Adaptive Secure Finite-Time Optimal Control of Unknown Nonlinear Systems With State Constraints via Generalized Fuzzy Hyperbolic Models

In this article, a novel adaptive critic learning (ACL) framework is constructed for a class of nonzero-sum (NZS) differential games problem of unknown continuous-time (CT) nonlinear systems with state constraints. First, generalized fuzzy hyperbolic model (GFHM)-based identifiers are established to reconstruct the unknown system dynamics. Then, under the ACL framework, a critic network with secure finite-time experience replay turning law is developed for each player to acquire the Nash equilibrium point solution in finite time while the finite-time stability is guaranteed via Lyapunov analysis. Meanwhile, the persistence of excitation (PE) condition is no longer needed in this work, by introducing an easy-to-check rank condition. Furthermore, by incorporating the immediate cost function associated with each player and the control barrier function (CBF), the algorithm ensures that the system states evolve in a secure environment. Finally, two numerical examples are presented to demonstrate the validity of the developed scheme.