This paper addresses an optimal cooperative tracking control method with disturbance rejection in the presence of no knowledge of internal dynamics for multi-nonholonomic mobile robot (NMR) systems. Unlike most existing methods, our method integrates kinematic and dynamic controllers into one using adaptive dynamic programming techniques based on the concept of differential game theory and neural networks, and is therefore entirely optimal. First, with the aim to reduce the computational complexity, the number of neural networks for each agent in the method is chosen to be less than one-third. Second, novel weight-tuning laws of the neural networks and online algorithms are proposed to approximate solutions of the Hamilton-Jacobi-Isaacs equations. By using Lyapunov theory, value functions and both cooperative control and disturbance laws are proved convergence to the approximately optimal values while the cooperative tracking errors and function approximation errors are uniformly ultimately bounded. Finally, the effectiveness of the proposed method is demonstrated by the results of the compared simulation and experiment on a multi-NMR system equipped with omnidirectional vision.
Approximate solutions of dual fuzzy polynomials by feed-back neural networks