Event Triggered observer-based control for linear systems with time varying uncertainties

Lucien Etienne 1, 2 Stefano Di Gennaro 1 Jean-Pierre Barbot 3, 2
3 NON-A - Non-Asymptotic estimation for online systems
Inria Lille - Nord Europe, CRIStAL - Centre de Recherche en Informatique, Signal et Automatique de Lille (CRIStAL) - UMR 9189
Abstract : In this paper, we investigate the stabilization of a linear plant subject to network constraints, partial state knowledge and time varying bounded parameter uncertainties. An event–triggered version of the Luenberger observer is proposed, and necessary conditions on the uncertainties are given in term of LMI's to enable output– based stabilization under different triggering strategies. The proposed observer is tested in simulations on a linearized inverted pendulum. I. INTRODUCTION In modern control system it is more and more common to use digital technology, where the control task consists of sampling the outputs of the plant then computing and implementing new actuator signals. The classic way to proceed is to sample in a periodic fashion the output, thus allowing the closed–loop system to be analyzed on the basis of sampled–data systems [1]. In network control system such as vehicle platooning and smart grid, communication between different agent on the network play a big role in the overall stability. Therefore, it can be of use to reduce the communication when sampling is not needed. Recent years have seen the development of a new paradigm where, instead of sampling periodically, i.e. with a time triggered policy, the system is triggered when needed, i.e. using an event triggered policy. A lot of works have been done on this subject, see [2], [18], [19], [16], [6] and references therein, while for an introduction to the topic see [7]. Our main focus in this work is to investigate the impact of the event triggered paradigm on observer– based (i.e. dynamical feedback) control systems. More precisely, the observer–based control problem is considered for linear systems in the presence of model uncertainties. Different kinds of event triggered policies allow practical or asymptotic stability. Furthermore, the result proposed are global in the sense that the stability does not depend on initial condition and initial observation error. As particular case, the proposed results can be obviously applied for full state feedback. Some studies are available on observer–based controller [3], [4], [12], [17]. In [3] and [4] practical stability is ensured in presence of a disturbance on the plant, while a L ∞ gain is guaranteed. In [12], the plant and the output are subject to perturbation and practical stability is also guaranteed. In [17], asymptotic stability is obtained in absence of perturbations. In [5], an uncertain plant is used to stabilize a system between two communications, in the case of availability of the full state. To the best of the authors' knowledge, no result are available when the system under consideration are not linear. With respect to these previous results, this paper considers the robustness issues of the event triggered observation and control with respect to time varying modeling uncertainties, allowing to state that if the continuous closed loop system is robust, then the uncertain system is stabilizable with the event triggered policy. Moreover, asymptotic stabilization of an uncertain system using an adapted event triggered policy is obtained.
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Communication dans un congrès
American Control Conference, Jul 2015, Chicago, United States. 2015, 〈10.1109/ACC.2015.7170950〉
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Lucien Etienne, Stefano Di Gennaro, Jean-Pierre Barbot. Event Triggered observer-based control for linear systems with time varying uncertainties. American Control Conference, Jul 2015, Chicago, United States. 2015, 〈10.1109/ACC.2015.7170950〉. 〈hal-01195559〉

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