Data-Driven Optimal Trajectory Tracking via a Novel Self-Learning Approach

Abstract

AbstractIn this chapter, the data-based optimal tracking control approach is developed by involving the iterative dual heuristic dynamic programming (DHP) algorithm for nonlinear systems. According to the iterative DHP method, the updating formula of the costate function and the new optimal control policy for unknown nonlinear systems are provided to solve the optimal tracking control problem. Moreover, three neural networks are used to facilitate the implementation of the proposed algorithm. The unknown nonlinear system dynamics is first identified by establishing a model neural network. To improve the identification precision, biases are introduced to the model network. The model network with biases is trained by the gradient descent algorithm, where the weights and biases across all layers are updated. The uniform ultimate boundedness stability with a proper learning rate is analyzed, by using the Lyapunov approach. The effectiveness of the proposed method is demonstrated through a simulation example.KeywordsAdaptive dynamic programmingData-based optimal tracking controlLyapunov methodNeural networkUniformly ultimately bounded stabilityValue iteration