Nonlinear adaptive control by switching linear controllers

Abstract

We consider a global adaptive stabilization problem for feedback nonlinear systems with nonlinear parametrization. In our previous work [15], we showed that for such systems global adaptive stabilization can be achieved by switching nonlinear controllers. In this paper, we further show that global adaptive stabilization can still be achieved by switching linear controllers. From the consideration of implementation, the linear controller has obvious advantages. The design of our adaptive stabilizer takes a two-step procedure. We first design a linear stabilizer with “undetermined” gains and then design a set of switching logics to tune online the gains in a switching manner. It is shown that under our proposed control, for any initial conditions, all closed-loop states are bounded and asymptotic regulation is achieved.