Double Iterative Algorithm Of Optimal Control For Unknown Systems Based On Wavelet Neural Networks

In many practical problems of modern engineering, the real system involvedmostly are unknown nonlinear dynamical systems, thus need the resolution of optimalcontrol of the real unknown systems. For complexity of the real systems and obstacle inpractice, the task of finding a solution to the problem of optimal control for unknownsystems have significance in both theory and application. In this paper, a research of the problem of optimal control for unknown nonlinearsystems is made. First, an iterative algorithm to solve the problem of optimal control forcomplicated systems, namely Dynamic Integrated System Optimization and ParameterEstimation (DISOPE), is introduced. After that, the 2-D character and the optimality andthe convergence of the algorithm are investigated from a new viewpoint oftwo-dimensional systems, and the inherent relations of the algorithm are revealed.Subsequently, a scheme of modeling unknown nonlinear systems is presented. In it afeedforward structure of wavelet neural networks is adopted, and with a hybrid errorperformance index, a novel on-line dynamic gradient algorithm for training neuralnetworks is put forward. As a result, the real system state and the derivative of the stateare accurately identified at the same time, thus a more accurate network model isobtained. Furthermore, by integrating the DISOPE algorithm with wavelets neuralnetwork model, a double iterative algorithm of optimal control for unknown systems isgiven with the special structure and the algorithm design; the performance of thealgorithm is also analyzed. At last, simulation results are provided to illustrate theapplicability and validity of the double iterative algorithm.