Abstract
This paper develops an event-triggered optimal control method that can deal with asymmetric input constraints for nonlinear discrete-time systems. The implementation is based on an explainable global dual heuristic programming (XGDHP) technique. Different from traditional GDHP, the required derivatives of cost function in the proposed method are computed by explicit analytical calculations, which makes XGDHP more explainable. Besides, the challenge caused by the input constraints is overcome by the combination of a piece-wise utility function and a bounding layer of the actor network. Furthermore, an event-triggered mechanism is introduced to decrease the amount of computation, and the stability analysis is provided with fewer assumptions compared to most existing studies that investigate event-triggered discrete-time control using adaptive dynamic programming. Two simulation studies are carried out to demonstrate the applicability of the constructed approach. The results present that the developed event-triggered XGDHP algorithm can substantially save the computational load, while maintain comparable performance with the time-based approach.
Highlights
Optimality is one of the most significant properties of a control system
The XGDHP technique is developed based on explicit analytical computations in the critic network, and the asymmetric input constraints are addressed by modifying the output layer of the actor network
We develop an event-triggered optimal control algorithm that can deal with asymmetric input constraints for unknown nonlinear discrete-time systems
Summary
Optimality is one of the most significant properties of a control system. The optimal control problem can be solved using the Hamilton–Jacobi-Bellman (HJB) equation. There are two limitations in their proposed method: 1) when the system states go to zero, the control inputs are still non-zero values, the mean values of the constraint range; 2) when the control inputs go to zero, the cost caused by the control inputs is not zero This approach is not applicable for the stabilization problem with an origin equilibrium point, which inspires our study. In [2] an extra assumption that the state norm is bounded by the supremum of control input norm is required, whereas in [28,18] the input-tostate stability (ISS) Lyapunov function is directly assumed to exist without pointing out its specific form and additional hyperparameters are involved in [18] These limitations prevent the proposed triggering condition from wider applications.
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