Department of Mathematics and Statistics

ANALYSIS SEMINAR

Location:

Organizers: Marian Bocea and Rafal
Goebel

Fall 2013 Analysis Seminar

Spring 2013 Analysis Seminar

Fall 2012 Analysis Seminar

Spring 2012 Analysis Seminar

Fall 2011 Analysis Seminar

Fall 2013 Analysis Seminar

Spring 2013 Analysis Seminar

Fall 2012 Analysis Seminar

Spring 2012 Analysis Seminar

Fall 2011 Analysis Seminar

Thursday, September 4 -

Abstract: In common words, the feedback stabilization problem can be stated like this: Suppose that at every initial location in the greater Chicagoland, one can print out a set of directions on how do drive to downtown Chicago. Is it then possible to put traffic signs at every intersection, so that following them will help one reach downtown, no matter where one starts? In presence of many one-way streets, extensive construction, etc., this may be a nontrivial challenge. More precisely, the feedback stabilization problem starts with a control system, which is a dynamical system with an input, or with a control variable. The control variable can be chosen by the user, with the goal of making the dynamical system behave in a desired way. The feedback stabilization problem assumes that for every initial condition there exists an open-loop control, i.e., a control as a function of time, that results in the solution from that initial condition converging to an a priori fixed equilibrium. The question is whether the same goal can be achieved with a closed-loop control, i.e., a control as the function of the state, no matter what the initial condition is. In presence of nonlinearities, constraints, etc., this may be a nontrivial challenge. The talk will be an introduction to this problem, with several easily accessible examples and a few important results.

Thursday, September 11 -

Thursday, September 18 - No Seminar

Thursday, September 25 -

Abstract: The talk will summarize the 1999 paper by Ancona and Bressan, under the same title, which presents a novel approach to the problem of feedback stabilization of an asymptotically controllable general nonlinear control system. The use of discontinuous feedback is necessary in this general case, which may lead to issues with the concept of a solution to a differential equation with a discontinuous right-hand side. Previous approaches to the problem focused on specifying a new sense in which solutions should be understood. Ancona and Bressan propose an approach in which the discontinuities are sufficiently tame, and solutions can be understood in the usual, Caratheodory, sense.

Thursday, October 2 -

Abstract: We prove that the solution of the discounted approximation of a degenerate viscous Hamilton--Jacobi equation with convex Hamiltonians converges to that of the associated ergodic problem. We characterize the limit in terms of stochastic Mather measures by naturally using the nonlinear adjoint method, and deriving a commutation lemma. Joint work with Mitake.

Thursday, October 9 -

Thursday, October 16 -

Thursday, October 23 -

Thursday, October 30 -

Thursday, November 6 -

Thursday, November 13 -

Thursday, November 20 -

Thursday, November 27 -

Thursday, December 4 -