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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 paper is concerned with linear quadratic Gaussian (LQG) control problem for discrete-time systems with both multiplicative noises and input delay. The main contributions are two-fold. First, when the state variables can be obtained exactly, the optimal LQG controller is derived which consists of the feedback form of the conditional expectation of the state and one additive deterministic term based on the coupled Riccati equations. Through the completing square approach, the optimal controller is obtained based on the complete solution to the forward and backward stochastic difference equations. Second, when the state variables are partially observed, we derive a suboptimal linear state estimate feedback controller for LQG models involving multiplicative noises and input delay. Since the separation principle does not hold and the optimal estimator cannot be obtained, the suboptimal linear state estimate feedback controller is derived by linearizing the linear optimal estimator and using the obtained results of the optimal LQG control. [ABSTRACT FROM PUBLISHER]

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 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 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]

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]

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 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]

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]

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 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 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]

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]

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.

This paper is concerned with the stabilization and optimal control of discrete-time systems with multiplicative noise and multiple input delays. First, it is shown that the systems are stabilizable if and only if some algebraic Riccati-type equations have a solution which satisfies a given condition. To the best of our knowledge, this is the first time to propose a necessary and sufficient stabilizing condition for general multiple-input delay systems with multiplicative noise. The method constructs a Lyapunov–Krasovskii function based on the optimal cost of a finite-horizon LQR problem. Next, under the assumption that the system is stabilizable, an infinite-horizon LQR problem is investigated. The optimal control and the optimal cost are given by the above algebraic Riccati-type equations. Finally, based on the above stabilizing condition, an exact delay range for the stabilization of the system is derived in a special case. [ABSTRACT FROM AUTHOR]

This paper is concerned with the problem of mixed optimal control for discrete-time systems with random coefficients where "mixed" means that there are two controllers: the deterministic controller and the random controller. Different from previous works, random coefficients and controllers with different information structures arise simultaneously in the optimal control problem, which lead to large difficulty. Using decoupling technique to solve the forward and backward stochastic difference equations, the necessary and sufficient conditions for the solvability of optimal control problem are given. An explicit expression of the optimal control strategies is derived based on a stochastic Riccati-type equation, which is new to the best of knowledge. Finally, a pension management problem is solved with the obtained theoretical results. [ABSTRACT FROM AUTHOR]

Abstract: This paper studies the distributed consensus problem for linear discrete-time multi-agent systems with delays and noises in transmission channels. Due to the presence of noises and delays, existing techniques such as the lifting technique and the stochastic Lyapunov theory are no longer applicable to the analysis of consensus. In this paper, a novel technique is introduced to overcome the difficulties induced by the delays and noises. A consensus protocol with decaying gains satisfying persistence condition is adopted. Necessary and sufficient conditions for strong consensus and mean square consensus are respectively given for non-leader–follower and leader–follower cases under a fixed topology. Under dynamically switching topologies and randomly switching topologies, sufficient conditions for strong consensus and mean square consensus are also obtained. Numerical examples are given to demonstrate the effectiveness of the proposed protocols. [Copyright &y& Elsevier]

Abstract: An indefinite linear quadratic (ILQ) optimal control problem is discussed for singular discrete-time-varying linear systems with multiple input delays. The problem is transformed to the one for standard systems by normalizability decomposition. An explicit controller is obtained by computing the gain of the smoothing estimation of dual systems. Necessary and sufficient conditions guaranteeing the existence of unique solution are given simultaneously. A numerical example illustrates the presented method. [Copyright &y& Elsevier]

Abstract: This paper is to study the discrete-time stochastic control with state and external disturbance dependent noise. A necessary and sufficient condition for the existence of control is presented, which transforms the controller design into solving four coupled matrix-valued equations. Moreover, a recursive algorithm for solving the four coupled matrix-valued equations is also given. [Copyright &y& Elsevier]

This paper is concerned with the linear quadratic regulation (LQR) problem for discrete-time systems involving input delay and colored multiplicative noise. Due to the correlation of the adjoining state, this problem will be more complicated than the case of white noise. In this paper, the necessary and sufficient condition for the solvability of optimal control problem is presented by solving the forward and backward stochastic difference equations (FBSDEs). Moreover, the optimal LQR controller is given in terms of the coupled difference equations developed in this paper. [ABSTRACT FROM AUTHOR]

This paper studies a linear-quadratic optimal control problem for discrete-time systems with multiplicative noise and random coefficients. Motivated by fiscal policy planning problems, where deterministic policies are required, this paper aims to find a deterministic optimal controller. The challenge is to seek a solution to forward and backward stochastic difference equations with structural inconsistency caused by random and deterministic terms. We derive necessary and sufficient conditions to solve this optimal control problem by employing a decoupling method. We also present an explicit expression of the optimal controller based on coupled stochastic Riccati-type difference equations. [ABSTRACT FROM AUTHOR]

This paper is concerned with the robust H2 and H∞ filtering problems for linear discrete-time systems with polytopic parameter uncertainty. We aim to derive a less-conservative design than existing linear matrix inequality (LMI) based sufficient conditions. It is shown that a more efficient evaluation of robust H2 or H∞ performance can be obtained by a matrix inequality condition which contains additional free parameters as compared to existing characterizations. When applying this new matrix inequality condition to the robust filter design, these parameters provide extra degrees of freedom in optimizing the guaranteed H2 or H∞ performance and lead to a less-conservative design. [Copyright &y& Elsevier]