Trajectories of a Control System in a Cone

Meeting Details

For more information about this meeting, contact Leonid Berlyand, Mark Levi, Alexei Novikov.

Speaker: Richard Vinter, Imperial College London

Abstract: Suppose we have a a solution to a differential inclusion (an F-trajectory). How close is it to the class of F-trajectories that evolve in a closed subset of the state space (the so-called `feasible' F-trajectories)? This question is of great importance in state constrained optimal control and system theory. Whether there exist suitable estimates of the distance to the set of feasible F-trajectories has implications for the non-degeneracy of standard optimality conditions, the characterization of the minimum cost function in terms of solutions to the Hamilton Jacobi equation and the reformulation of optimal control problems to improve their conditioning for numerical solution. The talk will focus on cases when the state constraint set has a edge (intersection of two half-spaces, for example). It is demonstrated by means of a recent counter-example that, contrary to expectations, a linear estimate of the distance in terms of the state violation h is not valid. We report the results of recent research, establishing the validity of 'superlinear' h log h estimates, and the optimality of the h log h estimate structure; also on the special cases for which linear estimates are now known to hold, notably that when the velocity set is strictly convex. We discuss the implications of these findings for systems theory and optimal control.

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Room Reservation Information

Room Number: 106 McAllister

Date: 10/27/2009

Time: 4:00pm - 4:55pm