Indirect adaptive control of multi-input-multi-output nonlinear singularly perturbed systems with model uncertainties

In this paper, two indirect adaptive control schemes for a class of multi-input-multi-output nonlinear singularly perturbed systems with partially unknown models and parameters are presented. Firstly, the original system dynamic equation is reformulated into a new form with identity control gain matrices, and a new multi-time-scale singularity-free neural network is employed to represent the new dynamic equation. Subsequently, an online identification scheme is proposed to update neural network weights where a set of auxiliary weight error vectors are used such that better convergence property can be achieved. Based on identification results, a singularity-free singular perturbation controller is developed to control the unknown nonlinear system. By using the singularity-free neural network and singular perturbation technique, the complexity in controller design for a singularly perturbed system is reduced, and the potential singularity problem is avoided. Moreover, a singularity-free dynamic surface control scheme is also proposed, and the “explosion of complexity” issue is relieved. Compared to conventional direct adaptive dynamic surface control schemes which use gradient-like updating laws and tracking errors to train the neural networks, the singularity-free dynamic surface controller is designed indirectly and the neural networks are updated using the identification errors. Therefore, better identification and control performance is achieved, and the potential singularity problem is also circumvented. The stability of the closed-loop system is rigorously proved via the Lyapunov approach, and the effectiveness of proposed identification and control schemes is demonstrated by simulations.