Systematic design of supervisory controllers for a class of uncertain nonlinearly parameterized systems

This paper studies the switching supervisory control problem for a class of nonlinear systems with nonlinearly parameterized uncertainties. We first consider the systems that admit a family of estimators corresponding to the possible parameter values, and assume that each estimator can be robustly stabilized by a candidate control law. With appropriately chosen monitoring signals, it is shown that the scale-free hysteresis switching mechanism is capable of selecting the estimator which “best” emulates the plant, even if the decay rates of the estimation errors are non-exponential. Then, the proposed methodology is validated by means of a subclass of nonlinear uncertain systems in the strict-feedback form, for which novel constructive designs of the estimators and the corresponding control laws are proposed to solve the supervisory control problem. An extension to the case of parameter mismatch shows that practical convergence is guaranteed by means of the same supervisory control structure and a modified design of monitoring signals. A numerical simulation example is employed to verify the effectiveness of the proposed methodology.