Additive-State-Decomposition-Based Adaptive Control for a Class of Nonlinear Systems with Input Uncertainties

Nonlinear systems are widely encountered in practical engineering applications, and uncertainties are commonly present within nonlinear systems. Therefore, designing adaptive controllers for nonlinear systems has significant theoretical and practical value. This paper presents a nonlinear adaptive controller design method that combines additive state decomposition with adaptive control. Specifically, using additive state decomposition twice on the nonlinear system, the original nonlinear system is broken into three simpler subsystems: a linear system with input uncertainty, a simple linear system, and a simple nonlinear system. Then, controllers are designed for each subsystem individually: a linear adaptive stabilizing controller is designed for the linear system with input uncertainty, a linear tracking controller is designed for the simple linear system, and a nonlinear stabilizing controller is designed for the simple nonlinear system. The sum of the designed three controllers can effectively control the entire nonlinear system. Moreover, the proposed method is compared with the traditional linearization-based adaptive control approach. Simulation results demonstrate that the proposed method outperforms the traditional method in handling input uncertainty.