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Anti-disturbance control based on disturbance observer for nonlinear systems with bounded disturbances. (English) Zbl 1395.93264
Summary: A composite anti-disturbance control problem for a class of nonlinear systems is studied in this paper. There are two types of disturbances in the systems, one is the matched disturbance with bounded variation rate, the other is the unmatched time-varying disturbances. A nonlinear disturbance observer is designed to estimate the matched disturbances, which can be presented separately from the controller design. By integrating DOBC with back-stepping method, a composite DOBC and back-stepping controller is proposed, and the disturbance estimations are introduced into the design of virtual control laws to compensate the unmatched disturbances. In addition, it is proved that all the states in the closed-loop system are uniformly ultimate bounded (UUB). Finally, a numerical example is given to demonstrate the feasibility and effectiveness of the proposed method.

##### MSC:
 93C10 Nonlinear systems in control theory 93C73 Perturbations in control/observation systems 93B07 Observability 93D05 Lyapunov and other classical stabilities (Lagrange, Poisson, $$L^p, l^p$$, etc.) in control theory 93B35 Sensitivity (robustness)
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