Periodic Event-Triggered Control for Linear Systems in the Presence of Cone-Bounded Nonlinear Inputs: A Discrete-Time Ap
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Periodic Event-Triggered Control for Linear Systems in the Presence of Cone-Bounded Nonlinear Inputs: A Discrete-Time Approach G. B. Merlin1 · L. G. Moreira2
· J. M. Gomes da Silva Jr.1
Received: 2 March 2020 / Revised: 20 July 2020 / Accepted: 8 September 2020 © Brazilian Society for Automatics–SBA 2020
Abstract This paper presents an observer-based periodic event-triggered strategy for linear systems subject to input cone-bounded nonlinearities. Considering a discrete-time framework, conditions in the form of linear matrix inequalities are derived to ensure global or regional stability of the origin of the closed-loop system under the event-triggered control strategy. These conditions are cast into convex optimization problems to determine the event-triggering function parameters, aiming at reducing the number of control updates with respect to periodic implementations. Both the emulation and the co-design problems are addressed. Numerical examples with logarithmic quantization and saturation nonlinearities are presented to illustrate the method. Keywords Event-triggered control · Cone-bounded nonlinearities · Observers · LMIs · Co-design.
1 Introduction Event-triggered control strategies have been attracting the attention of the control community in the last few years. The basic idea underlying these strategies regards updating the control signal only when a certain event, based on the measurement of states or outputs of the system, occurs (Heemels et al. 2012). The main motivation for the application of such a kind of updating control policy comes from the recently growth of the so-called networked control systems (NCS) (Hespanha et al. 2007), which brings some practiThis study was financed in part by CNPQ, Brazil (Grants PQ-305979/2019-9 and Univ-42299/2016-0) and IFSUL, Brazil (Project PD00190519/011).
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J. M. Gomes da Silva Jr. [email protected] G. B. Merlin [email protected] L. G. Moreira [email protected]
1
Departamento de Automação e Energia (DELAE), Universidade Federal do Rio Grande do Sul (UFRGS), Porto Alegre, Rio Grande do Sul, Brazil
2
Instituto Federal de Educação, Ciência e Tecnologia Sul-rio-grandense (IFSul), Charqueadas, Rio Grande do Sul, Brazil
cal constraints in terms of the amount and the frequency of data transmissions. In this case, less control updates implies less amount and frequency of data transmissions. This has a clear impact, for instance, on network congestion and energy consumption (critical in systems fed by batteries). Another interesting motivation is to avoid actuators fatigue, which can be critical, for instance in mechanical devices. Two basic problems can be formulated in the context of event-triggered control: the emulation and the co-design. In the emulation problem, the controller is supposed to be given and only the triggering function (or criterion) is designed. In the co-design, the controller and the triggering function are simultaneously synthesized. Despite the fact that the majority of control systems nowadays are implemente
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