Two Robust Adaptive Backstepping Control Problem

Two problems of robust adaptive backstepping control are studied in this paper. The main results can be listed as follows:In the first part, for a class of interconnected systems with unmodeled dynamics, the problem of reduced-order robust decentralized adaptive back-stepping control is considered in this paper. Firstly, by a series of coordinate changes, the original system is re-parameterized. Then, by introducing a reduced-order observer, an error system is obtained. Based on the system, a design scheme of reduced-order adaptive backstepping controller is given. It is proved that all the signals in the adaptive control system are globally uniformly bounded, and the regulation error converges to zero asymptotically. Due to the order deduction of the controller, the design scheme in this paper has more practical values. A simulation example further demonstrates its effectiveness.In the second part, for a class of magnetic levitation systems, under the weaker assumptions, the states of closed-loop system lying in a compact set is guaranteed by introducing a supervisory control. Then by the approximation property of RBF networks and backstepping design technique, the design of a robust adaptive controller is given, and the stability and tracking performance of adaptive control system are analyzed rigorously. Simulation result verifies the effectiveness of this method.