Control of Mechanical Systems Using Set Based Methods

This paper considers large discrete-time linear systems obtained from discretized partial differential equations, and controlled by a quantized law, i.e., a piecewise constant time function taking a finite set of values. We show how to generate the control by, first, applying model reduction to the original system, then using a “state-space bisection” method for synthesizing a control at the reduced-order level, and finally computing an upper bound on the deviations between the controlled output trajectories of the reduced-order model and those of the original model. The effectiveness of our approach is illustrated on several examples of the literature. A. Le Coënt CMLA, ENS Cachan, CNRS, Université Paris-Saclay 61 av. du Président Wilson, 94235 Cachan cedex Tel.: +33147405900 Fax: +33147405901 E-mail: [email protected] F. de Vuyst CMLA, ENS Cachan, CNRS, Université Paris-Saclay 61 av. du Président Wilson, 94235 Cachan cedex E-mail: [email protected] C. Rey Safran Tech 1 Rue GeneviÃĺve AubÃľ, 78772 Magny les Hameaux, France E-mail: [email protected] L. Chamoin LMT Cachan, ENS Cachan, CNRS, Université Paris-Saclay 61 av. du Président Wilson, 94235 Cachan cedex E-mail: [email protected] L. Fribourg LSV, ENS Cachan, CNRS, Université Paris-Saclay 61 av. du Président Wilson, 94235 Cachan cedex E-mail: [email protected]