GA-based decoupled adaptive FSMC for nonlinear systems by a singular perturbation scheme

Generally, the difficulty with multivariable system control is how to overcome the coupling effects for each degree of freedom. The computational burden and dynamic uncertainty of multivariable systems makes the model-based decoupling approach hard to implement in a real-time control system. In this study, an intelligent adaptive controller is proposed to handle these behaviors. The structure of these model-free new controllers is based on fuzzy systems for which the initial parameter vector values are found based on the genetic algorithm. One modified adaptive law is derived based on Lyapunov stability theory to control the system for tracking a user-defined reference model. The requirement of the Kalman-Yacubovich lemma is fulfilled. In addition, a non-square multivariable system can be decoupled into several isolated reduced-order square multivariable subsystems by using the singular perturbation scheme for different time-scale stability analysis. The adjustable parameters for the intelligent system can be initialized using a genetic algorithm. Novel online parameter tuning algorithms are developed based on the Lyapunov stability theory. A boundary-layer function is introduced into these updating laws to cover parameter and modeling errors and to guarantee that the state errors converge into a specified error bound. Finally, a numerical simulation is carried out to demonstrate the control methodology that can rapidly and efficiently control nonlinear multivariable systems.