In this paper, the optimal control problem for finite-time missile-target interception systems is posed in a finite-horizon two-player zero-sum (ZS) differential game framework using a periodic event-triggered (PET) scheme. To solve the optimal control problem, a time-varying Hamilton-Jacobi-Issac (HJI) equation and a time-dependent cost function are constructed to deal with finite-horizon constraints, and an event-based periodic adaptive dynamic programming (ADP) algorithm is employed to find the Nash equilibrium solution for the designed HJI equation. Comparing with the traditional continuous event-triggered (ET) scheme, the proposed PET scheme only verifies the event-triggered conditions at periodic sampling instants, which reduces resource consumption in monitoring and excludes the Zeno behavior. A single critic neural network (CNN) is used to implement the proposed event-based optimal control algorithm, which reduces approximate errors bust also simplifies structures. Further, an additional error term is added in the designed weight updating law to such that the terminal constraint is also minimized over time. By resorting to Lyapunov function approach, some sufficient conditions are derived to achieve the uniformly ultimately bounded (UUB) of the ET closed-loop system and the estimation weight error of CNN. Finally, a missile-target interception system is introduced to illustrate the efficiency of the presented methods.
A Unified Approach to the Finite-Horizon Linear Quadratic Optimal Control Problem*
