Dynamic Event-Driven ADP for N-Player Nonzero-Sum Games of Constrained Nonlinear Systems

Abstract

In this paper, the dynamic event-driven optimal control problem is investigated for a class of continuous-time nonlinear systems subject to asymmetric input constraints in the framework of nonzero-sum (NZS) games. Initially, by constructing a modified value function, the respective asymmetric input constraint requirements of the controllers involved in the NZS games are successfully satisfied. Then, based on the Bellman’s optimality principle, the N-coupled Hamilton-Jacobi equations are derived for the N-player NZS games. After that, the adaptive dynamic programming (ADP) method is employed to seek for the optimal control policies, in which the simpler single critic neural network structure, instead of the dual network structure of actor-critic in the typical ADP algorithm, is applied. Furthermore, an improved critic network weight updating law is proposed to ensure the stability of the closed-loop system without a hard-to-find initial admissible control scheme. In addition, in order to reduce the update frequency of the controllers to a greater extent, a dynamic event-driven mechanism with adjustable threshold is developed. Finally, a simulation example is given to demonstrate the validity of the developed event-driven control scheme. Note to Practitioners—This paper aims to address the NZS games problem for a category of multi-player continuous-time nonlinear systems featuring multiple input constraints. The applicability of this approach can be widely extended to practical domains, including control applications for reconfigurable robot systems, networked communication systems, etc. The majority of researches on multi-player NZS games problem are focused on the impact of symmetric input constraints. Especially under the premise of ensuring controller optimality, the challenge lies in how to ensure effective control functionality while subjecting the controller to asymmetric constraints. Furthermore, the existing ADP algorithms often depend on an initial admissible control, significantly elevating the implementation difficulty of control solutions in practical applications. To address these challenges, an improved ADP algorithm is developed for input-constrained nonlinear systems within a NZS game framework. This method not only guarantees that the optimal controllers under asymmetric constraints can stabilize all signals, but also avoids the search for challenging-to-find initial admissible controls, thus streamlining the control implementation process.