Dyanmic Programming in Control Theory: An Introduction (II)
許順吉教授Department of Mathematics, National Central University, 中央大學數學系 早上 10:00–12:00 鴻經館 430 室In the first talk we consider deterministic control problem. We formulate the dynamicprogramming priniciple. For discrete time model, in principle one can use this tosolve the problem. That is, a complicated problem due to longer time period becomeseasier to treat by consider the problem in several steps, in each step we have a simplerproblem to solve. In continuous time model, the same idea can be applied, but it ismore useful to use the dynamic programming principle in an infinitesimal form. Theresult is the HJB (Hamilton-Jacobi-Bellman) equation, which is a nonlinear partialdifferential equation. In the second talk, we discuss HJB equation ,the generalizedsolution and verification theorem . The latter is a theorem stating that a solution ofcontrol problem can be derived from a solution of HJB equation.. We will alsointroduce viscosity solution. We discuss the uniqueness of the solution.
Reference：
1. Hanspeter Schmidli, Stochastic Control in Insurance
2. W. H. Fleming and H.M. Soner, Control Markov Processes and Viscosity Solutions