Boundary control problems with convex cost and dynamic programming in infinite dimension part II: Existence for HJB
Silvia Faggian · Discrete and Continuous Dynamical Systems · 2005
This is the second of two papers on boundaryoptimal control problems with linear state equation and convex cost arising from boundary control of PDEs and the the associated Hamilton--Jacobi--Bellmanequation. In the first paper we studied necessary and sufficientconditions of optimality (Pontryagin Maximum Principle). In thissecond paper we will apply Dynamic Programming to show that thevalue function of the problem is a solution of an integral versionof the HJB equation, and moreover that it is the pointwise limitof classical solutions of approximating equations.