Optimization and Systems Theory Seminar
Friday, March 16, 2001, 11.00-12.00, Room 3721, Lindstedtsvägen 25


Leonid Engelson
Centre for Traffic Simulation Research
KTH
E-mail: lee@infra.kth.se

Projected dynamical systems with delays: Definition, stability and applications

The classical dynamical systems theory assumes that the right-hand side of the ordinary differential equation is continuous and therefore can not handle problems with constraints.

Seven years ago, Anna Nagurney introduced Projected Dynamical Systems that recognise the constrained state space. She proved basic existence and uniqueness theorems and developed methods for stability analysis of such systems. The results were applied to investigate dynamic properties of equilibrium problems in economics and transportation.

We extend some of Nagurney'ss results to dynamical systems with delays. The right-hand side of the delay equation is not continuous due to the projection operator that forces the system to stay within the feasible set. Stationary points of the equation coincide with solutions to the associated variational inequality problem. We show that stability of a regular stationary point can be investigated via a lower dimension ordinary dynamical equation with delay. Possible applications of the stability criterion are illustrated by an example of traffic network with a reactive route guidance system.

Calendar of seminars
Last update: March 6, 2001 by Anders Forsgren, anders.forsgren@math.kth.se.