Optimal Event-triggered Control of Nonlinear Systems: A Min-max Approach

This paper presents a co-optimization scheme for an event-triggered control system to simultaneously optimize both the sampling instants and the control policy. A continuous time nonlinear affine system is considered and a novel performance index is defined to regulate the system states with minimum energy and optimal feedback frequency. To achieve this, a min-max optimization problem is formulated with the control policy and error due to event-triggered feedback as two non-cooperative policies. Using the two-player non-cooperative zero-sum game theory, solution to the min-max optimization problem is determined. The sampling instants are optimized by designing an event-triggering mechanism with worst-case sampling error policy as threshold while the control policy is designed to minimize the performance index. Solution to this min-max problem is obtained by approximating the solution of the Hamilton-Jacobi-Issac (HJI) equation. Artificial neural networks (NNs) are employed for the approximation in a forward-in-time and on-line manner. To neutralize the effect of the aperiodic availability of the state information on learning accuracy, a hybrid learning scheme is proposed. The local ultimate boundedness of the closed-loop event-triggered system is demonstrated using Lyapunov direct method and Zeno free behavior of the system is also guaranteed. Finally, simulation results are included to validate the proposed design.