On Lyapunov sampling for event-driven controllers
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This paper investigates an event condition for event-driven controllers based on Lyapunov functions. Considering that constant values of a Lyapunov function define contour curves that form closed regions around the equilibrium point, in this paper we present a sampling mechanism that enforces job executions (sampling, control algorithm computation and actuation) each time the system trajectory reaches a given contour curve. By construction, the sequence of generated samples is stable in the discrete Lyapunov sense. However, in order to ensure that the system trajectory will tend to zero as time tends to infinity, it must be ensured that the sequence of samples is infinite. We provide conditions to ensure this property. The approach is illustrated by simulated examples.
CitacióVelasco, M.; Martí, P.; Bini, E. On Lyapunov sampling for event-driven controllers. A: IEEE Conference on Decision and Control and Chinese Control Conference. "48th IEEE Conference on Decision and Control held jointly with 2009 28th Chinese Control Conference". Shangai: 2009, p. 6238-6243.