LQ-optimal Sample-data Control under Stochastic Delays: Gridding Approach for Stabilizability and Detectability

We solve a linear quadratic optimal control problem for sampled-data systems with stochastic delays. The delays are stochastically determined by the last few delays. The proposed optimal controller can be efficiently computed by iteratively solving a Riccati difference equation, provided that a discrete-time Markov jump system equivalent to the sampled-data system is stochastic stabilizable and detectable. Sufficient conditions for these notions are provided in the form of linear matrix inequalities, from which stabilizing controllers and state observers can be constructed.Comment: 28 pages, 3 figure

Filtering for networked stochastic time-delay systems with sector nonlinearity

Copyright [2009] IEEE. This material is posted here with permission of the IEEE. Such permission of the IEEE does not in any way imply IEEE endorsement of any of Brunel University's products or services. Internal or personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution must be obtained from the IEEE by writing to [email protected]. By choosing to view this document, you agree to all provisions of the copyright laws protecting it.This paper is concerned with the filtering problem for a class of discrete-time stochastic nonlinear networked control systems with network-induced incomplete measurements. The incomplete measurements include both the multiple random communication delays and random packet losses, which are modeled by a unified stochastic expression in terms of a set of indicator functions that is dependent on certain stochastic variable. The nonlinear functions are assumed to satisfy the sector nonlinearities. The purpose of the addressed filtering problem is to design a linear filter such that the filtering-error dynamics is exponentially mean-square stable. By using the linear-matrix-inequality (LMI) method and delay-dependent technique, sufficient conditions are derived which are dependent on the occurrence probability of both the random communication delays and missing measurement. The filter gain is then characterized by the solution to a set of LMIs. A simulation example is exploited to demonstrate the effectiveness of the proposed design procedures

Distributed Kalman Filters over Wireless Sensor Networks: Data Fusion, Consensus, and Time-Varying Topologies

Kalman filtering is a widely used recursive algorithm for optimal state estimation of linear stochastic dynamic systems. The recent advances of wireless sensor networks (WSNs) provide the technology to monitor and control physical processes with a high degree of temporal and spatial granularity. Several important problems concerning Kalman filtering over WSNs are addressed in this dissertation. First we study data fusion Kalman filtering for discrete-time linear time-invariant (LTI) systems over WSNs, assuming the existence of a data fusion center that receives observations from distributed sensor nodes and estimates the state of the target system in the presence of data packet drops. We focus on the single sensor node case and show that the critical data arrival rate of the Bernoulli channel can be computed by solving a simple linear matrix inequality problem. Then a more general scenario is considered where multiple sensor nodes are employed. We derive the stationary Kalman filter that minimizes the average error variance under a TCP-like protocol. The stability margin is adopted to tackle the stability issue. Second we study distributed Kalman filtering for LTI systems over WSNs, where each sensor node is required to locally estimate the state in a collaborative manner with its neighbors in the presence of data packet drops. The stationary distributed Kalman filter (DKF) that minimizes the local average error variance is derived. Building on the stationary DKF, we propose Kalman consensus filter for the consensus of different local estimates. The upper bound for the consensus coefficient is computed to ensure the mean square stability of the error dynamics. Finally we focus on time-varying topology. The solution to state consensus control for discrete-time homogeneous multi-agent systems over deterministic time-varying feedback topology is provided, generalizing the existing results. Then we study distributed state estimation over WSNs with time-varying communication topology. Under the uniform observability, each sensor node can closely track the dynamic state by using only its own observation, plus information exchanged with its neighbors, and carrying out local computation

Optimal network implementable controllers for networked systems

In this thesis, we study the problem of network implementable controllers for network distributed systems. Network distributed control problem gains importance by the increase in networked system applications in many areas which require network distributed control and estimation. By network implementable controller, we mean controller can be implemented over the given network with the predefined/given delay and sparsity constraints. We define all stabilizing controllers by re-interpreting plant and controller. We define a congruent stable plant of the original plant which is not necessarily stable, such that the controller of the congruent plant is linearly function of the original plant\u27s controller. When we put structural constraints on all stabilizing controllers of the stable congruent plant, these controllers embody controllers of the main plant. Therefore, all stabilizing controllers of the original plant are defined as all stabilizing controllers of the congruent plant with structural constraints. In the view of this problem, we obtain all stabilizing controller parametrization of the original plant wherein equality constraints are introduced on the Youla parameter. Moreover, we define a necessary and sufficient problem to attain a controller in the form of norm minimization problem benefiting formulated all stabilizing controller parametrization and provide a solution method for it. Moreover, we introduce a doubly-coprime factorization of blkdiag(I_{n_x}, K) which allows us to have a network implementable state-space realization of a structured controller, K, which inherits sparsity and delay constraints introduced by the given network in z-domain, of a network distributed system with order n_x. By network implementable state-space realization, we mean state-space realization can be expressed as a strictly causal interaction of some sub-systems over the given network. We call such structured controllers as network realizable controller, i.e. controllers whose network implementable state-space realization can be obtained. Moreover, using the formulated controller problem, we provide a network realizable controller problem by introducing sparsity and delay constraints on the Youla parameter. Introduced network realizable controller problem is in the form of norm minimization problem with structural constraints introduced on Youla parameter. Afterwards, we obtain its equivalent unconstrained network realizable controller problem which allows us to attain a solution in infinite dimensional space benefiting existing solution methods of H_2 problem. Moreover, we define a model matching problem and present an optimal network realizable controller problem. The formulated optimal network realizable controller problem is a constrained problem. To obtain an unconstrained problem formulation, we define a relaxation by a Lagrange multiplier and benefit from the vectorization method introduced in the literature. Formulated unconstrained problem allows us to obtain a solution using existing solution methods wherein solution lies in infinite dimensional space. Once the optimal network realizable controller is obtained, we obtain a network implementable state-space realization of it using the method we have introduced. Furthermore, we provide an alternative all stabilizing network realizable controller \linebreak parametrization benefiting existing Youla parametrization which requires to have an initial controller. We show that when the given initial controller is network realizable, one can parametrize all stabilizing network realizable controllers with a network realizable Youla parameter. Moreover, we introduce network realizable controllers in the form of delayed controllers for strongly connected networked plants which allow us to parametrize all stabilizing network realizable controllers with the Youla parametrization aforementioned. We derive a model matching problem and define a necessary and sufficient optimal network realizable controller problem as a function of initial network realizable controller with sparsity and delay constraints introduced on Youla parameter. Moreover, we provide its equivalent unconstrained problem benefiting vectorization method wherein a solution in infinite dimensional space can be obtained benefiting existing solution methods