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Adaptive backstepping controller design using stochastic small-gain theorem. (English) Zbl 1114.93104

Summary: A more general class of stochastic nonlinear systems with unmodeled dynamics and uncertain nonlinear functions are considered in this paper. With the concept of input-to-state practical stability (ISpS) and nonlinear small-gain theorem being extended to stochastic case, by combining stochastic small-gain theorem with backstepping design technique, an adaptive output-feedback controller is proposed. It is shown that the closed-loop system is practically stable in probability. A simulation example demonstrates the control scheme.

MSC:

93E35 Stochastic learning and adaptive control
93B52 Feedback control
93C40 Adaptive control/observation systems
93D25 Input-output approaches in control theory
93E03 Stochastic systems in control theory (general)
93C15 Control/observation systems governed by ordinary differential equations
93C10 Nonlinear systems in control theory
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