Traffic Characterization of Event-Triggered Control Systems: A Geometric-Algebraic Perspective
For control system designers, this provides a rigorous geometric-algebraic framework to analyze and select parameters for event-triggered control, though the contribution is incremental as it builds on existing optimization reformulations.
This work characterizes inter-event time transitions in event-triggered control systems by reformulating a nonconvex quadratic constraint problem into a linear cone problem, establishing necessary and sufficient feasibility conditions, and computing all feasible transition relations. Numerical simulations show how feasibility evolves with control parameter σ.
This paper characterizes the triggering behaviors of event-triggered control systems from a geometric-algebraic perspective. We first model the feasibility of inter-event time transition relations as a nonconvex quadratic constraint satisfaction problem and reformulate it as an equivalent linear cone problem, which provides a clearer geometric description of the feasible region, making subsequent analysis more reliable. Building on this formulation, we establish necessary and sufficient conditions that rigorously determine whether a given transition relation is feasible. Based on this condition, we propose an algorithm that computes the set of all feasible transition relations. Numerical simulations further demonstrate how the feasibility of specific transitions evolves with the control parameter σ, with visualizations of the feasible state space offering intuitive insight into parameter selection and system design.