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Hamilton-Jacobi theory for stratified systems and for problems with state constraints and reflected dynamics

Mercoledi' 25 gennaio 2012 - Peter R. Wolenski

ARGOMENTI: Seminari

SEMINARI DI EQUAZIONI DIFFERENZIALI E APPLICAZIONI
Mercoledi' 25 gennaio 2012 alle ore 12:30 in aula 2BC30, Peter R. Wolenski (Louisiana State University) terra' un seminario dal titolo "Hamilton-Jacobi theory for stratified systems and for problems with state constraints and reflected dynamics".

-Abstract
Bressan and Hong recently introduced an optimal control model (called a stratified system) whose dynamics have structured discontinuities in the state variable. Their main result was a viscosity-type characterization of the value function which required different Hamiltonian functions in the definitions of lower and upper solution. We shall discuss this model in detail, and by inserting additional assumptions on the data, present a characterization of the value function as the lsc solution to a bilateral Hamilton-Jacobi equation (utilizing only one Hamiltonian function). Our methods also provide a new approach to state constrained problems and to problems with reflected dynamics, in which we show how so-called boundary trajectories can be analyzed directly rather than require approximation by tracking tools.

Rif. int. M. Bardi, C. Marchi, G. Colombo

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