Event-Triggered Adaptive Dynamic Programming Theory And Method For Nonlinear Systems

The optimal control problem is widely concerned in practice.Most of systems in the real case are nonlinear.Hence,the classical control theory is not efficient for optimal control problems.Adaptive dynamic programming(ADP),inspired by dynamic programming,reinforcement learning,and neural network,provides a new way to solve optimal control problems for nonlinear systems.In this paper,combining adaptive dynamic programming(ADP)method and event-triggered scheme,the event-triggered adaptive dynamic programming(ETADP)method is developed.The main contributions of this paper can be briefly listed as follows.(1)A novel event-triggered heuristic dynamic programming algorithm is developed to solve the optimal control problems for nonlinear systems with unknown dynamics.The triggering condition group is developed,and the stability of the system is proven.The algorithm needs less assumption.(2)With the different event-triggered controllers,two ETADP algorithms are developed to solve optimal tracking control problems for nonlinear discrete-time systems.Two triggering condition groups are designed,and it is proved that the system can track the desired trajectory accurately.(3)A multiple ETADP algorithm is developed for multi-controller nonzero-sum games.Triggering condition groups are designed for each controller,which can stabilize the system and guarantee the triggering independence of controllers.(4)A multiple ETADP algorithm is developed for zero-sum games.The event of each controller is designed corresponding to the other controller.The multiple event-triggered scheme can stabilize the systems and guarantee the triggering independence of controllers.The structure of developed algorithms is the actor-critic structure,which is implemented by neural networks.The critic network is applied to approximate the value function,the action network is applied to approximate the control policy,and the model network is applied to approximate systems with unknown dynamics.Besides,the stability of the system is proved.Simulations are presented to show the effectiveness of developed algorithms.According to the research,ETADP method has been proven to have an outstanding ability of self-learning.And it needs less sampled data,less space of computation and memory,and less cost of communication.Hence,the ETADP method can provide a theoretical basis for solving optimal control problems in practice.