Data-driven optimal stabilization for discrete-time nonlinear systems by approximate value iteration

In this paper, we propose a data-driven optimal feedback controller design method based on approximate value iteration which is a kind of dynamic programming method. With the data set containing sufficient dynamic information of the plant, the data-driven dynamic programming operator is well defined. An approximate of the optimal cost function is obtained by successively using the data-driven dynamic programming operator on a initial function. Based on the approximate of the optimal cost function, a sub-optimal controller is designed. The data used in data-driven dynamic programming operator belongs to the data subset, whose elements make the difference of a positive-definite function to be negative-definite. Hence, the stability of the closed-loop is guaranteed. Because the controller is designed directly from data, complexity in building the model and modeling error are avoided.