Event-triggered robust optimal adaptive fuzzy guidance scheme based on finite-horizon zero-sum differential games with input constraints

This paper develops an adaptive fuzzy guidance strategy using zero-sum (ZS) differential games, incorporating event-triggered mechanisms to optimize data transmission while ensuring system stability. With the proposed guidance method, the missile can successfully engage a maneuvering target despite uncertainties and input constraints within the guidance system. Firstly, the nonlinear ZS differential game system is utilized to describe the mathematical model of interception guidance. Subsequently, an optimal control strategy is developed using game theory to ensure that the missile effectively captures the maneuvering target. To reduce unnecessary data transfers in the guidance process, an event-based sampling method is introduced as part of the control strategy design. Moreover, a generalized fuzzy hyperbolic model (GFHM) is adopted to approximate both the optimal cost function and the event-based robust optimal control strategy. To ensure convergence of the weight approximation errors, weight updating laws are established in accordance with the gradient descent method, where the requirement of an admissible initial control is relaxed by incorporating an additional function. Then, the stability of the closed-loop system is analyzed using Lyapunov functions, which demonstrates that the weight approximate errors are uniformly ultimately bounded (UUB). Finally, simulations involving a missile intercepting a maneuvering object are presented to support the developed control approach.