Optimal Impulsive Control for Continuous-Time Nonlinear Systems Based on ADP

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