Adaptive fuzzy control for a class of unknown nonlinear dynamical systems

In this study, we investigate an adaptive fuzzy controller design for a class of nonlinear multi-input multi-output (MIMO) systems in interconnected form. The systems considered comprise n   subsystems and an unknown interconnection term is included in every equation for each subsystem. The interconnection term is a function of all the states from the first to the (n−1)(n−1)th subsystems. Moreover, the effects of dead-zone models are considered in each subsystem of the systems. These properties of the systems cause the difficulties and add further complexity to the design. In order to overcome these difficulties, we use the following methods: (1) the fuzzy logic systems are employed to approximate the appropriate unknown functions of the systems, (2) a novel backstepping design procedure is constructively designed, and (3) compensative adaptation laws are provided to compensate for the effects of the dead-zone inputs. We show that all the signals in the closed-loop system are bounded and that the outputs converge to a compact set by using the Lyapunov analysis theorem. Simulated examples are presented that validate the effectiveness of the approach.