Event-Triggered Zero-Sum Game for Input Saturated Nonlinear Systems With State Constraints
Chunbin Qin, Mingyu Pang, Zhongwei Wang, Suyang Hou, Dehua Zhang
Abstract
In safety-critical applications, saturated nonlinear systems often face significant control challenges due to the simultaneous presence of strict state constraints, input saturation, and uncertain external disturbances. To address these challenges, this paper proposes a novel event-triggered optimal control (ETOC) method. The core of our approach lies in a unified framework that handles all three issues simultaneously. We first introduce a smooth mapping function to transform the original system with state constraints into an equivalent unconstrained system. Subsequently, the control problem is formulated as a two-player zero-sum game (ZSG), where one player is the controller designed to handle input saturation and the other is the worst-case external disturbance. This unified formulation ensures that the system strictly adheres to the state constraints. Unlike traditional methods that typically require formulating and solving complex modified event-triggered Hamilton-Jacobi-Bellman (HJB) equations incorporating triggering errors, our approach approximates the optimal policy for the transformed system and implements it via an event-triggered mechanism. By utilizing a single-critic neural network (NN) and incorporating an experience replay mechanism, the algorithm’s learning stability is enhanced, and the restrictive persistence of excitation (PE) condition is relaxed. Theoretical analysis and simulations confirm that our ETOC strategy guarantees optimal performance, strict adherence to state constraints, and a significant reduction in communication burden, showcasing its efficiency and practicality.