Indirect Adaptive Control of Unknown Nonlinear Systems with Parametric and Dynamic Uncertainties: A new Neuro-Fuzzy Method, Employing a Novel Approach of Parameter Hopping

AbstractThe indirect adaptive regulation of unknown nonlinear dynamical systems under the presence of dynamic and parameter uncertainties, is considered in this paper. The method is based on a new Neuro-Fuzzy Dynamical Systems definition named Fuzzy-Recurrent High Order Neural Network (F-RHONN), which however takes into account the fuzzy output partitions of the initial fuzzy dynamical system (FDS) operating in conjunction with appropriate HONNFs, that approximates the fuzzy rules. The proposed scheme does not require a-priori experts’ information on the number and type of input variable membership functions making it less vulnerable to initial design assumptions. Once the system is identified around an operation point, it is regulated to zero adaptively. Weight updating laws for the involved HONNFs are provided, which guarantee that under the presence of ‘small’ dynamic uncertainties both the identification error and the system states reach zero exponentially fast, while keeping all signals in the closed loop bounded. The existence of the control signal is always assured by introducing a method of parameter hopping, which is incorporated in the weight updating law. The applicability is tested on the Lorenz model, where it is shown that by following the proposed procedure one can obtain asymptotic regulation quite well in the presence of unmodeled dynamics.