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Variance-constrained dissipative observer-based control for a class of nonlinear stochastic systems with degraded measurements. (English) Zbl 1214.93104
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:
 93E03 General theory of stochastic systems 93B35 Sensitivity (robustness) of control systems 93C10 Nonlinear control systems 90C22 Semidefinite programming
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