Direct adaptive model-free control of a class of uncertain nonlinear systems using Legendre polynomials

In this paper, a simple model-free controller for a class of uncertain nonlinear systems is presented using Legendre polynomials. According to the orthogonal functions theorem, Legendre polynomials are universal approximators. From this point of view, they are similar to fuzzy systems and can be used as a controller to approximate the ideal control law. Legendre coefficients are estimated online using the adaptation rule obtained from stability analysis. In comparison with fuzzy systems and neural networks, Legendre polynomials are simpler and less computational. Moreover, there are very few tuning parameters in Legendre polynomials. The case studies are an inverted pendulum and an articulated robot manipulator. Simulation results verify the effectiveness of the proposed controller and its robustness against large uncertainties. Comparisons with model-free controller using extended state observer and adaptive fuzzy systems show the superiority of proposed controller in disturbance rejection.