Dynamic Self-Triggered Control for Nonzero-Sum Games of Unknown Nonlinear Constrained Systems via Generalized Fuzzy Hyperbolic Models

Fan Liu, Hanguang Su, Huaguang Zhang, Biao Luo, Jiawei Wang

Abstract: In this article, a novel adaptive dynamic programming algorithm is devised to handle the multiplayer nonzero-sum (NZS) games of completely unknown nonlinear systems, subject to state and input constraints under the dynamic self-triggered mechanism. Initially, in order to eliminate the demand for system dynamics, a generalized fuzzy hyperbolic model based identifier is established, which only relies on input–output data. Then, the equivalent transformation of the reconstructed system is implemented by virtue of barrier functions. With the aid of the nonquadratic utility function, the Hamilton–Jacobi equation of the NZS game is derived. After that, an adaptive critic scheme with experience replay is employed to acquire the Nash equilibrium solution. Furthermore, a novel dynamic self-triggered rule is proposed with the dead-zone operation, which not only significantly reduces source consumption but also overcomes the implementation difficulty of monitoring hardware in the event-triggered mechanism. Moreover, the stability of the system and the uniform ultimate boundedness of the critic weights are guaranteed. Ultimately, two simulation examples are given to validate the feasibility of the developed method.