An Improved Trajectory Tracking Mechanism With Adaptive Critic for Event-Based Multiplayer Zero-Sum Games

In this paper, based on the adaptive critic control method, an improved event-based trajectory tracking mechanism of continuous-time (CT) nonlinear multiplayer zero-sum games (MZSGs) is established. It is worthy of note that previous papers studying the trajectory tracking issue of nonlinear CT MZSGs only apply to the case where the reference trajectory eventually converges to zero. Consequently, this paper develops an improved mechanism to overcome this weakness. Later, an event-triggered framework is brought in to reduce the amount of computation and improve control efficiency. In this process, an innovative triggering condition is provided. At the same time, the infamous Zeno behavior is ruled out through theoretical analysis. Furthermore, the event-based near-optimal controls and event-based near-worst disturbances for tracking error dynamics are gained by building and adjusting a single critic neural network. Immediately after, by utilizing the Lyapunov method, the uniform ultimate boundedness stability of the tracking error and the weight estimation error is ensured. Lastly, an example containing two case studies is offered to validate the validity of the established mechanism. Note to Practitioners—Complex industrial processes often involve multiple control inputs and may also be affected by multiple disturbances at the same time, which can be referred to as a MZSG. Since many industrial processes can be viewed as a tracking question of nonlinear systems and the event-triggered mechanism can decrease the computational cost, the tracking problem for event-based nonlinear MZSGs is studied in this paper, which is significant for control practitioners. Moreover, the Hamilton-Jacobi-Isaacs equation is often difficult to solve when dealing with the game problem. Hence, an adaptive critic technique is presented to acquire the near-optimal controls and the near-worst disturbances, which replaces the traditional actor-critic framework and thus simplifies the theoretical analysis. Note that this paper proposes an innovative triggering condition to relax the restriction on the choice of disturbance rejection level. Compared to previous works dealing with the tracking problem of nonlinear MZSGs, the method presented in this paper makes the choice of the reference trajectory more flexible and thus enhances the applicability in general industrial processes. Finally, stability analysis and simulation results are given. Note that for different practical situations, practitioners can adjust the related parameters to achieve the tracking control of MZSGs and minimize the computational cost.