Displaying similar documents to “Every normal linear system has a regular time-optimal synthesis”

A weak regularity theorem for real analytic optimal control problems.

Hector J. Sussmann (1986)

Revista Matemática Iberoamericana

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We consider real analytic finite-dimensional control problems with a scalar input that enters linearly in the evolution equations. We prove that, whenever it is possible to steer a state x to another state y by means of a measurable control, then it is possible to steer x to y by means of a control that has an extra regularity property, namely, that of being analytic on an open dense subset of its interval of definition. Since open dense sets can have very small measure, this is a very...

Regular syntheses and solutions to discontinuous ODEs

Alessia Marigo, Benedetto Piccoli (2002)

ESAIM: Control, Optimisation and Calculus of Variations

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In this paper we analyze several concepts of solution to discontinuous ODEs in relation to feedbacks generated by optimal syntheses. Optimal trajectories are called Stratified Solutions in case of regular synthesis in the sense of Boltyanskii–Brunovsky. We introduce a concept of solution called Krasowskii Cone Robust that characterizes optimal trajectories for minimum time on the plane and for general problems under suitable assumptions.

Optimal control for a class of compartmental models in cancer chemotherapy

Andrzej Świerniak, Urszula Ledzewicz, Heinz Schättler (2003)

International Journal of Applied Mathematics and Computer Science

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We consider a general class of mathematical models P for cancer chemotherapy described as optimal control problems over a fixed horizon with dynamics given by a bilinear system and an objective which is linear in the control. Several two- and three-compartment models considered earlier fall into this class. While a killing agent which is active during cell division constitutes the only control considered in the two-compartment model, Model A, also two three-compartment models, Models...