Stabilization by a relay control using non-quadratic Lyapunov functions

International audienceIn this article we consider the stabilization problem by a relay control using non-quadratic Lyapunov functions. First, a general result is proposed for the case of nonlinear systems. A full state relay feedback controller is designed in order to ensure the local asymptotic stability of the closed-loop system. Then, the result is applied to the particular case of LTI systems. A constructive method based on LMI conditions is given in order to design nonlinear switching surfaces and provide an estimation of a non-ellipsoidal domain of attraction. In addition, the approach is extended to observer-based relay feedback. Both linear and nonlinear switching surfaces dependent on the estimated state are designed while using a Luenberger observer. Finally, illustrative examples are proposed in order to show the efficiency of the proposed methods and simulations are performed for a Buck converter structure

Addressing COVID-19 in the surgical ICU: Incidence of antibodies in healthcare personnel at a quaternary care center

Background: There is concern that frontline healthcare personnel (HCP) are at increased risk of exposure to COVID-19 compared to the general population. Multiple studies have demonstrated significant seroprevalence of COVID-19 antibodies in HCP. Increased seropositivity has been associated with reduced use of personal protective equipment (PPE) along with reported PPE shortages. This investigation aims to determine the seroprevalence of COVID-19 in frontline HCP working at a quaternary care center that was heavily impacted by the initial surge of COVID-19, while also identifying underlying factors associated with increased seropositivity. Methods & Materials: HCP who participated in the management of COVID-19 patients were recruited from April 27 to May 13 of 2020. Unidentifiable demographic data was collected, including a questionnaire to identify potential exposure, symptoms, medical comorbidities, and adherence to PPE usage on a scale of 1 to 5 (1 being always, 5 being never). Serological testing was performed using CMC-19D SARS-CoV-2 (COVID-19) Rapid Antibody Test manufactured by Audacia Bioscience. Seropositivity was captured by formation of a dark band at the G (IgG) and C (control) positions on the test device, while IgM alone was considered a false positive. Pearson chi-squared and Fisher exact tests were performed to analyze categorical variables. SPSS version 27.0 was used for statistical analysis (SPSS, Armonk, NY). Conclusion: Overall seropositivity of IgG antibodies was 10.6%. Non-ICU personnel showed higher seroprevalence compared to ICU personnel, this may be attributed to decreased reported adherence to strict PPE usage in non-ICU areas compared to ICU areas during patient contact. Compared to MICU, SICU personnel appeared to be less compliant with frequency of PPE use outside patient rooms. Adherence to PPE usage outside patient contact was a predictor of seropositivity, and non-ICU personnel had a tendency toward high seroprevalence.https://scholarlycommons.henryford.com/sarcd2021/1003/thumbnail.jp

Control and observation of switched affine systems

Cette thèse est dédiée à l'étude du problème de la stabilisation des systèmes affines à commutations. L'objectif est de concevoir des lois de commutation dépendantes de l'état qui stabilisent le système en boucle fermée. Premièrement, un aperçu de quelque résultat existant dans la littérature est présenté. Ensuite, un résultat général permettant la synthèse de lois de commutations pour la stabilisation des systèmes nonlinéaires affines en l'entré est proposé. La particularisation de ce résultat aux cas des systèmes affines à commutations et des systèmes linéaires à temps invariant avec une commande à relais a permis de synthétiser des lois de commutations garantissant leur stabilité asymptotique locale ou globale en boucle fermée. Grace à l'utilisation des fonctions de Lyapunov commutées une méthode numérique basée sur des LMIs permettant la conception de surfaces de commutations nonlinéaires est proposée. Une méthode permettant la synthèse de lois de commutations robustes vis-à-vis des perturbations sur les mesures est également développée pour assurer la stabilisation des systèmes affines à commutations. Le résultat est ensuite particularisé au cas des systèmes linéaires temps invariant avec commande à relais robuste. Enfin, le problème de la synthèse de lois de commutations basée-observateur est considéré. Des surfaces de commutations linéaires et nonlinéaires sont proposées en utilisant des fonctions de Lyapunov quadratiques et non-quadratiques. Des conditions de stabilisation asymptotique locale et globale sont développées. Les lois de commutations conçues dépendent de l'état reconstruit en utilisant un observateur de type Luenberger. De plus, le principe de séparation est démontré pour les systèmes affines à commutations ainsi que pour les systèmes linéaires temps invariant avec une commande à relais.This thesis is dedicated to the study of the stabilization problem of switched affine systems with state-dependent switching laws. First, an overview of some existing results is proposed. In order to define the closed-loop system's solutions and to analyze its behavior over the switching surfaces the Filippov formalism is used. The stabilization problem is addressed using a Lyapunov approach which allows to derive numerical approaches based on LMIs. Throughout this thesis both switched affine systems and LTI systems with relay controllers are considered. Using a general framework for the class of nonlinear input-affine systems, a full state-dependent switching controller is designed in order to ensure both local and global asymptotic stability of the closed-loop system. Thanks to switching (Lur'e type) Lyapunov functions, a numerical approach based on LMIs that allows to derive a nonlinear stabilizing switching law is proposed. Moreover, a design approach of robust state-dependent switching laws for switched affine systems stabilization are proposed. The robustness property is studied with respect to bounded exogenous disturbances that affect the state measurements which are used for the design of the switching laws. Finally, observer-based switching controllers are designed to guarantee both local and global asymptotic stability of the closed-loop system. Using both quadratic and non-quadratic Lyapunov functions, linear and nonlinear switching surfaces are designed. The derived switching surfaces depend on the estimated state which is computed by a Luenberger observer. For both switched affine systems and LTI systems with relay controller the separation principle is proved

