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Zbl 1214.93104
Wang, Zidong; Lam, James; Ma, Lifeng; Bo, Yuming; Guo, Zhi
Variance-constrained dissipative observer-based control for a class of nonlinear stochastic systems with degraded measurements. (English)
[J] J. Math. Anal. Appl. 377, No. 2, 645-658 (2011). ISSN 0022-247X

Summary: This paper is concerned with the variance-constrained dissipative control problem for a class of stochastic nonlinear systems with multiple degraded measurements, where the degraded probability for each sensor is governed by an individual random variable satisfying a certain probabilistic distribution over a given interval. The purpose of the problem is to design an observer-based controller such that, for all possible degraded measurements, the closed-loop system is exponentially mean-square stable and strictly dissipative, while the individual steady-state variance is not more than the pre-specified upper bound constraints. A general framework is established so that the required exponential mean-square stability, dissipativity as well as the variance constraints can be easily enforced. A sufficient condition is given for the solvability of the addressed multiobjective control problem, and the desired observer and controller gains are characterized in terms of the solution to a convex optimization problem that can be easily solved by using the semi-definite programming method. Finally, a numerical example is presented to show the effectiveness and applicability of the proposed algorithm.

MSC 2000:: *93E03 General theory of stochastic systems
93B35 Sensitivity (robustness) of control systems
93C10 Nonlinear control systems
90C22 Semidefinite programming

Keywords: nonlinear systems; stochastic systems; dissipative control; variance-constrained control; degraded measurements

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Zentralblatt MATH Berlin [Germany]