Multivalued robust tracking control of fully actuated Lagrange systems: Continuous and discrete–time algorithms

International audienceIn this paper the robust trajectory tracking problem of a class of nonlinear systems described by the Euler–Lagrange equations of motion is studied. We start considering a plant under the effects of an unknown external perturbation and also with uncertainties on its parameters. After that a class of passivity-based multivalued control laws is proposed and the well–posedness together with the stability of the closed–loop are established in the continuous–time setting. The discrete–time version of the plant and the controller are studied and well–posedness together with stability results are obtained, using the so-called implicit discretization approach introduced in [1, 2]. Numerical simulations are presented and demonstrate the effectiveness of the proposed discrete-time controller

Set-valued sliding-mode control of uncertain linear systems: continuous and discrete-time analysis

International audienceIn this paper we study the closed-loop dynamics of linear time-invariant systems with feedback control laws that are described by set-valued maximal monotone maps. The class of systems considered in this work is subject to both, unknown exogenous disturbances and parameter uncertainty. It is shown how the design of conventional sliding mode controllers can be achieved using maximal monotone operators (which include the set-valued signum function). Two cases are analyzed: continuous-time and discrete-time controllers. In both cases well-posedness together with stability results are presented. In discrete time we show how the implicit scheme proposed for the selection of control actions makes sense resulting in the chattering effect being almost suppressed even with uncertainty in the system

Early Pension Withdrawals in Chile During the Pandemic

Chile, with one of the largest and best funded defined contribution programs in Latin America, held over USD $200 bn in assets at the onset of the Covid-19 crisis, or more than 80$50 bn from the system. This paper explores several hypotheses regarding why people withdrew their pension money early, and it also presents evidence regarding the likely impact of this short-term policy on long-term retirement wellbeing. We conclude with lessons for global policymakers seeking to protect pension assets critical for retirement security

A set-valued nested sliding-mode controller

International audienceWe propose a set-valued controller with a signum multifunction nested inside another one. We prove that the controller is well-posed and achieves robust ultimate boundedness in the presence of mismatched, non-vanishing disturbances. Even more, the selected output can be made arbitrarily small. Also, by applying the implicit Euler scheme introduced by Acary and Brogliato [2010], Acary et al. [2012] for matched disturbances, we derive a selection strategy for the discrete-time implementation of the set-valued control law. The discrete-time scheme diminishes chattering substantially

Set-valued discrete-time sliding-mode control of uncertain linear systems

International audienceThis paper focuses on the discrete-time sliding-mode control problem, that is, given an uncertain linear system under the effect of external matched perturbations, to design a set-valued control law that achieves the robust regulation of the plant and at the same time reduces substantially the chattering effect in both the input and the sliding variables. The cornerstone is the implicit Euler discretization technique together with a differential inclusion framework which allow us to make a suitable selection of the control values that will compensate for the disturbances. Numerical examples confirm the effectiveness of the proposed methodology

A notion of equivalence for linear complementarity problems Applications to the design of nonsmooth bifurcations

peer reviewedMany systems of interest to control engineering can be modeled by linear complementarity problems. We introduce a new notion of equivalence between linear complementarity problems that sets the basis to translate the powerful tools of smooth bifurcation theory to this class of models. Leveraging this notion of equivalence, we introduce new tools to analyze, classify, and design nonsmooth bifurcations in linear complementarity problems and their interconnection