Robust Adaptive Control Of Nonlinear Systems With Unmodeled Dynamics Represented By Input-Output Models

We know that almost practical systems are nonlinear. It is difficult to develop accurate models for systems. On the other hand, we often simplify the model, or choose the lower-order model. But it may bring some uncertainty to the system. Many papers neglect the unmodeled dynamics, and design the robust adaptive control under the ideal circumstances. But the performance is not satisfied. With the development of modern control theory and increasing requirements on industry controls, it is very important to consider uncertainty of the system. Since the unmodeled dynamics are complicated, it brings a lot of difficulties in the development of the controllers.This paper presents a robust adaptive control scheme for a class of important nonlinearly system represented by input-output models with uncertainties. The scheme does not require the unknown parameters to satisfy the linear dependence condition and parameter estimation is not needed. With the proposed control scheme, all the variables in the closed-loop system are bounded in the presence of unmodeled dynamics and bounded disturbance.Using the Lyapunov function method, adaptive nonlinear damping terms are presented to counteract the effects of the uncertainties , andchanging supply function is used to restrain the effect of the unmodeled dynamics without using a additional dynamical signal. It is also shown that the proposed robust adaptive control scheme guarantees the stability of the nonlinear system. Furthermore, the mean-square tracking error can be made arbitrarily small by choosing some design parameters appropriately. Simulation results show the controllers presented in this paper guarantee the system to be globally stable and have stronger robustness.