High Order Neuro-Fuzzy Dynamic Regulation of General Nonlinear Multi-Variable Systems

Abstract

The direct adaptive dynamic regulation of unknown nonlinear multi variable systems is investigated in this chapter in order to address the problem of controlling non-Brunovsky and non-square systems with control inputs less than the number of states. The proposed neuro-fuzzy model acts as a universal approximator. While with the careful selection of a Lyapunov-like function, the authors prove the stability of the proposed control algorithm. Weight updating laws derived from the Lyapunov analysis assure the boundedness of the closed-loop signals incorporating the well-known modified parameter hopping. In addition, the proposed algorithm shows robustness when facing modelling errors, and therefore, the state trajectories present uniform ultimate boundedness. The proposed dynamic controller proved to control those general nonlinear systems, which are difficult or even impossible to control with other algorithms. Simulation results on well-known benchmark problems demonstrate the applicability and effectiveness of the method.