Dynamic event-triggered control for nonlinear systems via differential algebraic representation

Abstract

This paper deals with the event-triggered gain-scheduling control of nonlinear systems based on the differential algebraic representation (DAR) approach. Since the parameters of the gain-scheduled controller depend on the sampled state information, a mismatch is induced between the controller and the DAR of the plant. To deal with this issue, we propose a novel dynamic event-triggered control strategy with a compensation term for the mismatch. Then, we propose a co-design condition, in the form of linear matrix inequalities (LMIs), to design the gain-scheduling controller and the event-triggering mechanism. We show that Zeno behavior is avoided with the proposed event-triggering mechanism. Moreover, as the LMI conditions are derived by constraining the region of validity of the DAR, we estimate the region of attraction of the closed-loop equilibrium lying inside this region of validity. Finally, a multi-objective optimization problem is provided to enlarge the estimate of the region of attraction and minimize the number of transmissions. Numerical simulations illustrate the advantages of the proposed condition in reducing conservativeness when compared to related work, as well as reducing the number of events.