Observer-Based Event-Triggered Optimal Control for Linear Systems

In this paper. we propose an event-triggered optimal control method for linear systems based on state observer. Firstly, combining with the optimal control theory, the modeling and analysis of the control systems with state feedback observer are studied. Secondly, by setting the minimum performance index in which we considering the system state and the observer state to make the system reach the equilibrium point from the initial state, the optimal feedback control law of the system is obtained on basis of the minimum principle. Thirdly, a state-feedback control system based on an event-triggered observer is studied, where the state of the plant is only transmitted to the observer when the event condition is violated. Then, the asymptotic stability of the control plant and the observer error system is guaranteed by conditions in terms of LMIs(Linear Matrix Inequalities). Finally, a numerical example is worked out to illustrate the validity and effectiveness of the method.