Robust Adaptive Control Of Nonlinearly Parameterized System With Unmodeled Dynamics

Essentially, practical systems are nonlinear and have various uncertainties. With the development of modern control theory and increasing requirements on industry controls, there have good prospects of researching on nonlinear systems with uncertainties both in theory and in applications. Robust adaptive control of nonlinearly parameterized system with uncertainties is a new subject and many specialists have dedicated themselves to this field and obtained some academic achievements recently. But few reports have considered other uncertainties than the parameter uncertainties.This paper presents a design approach to robust adaptive controllers for a class of important nonlinearly parameterized systems under consideration of the effects of system uncertainties. The approach can be used in the case where there exist parameter uncertainties, unmodeled dynamics and unknown bounded disturbances. With the proposed robust adaptive scheme, the system is globally stable and all the variables in the closed-loop system are bounded in the presence of uncertainties.Using the Lyapunov function method, a dynamic signal is used to restrain the unmodeled dynamics and adaptive nonlinear damping terms are presented to counteract the effects of the uncertainties. Utilizing backstepping procedure, generalexpression of control strategy for global state adaptive regulation is acquired. It is shown that the proposed robust adaptive control scheme guarantees the stability of the nonlinear system. Furthermore, all the states can be made arbitrarily to reach the equilibrium by choosing the design constants appropriately. Simulation results show that compared with the adaptive controllers reported in the literature, the controllers presented in this paper guarantee the system globally stable and have stronger robustness.In addition, we extend this adaptive regulation design scheme to the robust adaptive tracking problems. This paper presents a design approach to robust adaptive controllers for the nonlinearly parameterized model of optical tracking telescope. Simulation results show that compared with the adaptive controllers reported in the literature, the controllers presented in this paper can improve the control performance greatly. This Illustrates that the robust adaptive design approach of this paper can be widely used in practical nonlinear systems.