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A Self-Triggered Control Strategy to Guarantee Forward Invariance and Uniform Positive Inter-Event Times for Constrained Systems

Creative Commons 'BY' version 4.0 license

Self-triggered control algorithms have the key feature that plant measurements are only needed at isolated time instances. The information obtained at those time instances is used by self-triggered control algorithms to update the input to the plant and to determine the next sampling time event. In between these events, the input is usually held constant. In this \paperthesis, a self-triggered control strategy is proposed for forward invariance of a set for constrained (controlled) differential inclusions. Using a (not necessarily periodic) zero-order hold control scheme, this \paperthesis addresses two key issues: i) the computation of the next sampling time event, and ii) the assurance of a uniform lower bound on the inter-event times, both while guaranteeing forward invariance. Our results allow the sets to render forward invariant to be unbounded. Very importantly, the results impose mild regularity properties on the data defining the dynamics of the control system and of the forward invariance certificates, which are given in terms of barrier functions. Simulations showcase the proposed algorithms and provide comparisons with the literature.

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