Nacim Meslem

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In this paper, we show how to compute an over-approximation for the reachable set of uncertain nonlinear continuous dynamical systems by using guaranteed set integration. We introduce two ways to do so. The first one is a full interval method which handles whole domains for set computation and relies on state-of-the-art validated numerical integration(More)
In this paper, we investigate nonlinear reachability computation in presence of model uncertainty, via guaranteed set integration. We show how this can be done by using the classical Müller’s existence theorem. The core idea developed is to no longer deal with whole sets but to derive instead two nonlinear dynamical systems which involve no model(More)
We address nonlinear reachability computation for uncertain monotone systems, those for which flows preserve a suitable partial orderings on initial conditions. In a previous work [1], we introduced a nonlinear hybridization approach to nonlinear continuous reachability computation. By analysing the signs of off-diagonal elements of system’s Jacobian(More)
This paper deals with set membership state estimation for continuous-time systems from discrete-time measurements, in the unknown but bounded error framework. The classical predictor-corrector approach to state estimation uses interval Taylor methods for solving the prediction phase, which are known to have poor performance in presence of large model or(More)
In this paper we show how to compute the reachable space for uncertain nonlinear continuous dynamical systems by using guaranteed set integration. We introduce two ways to do so. The first one is a full interval method which handles whole domains for set computation and relies on Taylor series and interval analysis. The second one relies on the theory of(More)
In this paper we design an interval observer for nonlinear uncertain continuous-time dynamical systems, in the unknown-but-bounded error framework. We show how to generate two coupled hybrid observers, which yield the best conservative upper and lower component-wise bounds for the state, provided bounds are available for initial conditions and(More)
This paper is about state estimation for nonlinear uncertain continuous-time systems in a bounded-error context. We introduce a method for designing a guaranteed interval observer which is based on (i) the application of Müller’s theorem for bracketing the solution of ordinary differential equations in a way which ensures the positivity of the observation(More)