Finite-time and asymptotic left inversion of nonlinear time-delay systems

International audienceIn this paper we investigate the left invertibility problem for a class of nonlinear time-delay systems. In both cases of time delay systems with and without internal dynamics the invertibility conditions are given. A new approach based on the use of higher order sliding mode observer is developed for finite-time left invertibility and for asymptotic left inversion. Causal and non-causal estimation of the unknown inputs are respectively discussed. The results are illustrated by numerical examples in order to show the efficiency of the method and its limits

Symbolic models for incrementally stable singularly perturbed hybrid affine systems

International audienceIn this paper, we consider the problem of symbolic models design for the class of incrementally stable singularly perturbed hybrid affine systems. Contrarily to the existing results in the literature where only switching are taken into account, here we consider a more general class of hybridsystems including switches, impulsions and dynamics evolving in different timescales. Firstly, a discussion about incremental stability of the considered class of systems is given. Secondly, a new method for designing symbolic models for incrementally stable singularly perturbed hybrid affine systems is proposed. Inspired from singularly perturbed techniques based on decoupling the slow dynamics from the fast ones,the obtained symbolic abstraction is designed by discretizing only a part of the state space representing the slow dynamics. An e -approximate bisimulation relation between the original singularly perturbed hybrid affine system and the symbolic model obtained by discretizing the slow dynamics is provided. Indeed, since the discrete abstraction is designed for a system of lower dimension, the number of its transitions is drasticallyreduced. Finally, an example is proposed in order to illustrate the efficiency of the proposed results

Reference Tracking for Linear Time Invariant Systems with a Relay Control

International audienceThis paper investigates the problem of tracking a reference trajectory for Linear Time Invariant (LTI) systems using a relay feedback. First of all, the problem of a reference tracking is reformulated as a stabilization problem of the tracking error. Then, under some conditions on the reference inputs a design approach of a relay feedback controller that guarantees a perfect tracking of the reference trajectory is provided. Moreover, conditions in LMI form are proposed in order to synthesize a relay feedback and provide an estimation of the domain of attraction. Secondly, the case where the reference inputs can take the same values as the control input is considered. In this context, achieving a perfect tracking is no longer possible. Thus, using the comparison principle, a relay feedback controller that guarantees a practical stabilization of the tracking error is proposed. An estimation of the domain of attraction along with the bound of the tracking error are equally provided. Finally, computer simulations show the efficiency of the developed method over a numerical example

Safety controller design for incrementally stable switched systems using event-based symbolic models

International audienceIn this paper, we investigate the problem of lazy safety controllers synthesis for event-based symbolic models of incrementally stable switched systems with aperiodic time sampling. First of all, we provide a novel event-based scheme for symbolic models design. The obtained symbolic models are computed while considering all transitions of different durations satisfying a triggering condition. In addition, they are related to the original switched system by a feedback refinement relation and thus useful for control applications. Then, using the particular structure of the obtained event-based symbolic model, a lazy safety controller is designed while choosing transitions of longest durations. Secondly, for the same state sampling parameter and desired precision, we show that the obtained event-based symbolic model is related by a feedback refinement relation to the classical symbolic model designed for incrementally stable switched systems with periodic time sampling. Based on this relationship, we prove analytically that the size of the set of controllable states obtained with the lazy safety controller designed for an event-based symbolic model is larger than the one obtained with a safety controller designed for the classical symbolic model. Finally, an illustrative example is proposed in order to show the efficiency of the proposed method and simulations are performed for a Boost DC-DC converter structure

Symbolic models for incrementally stable switched systems with aperiodic time sampling

International audienceIn this paper, we consider the problem of symbolic model design for the class of incrementally stable switched systems. Contrarily to the existing results in the literature where switching is considered as periodically controlled, in this paper, we consider aperiodic time sampling resulting either from uncertain or event-based sampling mechanisms. Firstly, we establish sufficient conditions ensuring that usual symbolic models computed using periodic time-sampling remain approximately bisimilar to a switched system when the sampling period is uncertain and belongs to a given interval; estimates on the bounds of the interval are provided. Secondly, we propose a new method to compute symbolic models related by feedback refinement relations to incrementally stable switched systems, using an event-based approximation scheme. For a given precision, these event-based models are guaranteed to enable transitions of shorter duration and are likely to allow for more reactiveness in controller design. Finally, an example is proposed in order to illustrate the proposed results and simulations are performed for a Boost dc-dc converter structure

Left inversion of nonlinear time delay system

International audience— This paper investigates the left invertibility for nonlinear time delay system with internal dynamics. Under the assumption imposed on the internal dynamics, it has been shown that the unknown inputs can be estimated. Causal and non causal estimation of the unknown inputs are respectively discussed, and the high-order sliding mode observer is used to estimate the observable states

Stabilization of LTI systems by relay feedback with perturbed measurements

International audienceThis paper investigates the stabilization of Linear Time Invariant (LTI) systems by relay feedback. Generally the states measurements are subject to perturbations and noises. However, their effect is often ignored in the design of relay feedback. Here a state-dependent switching law isdesigned in a robust manner, while taking into account the perturbed states. The stability analysis of the closed loop system leads to qualitative conditions. Then, an LMI reformulation of the stability conditions is proposed to allow a numerical implementation of the results. Computer simulations show the efficiency of the developed method over a numerical example