Robust adaptive control of nonlinearly parameterized systems with unmodeled dynamics

Abstract

Many physical systems such as biochemical processes and machines with friction are of nonlinearly parameterized systems with uncertainties. How to control such systems effectively is one of the most challenging problems. This paper presents a robust adaptive controller for a significant class of nonlinearly parameterized systems. The controller can be used in cases where there exist parameter and nonlinear uncertainties, unmodeled dynamics and unknown bounded disturbances. The design of the controller is based on the control Lyapunov function method. A dynamic signal is introduced and adaptive nonlinear damping terms are used to restrain the effects of unmodeled dynamics, nonlinear uncertainties and unknown bounded disturbances. The backstepping procedure is employed to overcome the complexity in the design. With the proposed method, the estimation of the unknown parameters of the system is not required and there is only one adaptive parameter no matter how high the order of the system is and how many unknown parameters there are. It is proved theoretically that the proposed robust adaptive control scheme guarantees the stability of nonlinearly parameterized system. Furthermore, all the states approach the equilibrium in arbitrary precision by choosing some design constants appropriately. Simulation results illustrate the effectiveness of the proposed robust adaptive controller.