Direct and Indirect Adaptive Fuzzy Control for a Class of MIMO Nonlinear Systems

摘要

In this chapter, stable direct and indirect adaptive fuzzy controllers for a class of MIMO nonlinear systems with uncertain model dynamics are presented. In the direct scheme, fuzzy systems are used to construct adaptively an unknown ideal controller and their adjustable parameters are updated by using the gradient descent method in order to minimize the error between the unknown controller and the fuzzy controller. In the indirect scheme, the controller design is based on the approximation of the system's unknown nonlinearities by using fuzzy systems. The free parameters of the used fuzzy systems in this case are updated using a gradient descent algorithm that is designed to minimize the identification error between the unknown nonlinearities and their adaptive fuzzy approximations. Both approaches do not require the knowledge of the mathematical model of the plant, guarantee the uniform boundedness of all the signals in the closed-loop system, and ensure the convergence of the tracking errors to a neighbourhood of the origin. Simulation results for direct adaptive control scheme performed on a two-link robot manipulator illustrate the method. Future works will focus on extension of the approach to more general MIMO nonlinear systems and its improvement by introducing a state observer to provide an estimate of the state vector.