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- Nacim Ramdani, Nacim Meslem, Yves Candau
- IEEE Trans. Automat. Contr.
- 2009

—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)

- Nacim Ramdani, Nacim Meslem, Yves Candau
- HSCC
- 2008

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)

- Tarek Raïssi, Nacim Ramdani, Yves Candau
- Automatica
- 2004

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)

- Anda Ionescu, Yves Candau, Eric Mayer, Iolanda Colda
- Environmental Modelling and Software
- 2000

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)

The experimental survival curves of Bacillus stearothermophilus spores in aqueous suspension, for six constant temperatures ranging from 105 to 130 degrees C, displayed an initial shoulder before a linear decline. To interpret these observations, we supposed that, before the heat treatment, the designated spore suspension contained a countable and mortal… (More)

- Adriana Coman, Anda Ionescu, Yves Candau
- Environmental Modelling and Software
- 2008

- Yves Candau, Tarek Raïssi, Nacim Ramdani, Laurent Ibos
- Reliable Computing
- 2006

In this paper, the polar representation of complex numbers is extended to complex polar intervals or sectors; detailed algorithms are derived for performing basic arithmetic operations on sectors. While multiplication and division are exactly defined, addition and subtraction are not, and we seek to minimize the pessimism introduced by these operations.… (More)

- T. Raïssi, N. Ramdani, Y. Candau
- 2003

This paper deals with guaranteed parameter estimation in a bounded error context for nonlinear continuous-time systems. Perturbations are assumed bounded but otherwise unknown. The solution is a set of parameter vectors consistent with modelling hypotheses, measured data and prior error bounds. The algorithm proposed in this paper does not suffer from… (More)