A game theory approach to mixed H2/H∞ control for a class of stochastic time-varying systems with randomly occurring nonlinearities

Copyright @ 2011 Elsevier B.V. This is the author’s version of a work that was accepted for publication in Systems and Control Letters. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published and may be accessed at the link below.This paper is concerned with the mixed H2/H∞ control problem for a class of stochastic time-varying systems with nonlinearities. The nonlinearities are described by statistical means and could cover several kinds of well-studied nonlinearities as special cases. The occurrence of the addressed nonlinearities is governed by two sequences of Bernoulli distributed white sequences with known probabilities. Such nonlinearities are named as randomly occurring nonlinearities (RONs) as they appear in a probabilistic way. The purpose of the problem under investigation is to design a controller such that the closed-loop system achieves the expected H2 performance requirements with a guaranteed H∞ disturbance attenuation level. A sufficient condition is given for the existence of the desired controller by means of solvability of certain coupled matrix equations. By resorting to the game theory approach, an algorithm is developed to obtain the controller gain at each sampling instant. A numerical example is presented to show the effectiveness and applicability of the proposed method

Variance-constrained multiobjective control and filtering for nonlinear stochastic systems: A survey

The multiobjective control and filtering problems for nonlinear stochastic systems with variance constraints are surveyed. First, the concepts of nonlinear stochastic systems are recalled along with the introduction of some recent advances. Then, the covariance control theory, which serves as a practical method for multi-objective control design as well as a foundation for linear system theory, is reviewed comprehensively. The multiple design requirements frequently applied in engineering practice for the use of evaluating system performances are introduced, including robustness, reliability, and dissipativity. Several design techniques suitable for the multi-objective variance-constrained control and filtering problems for nonlinear stochastic systems are discussed. In particular, as a special case for the multi-objective design problems, the mixed H 2 / H ∞ control and filtering problems are reviewed in great detail. Subsequently, some latest results on the variance-constrained multi-objective control and filtering problems for the nonlinear stochastic systems are summarized. Finally, conclusions are drawn, and several possible future research directions are pointed out

Estimation, filtering and fusion for networked systems with network-induced phenomena: New progress and prospects

In this paper, some recent advances on the estimation, filtering and fusion for networked systems are reviewed. Firstly, the network-induced phenomena under consideration are briefly recalled including missing/fading measurements, signal quantization, sensor saturations, communication delays, and randomly occurring incomplete information. Secondly, the developments of the estimation, filtering and fusion for networked systems from four aspects (linear networked systems, nonlinear networked systems, complex networks and sensor networks) are reviewed comprehensively. Subsequently, some recent results on the estimation, filtering and fusion for systems with the network-induced phenomena are reviewed in great detail. In particular, some latest results on the multi-objective filtering problems for time-varying nonlinear networked systems are summarized. Finally, conclusions are given and several possible research directions concerning the estimation, filtering, and fusion for networked systems are highlighted

H

This paper discusses the H- index problem for stochastic linear discrete-time systems. A necessary and sufficient condition of H- index is given for such systems in finite horizon. It is proved that when the H- index is greater than a given value, the feasibility of H- index is equivalent to the solvability of a constrained difference equation. The above result can be applied to the fault detection observer design. Finally, some examples are presented to illustrate the proposed theoretical results

Optimal and Robust Control for a Class of Nonlinear Stochastic Systems

This thesis focuses on theoretical research of optimal and robust control theory for a class of nonlinear stochastic systems. The nonlinearities that appear in the diffusion terms are of a square-root type. Under such systems the following problems are investigated: optimal stochastic control in both finite and infinite horizon; robust stabilization and robust H∞ control; H₂/H∞ control in both finite and infinite horizon; and risk-sensitive control. The importance of this work is that explicit optimal linear controls are obtained, which is a very rare case in the nonlinear system. This is regarded as an advantage because with explicit solutions, our work becomes easier to be applied into the real problems. Apart from the mathematical results obtained, we have also introduced some applications to finance