### Saturday, May 9

## MS22

Dynamic Programming Methods for Optimal Control of Nonlinear Distributed Parameter Systems

3:30 PM-6:00 PM

*Salon D*

The dynamic programming approach for optimal control problems consists of recovering information (optimality conditions, feedback formulas for optimal controls, etc.) by looking at the properties of the associated value function which is characterized as the unique solution of the Hamilton-Jacobi-Bellman equation. Among the methods that have been developed to study this equation is the viscosity solution approach, especially for finite dimensional problems. Recently, many results have been proved also for infinite-dimensional problems of interest for applications, like boundary control problems for parabolic systems. The speakers will discuss many challenging problems that are under investigation, such as numerical approximations, control of hyperbolic systems, and control of fluids.

**Organizers: Piermarco Cannarsa**

*Universita di Roma "Tor Vergata," Italy*

**Fausto Gozzi**

*Universita' di Pisa, Italy*

**3:30 Qualitative and Numerical Study of a Semilinear Boundary Control Problem for a Fishery Model**
- Piermarco Cannarsa, Organizer,
*Roberto Ferretti*, and Andrea Schiaffino, Universita di Roma "Tor Vergata," Italy
**3:30 Singularities of Semiconcave Functions in Banach Spaces and Applications**
- Paolo Albano, Second University of Rome
**4:00 Some Regularity Properties of the Minimum Time Function**
- Fausto Gozzi, Organizer and
*Paola Loreti*, Istituto per le Applicazioni del Calcolo "Mauro Picone" Consiglio Nazionale delle Ricerche, Italy
**4:30 Singularities of the Minimum Time Function in Infinite Dimensions**
- Paolo Albano, Piermarco Cannarsa, Organizer, and
*Carlo Sinestrari*, Universita di Roma "Tor Vergata," Italy
**5:00 Fully Nonlinear Second Order Equations in Infinite Dimensions and Optimal Control of Stochastic PDE's**
- Fausto Gozzi, Organizer; and
*Andrzej Swiech*, Georgia Institute of Technology
**5:30 Parabolic Equations in Infinite Dimensions and Applications to Stochastic Control Problems**
- Fausto Gozzi, Organizer

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*MMD, 5/5/98*