Guaranteed optimal reachability control of reaction-diffusion equations using one-sided Lipschitz constants and model reduction

We show that, for any spatially discretized system of reaction-diffusion, the approximate solution given by the explicit Euler time-discretization scheme converges to the exact time-continuous solution, provided that diffusion coefficient be sufficiently large. By "sufficiently large", we mean that the diffusion coefficient value makes the one-sided Lipschitz constant of the reaction-diffusion system negative. We apply this result to solve a finite horizon control problem for a 1D reaction-diffusion example. We also explain how to perform model reduction in order to improve the efficiency of the method

Kinetic parameter estimation and modelling of sucrose esters synthesis without solvent

International audienc

Guaranteed control synthesis for continuous systems in Uppaal Tiga

We present a method for synthesising control strategies for continuous dynamical systems. We use Uppaal Tiga for the synthesis in combination with a set-based Euler method for guaranteeing that the synthesis is safe. We present both a general method and a method which provides tighter bounds for monotone systems. As a case-study, we synthesize a guaranteed safe strategy for a simplified adaptive cruise control application. We show that the guaranteed strategy is only slightly more conservative than the strategy generated in the original adaptive cruise control paper which uses a discrete non guaranteed strategy. Also, we show how reinforcement learning may be used to obtain optimal sub-strategies