Smooth and Heavy Solutions to Control Problems

Aubin, J.-P. (1985). Smooth and Heavy Solutions to Control Problems. IIASA Working Paper. IIASA, Laxenburg, Austria: WP-85-044

[thumbnail of WP-85-044.pdf]

Download (341kB) | Preview


We introduce the concept of viability domain of a set-valued map, which we study and use for providing the existence of smooth solutions to differential inclusions.

We then define and study the concept of heavy viable trajectories of a controlled system with feedbacks. Viable trajectories are trajectories satisfying at each instant given constraints on the state. The controls regulating viable trajectories evolve according a set-valued feedback map. Heavy viable trajectories are the ones which are associated to the controls in the feedback map whose velocity has at each instant the minimal norm. We construct the differential equation governing the evolution of the controls associated to heavy viable trajectories and we state their existence.

Item Type: Monograph (IIASA Working Paper)
Research Programs: System and Decision Sciences - Core (SDS)
Depositing User: IIASA Import
Date Deposited: 15 Jan 2016 01:56
Last Modified: 27 Aug 2021 17:12

Actions (login required)

View Item View Item