Liquid-Updating Impulsive Adaptive Dynamic Programming for Continuous Nonlinear Systems

This article focuses on designing the optimal impulsive controller (IMC) of continuous-time nonlinear systems. A general-event-based dynamics (GED) is constructed to describe the state transition characteristics across the impulsive actions for the continuous-time nonlinear systems. Then, based on the GED, a new IMC design scheme and an impulsive adaptive dynamic programming (IADP) algorithm are developed, which possess strong generality and feasibility. Next, by introducing a novel policy-improving mechanism the liquid-updating IADP (LIADP) algorithm is established, which is more flexible to fit into the memory-limited computing devices, thus improving the flexibility and realization efficiency of the ADP-based approaches. The developed methods are proved to converge to the optimal impulsive performance index function and obtain the optimal impulsive controllers for the continuous-time nonlinear systems. Finally, a numerical study is provided to verify the effectiveness of the present IADP and LIADP algorithms.