Event‐Triggered Approximate Optimal Control of Affine Nonlinear Systems Under Full‐State and Input Constraints

ABSTRACT This paper proposes a novel control scheme based on adaptive dynamic programming (ADP) to address the approximate optimal control problem of asymmetric full‐state and input constraints in general affine nonlinear systems. First, by introducing an asymmetric barrier penalty term into the cost function and constructing a novel auxiliary value function, the proposed method overcomes the stringent reliance of traditional approaches on the strict‐feedback structure of the controlled system. Additionally, the proposed cost function addresses asymmetric input constraints and removes the strict assumption on the system control gain matrix required by existing methods. Within the ADP framework, a single critic network is employed to approximate the auxiliary value function and derive an approximate optimal control policy. The dynamic event‐triggered mechanism is realized, while corresponding adaptive laws are developed to guarantee that network weight updates occur only at triggering instants. Finally, based on the proposed candidate Lyapunov function, this paper presents a rigorous convergence analysis, showing that the system state consistently remains within the predefined asymmetric constraint set. Simulation results validate the effectiveness of the proposed method.