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The Optimal Boundary and Regulator Design Problem for Event-Driven Controllers ⋆
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@MISC{Martí_theoptimal,
author = {Pau Martí and Manel Velasco and Enrico Bini},
title = {The Optimal Boundary and Regulator Design Problem for Event-Driven Controllers ⋆},
year = {}
}
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Abstract
Abstract. Event-driven control systems provide interesting benefits such as reducing resource utilization. This paper formulates the optimal boundary and regulator design problem that minimizes the resource utilization of an event-driven controller that achieves a cost equal to the case of periodic controllers. 1 Event-Driven Control System Model We consider the control system ˙x(t) = Ax(t) + B u(t) y(t) = C x(t) (1) with x ∈ R n×1, A ∈ R n×n, B ∈ R n×m, u ∈ R m×1, and C ∈ R 1×n. Let u(t) = uk = L x(ak) = L xk ∀t ∈ [ak, ak+1 [ (2) be the control updates given by a linear feedback controller designed in the continuous-time domain but using only samples of the state at discrete instants a0, a1,..., ak,... Between two consecutive control updates, u(t) is held constant. In periodic sampling we have ak+1 = ak + h, where h is the period of the controller. Let ek(t) = x(t)−xk be the error evolution between consecutive samples with t ∈ [ak, ak+1[. For several types of event-driven control approaches [1,2], event conditions can be generalized by introducing a function f(·, ·, Υ) : R n × R n → R that defines a boundary measuring the tolerated error with to respect the sampled state [3]. The condition that must be ensured is f(ek(t), xk, Υ) ≤ η (3)
Keyphrases
optimal boundary event-driven controller regulator design problem resource utilization event condition xk ak linear feedback controller control system tolerated error periodic controller continuous-time domain event-driven control system discrete instant several type event-driven control sampled state consecutive sample periodic sampling error evolution consecutive control event-driven control system model
