Data-Driven Nonlinear Near-Optimal Regulation Based on Multi-Dimensional Taylor Network Dynamic Programming

Using the data-driven control formulation, an iterative dynamic programming approach which is based on a multi-dimensional Taylor network is established to design the near optimal regulation of discrete-time nonlinear systems. For discrete-time general nonlinear systems, the iterative adaptive dynamic programming algorithm is developed and proved to guarantee the property of convergence and optimality. Three networks are constructed, namely, the identification network, critic network and action network. Moreover, a globalized dual heuristic programming technique with detailed implementation is developed. The cost function and its derivative can be approximated by this novel architecture. Besides, without the consideration of the system dynamics, this technique can learn the near-optimal control law simultaneously and adaptively. In addition, this technique greatly improves the existing results of the iterative adaptive dynamic programming algorithm in terms of reducing the requirement of the control matrix. Furthermore, because of the approach that is based on the multi-dimensional Taylor network, the amount of calculation needed is also greatly reduced. The simulation experiment is described to illustrate the effectiveness of the data-driven optimal regulation method proposed in this paper.