Tracking Control of High-Order Nonlinear Systems With Unknown Control Gains and Its Application: An Adaptive Fuzzy Control Method

In this work, an adaptive fuzzy tracking control law is designed to control a type of high-order nonlinear systems, in which each subsystem has unknown control gain and high-order power. During the control design process, fuzzy logic systems are employed to approximate the unknown nonlinear dynamics and the Nussbaum function method is introduced to deal with unknown control gains. Relying on the idea of backstepping control technique, some adaptive control laws are proposed to estimate unknown parameters that arise during the design process, and the final adaptive fuzzy tracking control law is design in the last step. After that, the stability of the closed-loop system is established by using the Lyapunov stability theory. The key features of the designed control law are: (i) ensuring that the output of the system asymptotically tracks the given reference signal, and (ii) ensuring that all variables in the closed-loop system are semi-globally uniformly ultimately bounded. Lastly, the effectiveness of the adaptive fuzzy tracking control law designed in this work is demonstrated through simulation examples.