Neural-network-based safe learning control for non-zero-sum differential games of nonlinear systems with asymmetric input constraints.

This paper primarily investigates a neural-network-based safe control scheme for solving the optimal control problem of continuous-time (CT) nonlinear systems with asymmetric input constraints under non-zero-sum (NZS) differential game scenarios. Initially, by constructing a novel non-quadratic function, the issue of asymmetric input constraints in the non-zero-sum differential game controllers is addressed. Subsequently, the safe Hamilton-Jacobi-Bellman (HJB) equation is derived from the direct integration of the control barrier function (CBF) into the traditional cost function, ensuring that the system states remain within a safe region. Then, the safe learning control scheme based on single critic neural network (NN) and adaptive dynamic programming (ADP) is proposed to approximate the optimal control strategy, differing from the dual-network update method commonly used in traditional ADP. Based on the constructed neural network weight adjustment rules, the optimal solution to the HJB equation can be derived within the safe learning control framework. Following this, Lyapunov's stability theory demonstrates that the errors in neural network weights and all signals within the closed-loop system are uniformly ultimately bounded (UUB). Finally, the effectiveness of the developed neural-network-based safe learning control method is validated through two simulation results. [ABSTRACT FROM AUTHOR]