Finite-Time Boundedness of Markov Jump System with Piecewise-Constant Transition Probabilities via Dynamic Output Feedback Control

This paper first investigates the problem of finite-time boundedness of Markovian jump system with piecewise-constant transition probabilities via dynamic output feedback control, which leads to both stochastic jumps and deterministic switches. Based on stochastic Lyapunov functional, the concept of finite-time boundedness, average dwell time, and the coupling relationship among time delays, several sufficient conditions are established for finite-time boundedness and H∞ filtering finite-time boundedness. The system trajectory stays within a prescribed bound. Finally, an example is given to illustrate the efficiency of the proposed method

A review on analysis and synthesis of nonlinear stochastic systems with randomly occurring incomplete information

Copyright q 2012 Hongli Dong et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.In the context of systems and control, incomplete information refers to a dynamical system in which knowledge about the system states is limited due to the difficulties in modeling complexity in a quantitative way. The well-known types of incomplete information include parameter uncertainties and norm-bounded nonlinearities. Recently, in response to the development of network technologies, the phenomenon of randomly occurring incomplete information has become more and more prevalent. Such a phenomenon typically appears in a networked environment. Examples include, but are not limited to, randomly occurring uncertainties, randomly occurring nonlinearities, randomly occurring saturation, randomly missing measurements and randomly occurring quantization. Randomly occurring incomplete information, if not properly handled, would seriously deteriorate the performance of a control system. In this paper, we aim to survey some recent advances on the analysis and synthesis problems for nonlinear stochastic systems with randomly occurring incomplete information. The developments of the filtering, control and fault detection problems are systematically reviewed. Latest results on analysis and synthesis of nonlinear stochastic systems are discussed in great detail. In addition, various distributed filtering technologies over sensor networks are highlighted. Finally, some concluding remarks are given and some possible future research directions are pointed out. © 2012 Hongli Dong et al.This work was supported in part by the National Natural Science Foundation of China under Grants 61273156, 61134009, 61273201, 61021002, and 61004067, the Engineering and Physical Sciences Research Council (EPSRC) of the UK under Grant GR/S27658/01, the Royal Society of the UK, the National Science Foundation of the USA under Grant No. HRD-1137732, and the Alexander von Humboldt Foundation of German

Almost sure stability of discrete-time Markov Jump Linear Systems

This paper deals with transient analysis and almost sure stability for discrete-time Markov Jump Linear System (MJLS). The expectation of sojourn time and activation number of any mode, and switching number between any two modes of discrete-time MJLS are presented firstly. Then a result on transient behavior analysis of discrete-time MJLS is given. Finally a new deterministically testable condition for the exponential almost sure stability of discrete-time MJLS is proposed

On control of discrete-time state-dependent jump linear systems with probabilistic constraints: A receding horizon approach

In this article, we consider a receding horizon control of discrete-time state-dependent jump linear systems, particular kind of stochastic switching systems, subject to possibly unbounded random disturbances and probabilistic state constraints. Due to a nature of the dynamical system and the constraints, we consider a one-step receding horizon. Using inverse cumulative distribution function, we convert the probabilistic state constraints to deterministic constraints, and obtain a tractable deterministic receding horizon control problem. We consider the receding control law to have a linear state-feedback and an admissible offset term. We ensure mean square boundedness of the state variable via solving linear matrix inequalities off-line, and solve the receding horizon control problem on-line with control offset terms. We illustrate the overall approach applied on a macroeconomic system

Model Predictive Control for Continuous-Time Singular Jump Systems with Incomplete Transition Rates

This paper is concerned with model predictive control (MPC) problem for continuous-time Markov Jump Systems (MJSs) with incomplete transition rates and singular character. Sufficient conditions for the existence of a model predictive controller, which could optimize a quadratic cost function and guarantee that the system is piecewise regular, impulse-free, and mean square stable, are given in two cases at each sampling time. Since the MPC strategy is aggregated into continuous-time singular MJSs, a discretetime controller is employed to deal with a continuous-time plant and the cost function not only refers to the singularity but also considers the sampling period. Moreover, the feasibility of the MPC scheme and the mean square admissibility of the closed-loop system are deeply discussed by using the invariant ellipsoid. Finally, a numerical example is given to illustrate the main results