A Novel Framework for Game-Based Optimal Event-Triggered Control of Multi-Input Nonlinear Systems

This paper concentrates on the game-based optimal event-triggered control problem for a class of multi-input nonlinear continuous-time systems. The main objective is to improve the system performance. Furthermore, the optimal eventtriggered conditions are derived to maximize the intersampling intervals. To simultaneously consider the optimality of control signals and event-triggered conditions, a novel two-layer game framework with redefined cost functions is developed. In the first layer, the continuous control and the threshold of the eventtriggered condition are regarded as two players of the zerosum differential game due to contrary benefits. In the second layer, event-based players game with others to reach the Nashsaddle equilibrium point in the framework of graphical game is studied. Furthermore, to tackle the issue that the analytical solution of Hamilton-Jacobian-Isaac (HJI) equation is intractable to be obtained, an adaptive dynamic programming (ADP)-based scheme using critic-only neural networks (NNs) is considered following by a zeno-free behavior proof. Finally, a simulation example is displayed to validate the theoretical results.