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Robust adaptive control of a class of nonlinear first order systems. (English) Zbl 0765.93039
Summary: We propose an adaptive controller for a class of first order nonlinear systems: $$\dot x=-\theta^{*T} f(x)-b^* u$$, subject to bounded input and output disturbances. Unmodelled dynamics are also considered in the stability analysis. A dead zone in the parameters update law is used. The dead zone size does not depend neither on the disturbances upperbounds nor on the magnitude of the unmodelled dynamics. Moreover, the disturbances and parameters upperbounds are not assumed to be a priori known.

MSC:
 93C40 Adaptive control/observation systems 93B35 Sensitivity (robustness) 93C10 Nonlinear systems in control theory 93C15 Control/observation systems governed by ordinary differential equations