Seminar in Mathematical Modeling and Analysis - Bart Taub

The seminars in Mathematical Modeling and Analysis are aimed at researchers, employees, and students.

This week's seminar is given by Bart Taub, University of Glasgow.

Abstract: We explore the impact of a constraint restricting the switching of an input process in optimal control. We motivate the model with an application to risk-sharing contracts in which the no-switching constraint is equivalent to no-defection constraints. We bring several techniques to bear to determine and analyse the solution: state space methods, Nevanlinna-Pick interpolation, Wiener-Hopf methods, and the fundamental equivalence of H∞ and H2 control as established by Sideris. Our fundamental finding is that the switching constraint is equivalent to an H∞ constraint. The effect of the constraint is to add a pole to the optimal control in addition to the pole arising naturally from the basic problem, and this affects the persistence of the output process.