A Framework for the Event-Triggered Stabilization of Nonlinear Systems

Abstract

Event-triggered control consists of closing the feedback loop whenever a predefined state-dependent criterion is satisfied. This paradigm is especially well suited for embedded systems and networked control systems since it is able to reduce the amount of communication and computation resources needed for control, compared to the traditional periodic implementation. In this paper, we propose a framework for the event-triggered stabilization of nonlinear systems using hybrid systems tools, that is general enough to encompass most of the existing eventtriggered control techniques, which we revisit and generalize. We also derive two new event-triggering conditions which may further enlarge the inter-event times compared to the available policies in the literature as illustrated by two physical examples. These novel techniques exemplify the relevance of introducing additional variables for the design of the triggering law. The proposed approach as well as the new event-triggering strategies are flexible and we believe that they can be used to address other event-based control problems.

Input-to-state stabilizing event-triggered control for linear systems with output quantization

“…γ <L (16) with r := ( γ L ) 2 − 1 . The time T (λ,λ, γ,L) corresponds to the maximally allowable transmission interval (MATI) of time-triggered controllers [4].…”

“…Consider system (12) with the flow and the jump sets as in (11) with Ψ, η 0 specified in (15) and T = T (λ,λ, γ,L) with T (λ,λ, γ,L) as defined in (16). Suppose that Assumptions 1, 2 are satisfied and the dynamic quantizer is designed as in (18)-(20).…”

“…Finally, property (5) means that the time domain of solutions to system (11)- (12) is unbounded. (16), (18), the design parameter λ creates a tradeoff between transmissions and quantization. When λ is reduced, the value of T in (16) will increase, which may result in a reduction in the amount of transmissions.…”

“…Then, by solving the LMI (14), we obtain ε y = 0.678, L = 0, γ = 4.9655. We take λ = 0.5,λ = 0.6, ν = 0.01 and we compute the value of T by using (16), which yields T = 0.1139. Furthermore, we obtainγ = 33.5917.…”

“…The quantized feedback information is transmitted to the controller by using a dynamic output-based eventtriggering condition in the sense of [5], [7], [16]. The triggering mechanism enforces the existence of a strictly positive lower bound on the inter-transmission times, which excludes Zeno behaviour for the transmission instants.…”