Computing control invariant sets is easy

In this paper we consider the problem of computing control invariant sets for linear controlled systems with constraints on the input and on the states. We focus in particular on the complexity of the computation of the N-step operator, given by the Minkowski addition of sets, that is the basis of many of the iterative procedures for obtaining control invariant sets. Set inclusions conditions for control invariance are presented that involve the N-step sets and are posed in form of linear programming problems. Such conditions are employed in algorithms based on LP problems that allow to overcome the complexity limitation inherent to the set addition and can be applied also to high dimensional systems. The efficiency and scalability of the method are illustrated by computing in less than two seconds an approximation of the maximal control invariant set, based on the 15-step operator, for a system whose state and input dimensions are 20 and 10 respectively

Computing control invariant sets in high dimension is easy

In this paper we consider the problem of computing control invariant sets for linear controlled high-dimensional systems with constraints on the input and on the states. Set inclusions conditions for control invariance are presented that involve the N-step sets and are posed in form of linear programming problems. Such conditions allow to overcome the complexity limitation inherent to the set addition and vertices enumeration and can be applied also to high dimensional systems. The efficiency and scalability of the method are illustrated by computing approximations of the maximal control invariant set, based on the 10-step operator, for a system whose state and input dimensions are 30 and 15, respectively.Comment: arXiv admin note: substantial text overlap with arXiv:1708.0479

Notes on wave-induced current predictors

rapport interne de GIPSA-labThe objective here is to build a predictor of the wave effect on the tidal current. The tide is, in fact, influenced by the superficial wave, in particular when the measure is taken at relatively low depths. Thus, while a cyclic behaviour of the tide, with periods of the order of some hours, is relatively easy to be forecast, the effect of the wave might be predicted employing the available measures of the tidal current. This effect is often characterized by much smaller periods, some second in general, and is less regular the tidal main oscillation. The predictiors proposed are dynamical models, based on observers, that can provide the future estimation of the value of the wave-induced current

New condition for invariance of ellipsoidal sets for discrete-time saturated systems

International audienceIn this paper, we consider the problem of characterizingthe invariant and contractive ellipsoids for discrete-timesaturated systems, as an estimate of the domain of attraction.The asymptotic stability of the controlled system is ensured bythe contractive nature of the invariant set. Sufficient conditionsfor the existence of a quadratic set-induced Lyapunov functionare established through the solution of a bilinear matrixinequalities (BMI) problem. Some computational considerationsare analyzed to overcome the problem of complexity. Anillustrative example is given to demonstrate the effectivenessof the proposed results, developed in this paper

Probabilistic reachable and invariant sets for linear systems with correlated disturbance

In this paper a constructive method to determine and compute probabilistic reachable and invariant sets for linear discrete-time systems, excited by a stochastic disturbance, is presented. The samples of the disturbance signal are not assumed to be uncorrelated, only a bound on the correlation matrices is supposed to be known. The concept of correlation bound is introduced and employed to determine probabilistic reachable sets and probabilistic invariant sets. Constructive methods for their computation, based on convex optimization, are given

Necessary and sufficient condition for stabilizability of discrete-time linear switched systems: a set-theory approach

International audienceIn this paper, the stabilizability of discrete-time linear switched systems is considered. Several sufficient conditions for stabilizability are proposed in the literature, but no necessary and sufficient. The main contributions are the necessary and sufficient conditions for stabilizability based on set-theory and the characterization of a universal class of Lyapunov functions. An algorithm for computing the Lyapunov functions and a procedure to design the stabilizing switching control law are provided, based on such conditions. Moreover a sufficient condition for non-stabilizability for switched system is presented. Several academic examples are given to illustrate the efficiency of the proposed results. In particular, a Lyapunov function is obtained for a system for which the Lyapunov-Metzler condition for stabilizability does not hold

Observer-Based Efficiency Enhancement in Cell-Cycle Specific Therapies

International audienceCell-cycle specific drugs affect cells when they are in specific phases of their periodic cycle. However, injecting drug's strategy can only by global. This rises the problem of optimizing a global constrained decision variable (drug delivery profile with limited volume) when its effect depends on many local unknown characteristics (the individual cells phases). In this paper, an observer-based framework is proposed that enables a rational decision making in this particular circumstance. Simulation on a simple case are proposed to show the relevance of the proposed framework

The Ockham's razor applied to COVID-19 model fitting French data

This paper presents a data-based simple model for fitting the available data of the Covid-19 pandemic evolution in France. The time series concerning the 13 regions of mainland France have been considered for fitting and validating the model. An extremely simple, two-dimensional model with only two parameters demonstrated to be able to reproduce the time series concerning the number of daily demises caused by Covid-19, the hospitalizations, intensive care and emergency accesses, the daily number of positive test and other indicators, for the different French regions. These results might contribute to stimulate a debate on the suitability of much more complex models for reproducing and forecasting the pandemic evolution since, although relevant from a mechanistic point of view, they could lead to nonidentifiability issues

Probabilistic reachable and invariant sets for linear systems with correlated disturbance

In this paper a constructive method to determine and compute probabilistic reachable and invariant sets for linear discrete-time systems, excited by a stochastic disturbance, is presented. The samples of the disturbance signal are not assumed to be uncorrelated, only a bound on the correlation matrices is supposed to be known. The concept of correlation bound is introduced and employed to determine probabilistic reachable sets and probabilistic invariant sets. Constructive methods for their computation, based on convex optimization, are given