for determining the global exponential stability of BAM neural networks with constant delays. [Copyright &y& Elsevier]

Abstract: In this Letter, power control problem is firstly studied at an angle of LQG measurement-feedback control problem. A stochastic uplink power control problem is considered for CDMA systems. An effective distributed algorithm is proposed based on stochastic linear quadratic optimal control theory assuming SIR measurements contain white noise. The presented scheme minimizes the sum of the power and the error of SIR. A measurement-feedback power controller is designed by constructing an optimization problem of a stochastic linear quadratic type in Krein space and solving the Kalman filter problem for the systems. [Copyright &y& Elsevier]

Abstract: In this paper, the finite horizon mixed control problem is studied for the systems governed by Itô-type nonlinear stochastic differential equations with state, control and external disturbance-dependent noise. It is shown that the mixed control under consideration is associated with the four cross-coupled Hamilton–Jacobi equations. A discrete approximation algorithm is presented for solving the coupled generalized differential Riccati equations arising from linear stochastic control. A necessary condition and a sufficient condition for the existence of the finite horizon stochastic control are derived. In particular, some previous results on deterministic and stochastic control can be viewed as corollaries of our main theorems. [Copyright &y& Elsevier]

Abstract: This paper studies the classic linear quadratic regulation (LQR) problem for both continuous-time and discrete-time systems with multiple input delays. For discrete-time systems, the LQR problem for systems with single input delay has been studied in existing literature, whereas a solution to the multiple input delay case is not known to our knowledge. For continuous-time systems with multiple input delays, the LQR problem has been tackled via an infinite dimensional system theory approach and a frequency/time domain approach. The objective of the present paper is to give an explicit solution to the LQR problem via a simple and intuitive approach. The main contributions of the paper include a fundamental result of duality between the LQR problem for systems with multiple input delays and a smoothing problem for an associated backward stochastic system. The duality allows us to obtain a solution to the LQR problem via standard projection in linear space. The LQR controller is simply constructed by the solution of one backward Riccati difference (for the discrete-time case) or differential (for the continuous-time case) equation of the same order as the plant (ignoring the delays). [Copyright &y& Elsevier]

Abstract: This Letter presents new sufficient conditions of globally exponential stability of neural networks with delays. We show that these results generalize recently published globally exponential stability results. In particular, several different globally exponential stability conditions in the literatures which were proved using different Lyapunov functionals are generalized and unified by using the same Lyapunov functional and the technique of inequality of integral. A comparison between our results and the previous results admits that our results establish a new set of stability criteria for delayed neural networks. Those conditions are less restrictive than those given in the earlier references. [Copyright &y& Elsevier]

Abstract: This paper is to study the linear minimum variance estimation for discrete-time systems with instantaneous and -time delayed measurements by using re-organized innovation analysis. A simple approach to the problem is presented in this paper. It is shown that the derived estimator involves solving different standard Kalman filtering with the same dimension as the original system. [Copyright &y& Elsevier]

Abstract: This paper is concerned with the finite horizon fixed-lag smoothing problem for discrete linear time-varying systems. The existence of an smoother is first related to certain inertia condition of an innovation matrix. The innovation matrix is traditionally computed via a Riccati difference equation (RDE) associated with the filtering of an augmented system which is computationally expensive. To avoid solving the RDE of high dimension, we introduce a re-organized innovation and apply innovation analysis and projection theory in Krein space to give a simple method of computing the innovation matrix. The smoother is computed as a projection in Krein space by performing two RDEs of the same dimension as that of the original system. [Copyright &y& Elsevier]

This paper is concerned with a polynomial approach to robust deconvolution filtering of linear discrete-time systems with random modeling uncertainties. The modeling errors appear in the coefficients of the numerators and denominators of both the input signal and system transfer function models in the form of random variables with zero means and known upper bounds of the covariances. The robust filtering problem is to find an estimator that minimizes the maximum mean square estimation error over the random parameter uncertainties and input and measurement noises. The key to our solution is to quantify the effect of the random parameter uncertainties by introducing two fictitious noises for which a simple way is given to calculate their covariances. The optimal robust estimator is then computed by solving one spectral factorization and one polynomial equation as in the standard optimal estimator design using a polynomial approach. An example of signal detection in mobile communication is given to illustrate the effectiveness of our approach. [Copyright &y& Elsevier]

This paper studies the problem of H∞ prediction for linear continuous-time systems. By developing a new method of characterizing the innovation process and applying a novel innovation analysis approach in Krein space, a necessary and sufficient condition for the existence of a finite horizon H∞ predictor is derived. The solution to the H∞ prediction is given in terms of solutions of Riccati and matrix differential equations. We further extend our study to give a necessary and sufficient condition for the H∞ filtering of linear continuous-time systems with both instantaneous and delayed measurements. [Copyright &y& Elsevier]

This paper is concerned with steady-state risk-sensitive filtering, prediction and smoothing problems for discrete-time singular systems. It is shown that a risk-sensitive estimator can be obtained by ensuring the minimum of an indefinite quadratic form to be maximum (minimum) when the risk-sensitivity parameter θ is negative (positive). An auxiliary state-space signal model and an innovation sequence in Krein space are introduced to simplify the derivation of the estimator. The estimator is calculated based on one J-spectral factorization for risk-seeking (θ<0) or one H2 spectral factorization for risk-averse (θ>0). A numerical example is given to demonstrate the applicability of the result. [Copyright &y& Elsevier]

In this paper, we derive the Stackelberg solution associated with a leader–follower rational expectations model. By solving the dynamic rational expectations optimization problem subject to forward and backward stochastic difference equations (FBSDEs), we obtain the Stackelberg strategy of the leader with an adapted open-loop information structure, in terms of the FBSDEs. Furthermore, we solve the associated FBSDEs by establishing a nonhomogeneous relationship between backward and forward stochastic processes. This leads to an explicit form of the Stackelberg strategy of the leader. [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]

This paper investigates the decentralized linear quadratic optimization and stabilization problem for Itô systems, where the system's controller has two parts: the deterministic and random parts. Unlike previous works, with positive semi-definite weighting matrices, finite-horizon optimization and infinite-horizon stabilization problems are considered. The chief challenge lies in solving the forward and backward stochastic differential equations and selecting the Lyapunov function. The relationship between the forward and backward processes is established using a modified version of the four-step scheme combined with the information pattern of the problem. The equivalent condition for the optimization problem is obtained based on the Riccati differential equation. Besides, the necessary and sufficient conditions for the stabilization problem are presented using the Lyapunov function defined by the optimal cost function. Finally, numerical examples illustrate the validity of the presented strategies. [ABSTRACT FROM AUTHOR]

Presents information on a study which deals with the optimal and self-tuning deconvolution problems for discrete-time systems. Problem formulation; Information on optimal deconvolution estimation; Conclusions.