Adaptive Dynamic Programming Approach on Optimal Control for Affinely Pseudo- Linearized Nonlinear System

Abstract

This paper concerns the optimal control problem of a general affinely pseudo-linearized nonlinear system and puts forward the solving scheme based on adaptive dynamic programming and neural network. In detail, a new more general affinely pseudo-linearized nonlinear system model is presented and covers more practical scenarios than existing models in engineering. In consideration of the Bellman optimal principle, the corresponding model particulars are then analyzed and its adaptive dynamic programming solving scheme is derived. That is, the modified policy iteration is used to estimate the value function and optimal control at each sampled state, and then the calculated state-control pairs and state critic values are utilized to train two neural networks (one works as state evaluator and the other works as optimal control generator, respectively). Through the above, the discrete state space is smoothed into a continuous state space, and the notorious dimensional curse problem could be addressed. Moreover, in order to improve the efficiency and precision of the network training, the samples calculating and network training processes are simultaneously carried out in this paper. In the end, a related simulation experiment is applied and the results demonstrate that the proposed method has more effectiveness and validation for the optimal control problem of the newly proposed general system model than the compared methods.