Control of parameter dependent systems

Martin Lazar (1) , Jérôme Lohéac (2)

1 University of Dubrovnik
2 CRAN - Centre de Recherche en Automatique de Nancy

In this chapter we provide an overview of recent progress on the problem of controllability of parameter dependent systems. We explore a different control notions successfully developed through the last decade. The aim of the control function is to steer the system to a state satisfying some properties prescribed either at some time instant T > 0 or during a given time interval. These properties may be separated with respect to parameter values and can refer just to a single system itself (e.g. greedy control), or may consider solutions corresponding to the whole parameter range (e.g. ensemble control, averaged control). In the latter case control functions are designed as parameter invariant, implying a same control is to be applied to the system independently of a particular realisation of the parameter, while in the first case controls vary along with the parameter. Beside the positive theoretical results, for each notion we provide a precise computational algorithm accompanied by a numerical example.

Mots clés: Averaged control; greedy control; ensemble control; parameter dependent systems; reduced basis

Domaines: Systèmes dynamiques [math.DS]; Optimisation et contrôle [math.OC]

Martin Lazar, Jérôme Lohéac. Control of parameter dependent systems. Handbook of Numerical Analysis, 23, pp.265-306, 2022, Numerical Control: Part A, 1570-8659. ⟨10.1016/bs.hna.2021.12.008⟩. ⟨hal-03035494⟩