Plenary lecture 3: multi-time dynamic programming for multiple integral actions
Constantin Udrişte · 2009
This paper introduces a new type of dynamic programming PDE for optimal control problems with performance criteria involving multiple integrals. The main novel feature of the multitime dynamic programming PDE, relative to the standard Hamilton-Jacobi-Bellman PDE, is that it is connected to the multitime maximum principle. In other words, we present an interesting and useful connection between the multitime maximum principle and the multitime dynamic programming, characterizing the optimal control by means of a multitime Hamilton-Jacobi-Bellman PDE system that may be viewed as a feedback law. In the case of performance criteria involving multiple integrals with quadratic integrands, the new equations lead to multitime variant of the Riccati equation. Section 1 introduces the multitime Hamilton-Jacobi PDE from geometrical point of view. Section 2 shows how a multitime control dynamics determines the multitime Hamilton-Jacobi-Bellman PDE via the value functions. Section 3 describes the connection between multitime dynamic programming and the multitime maximum principle.