Plenary lecture 3: multitime dynamic programming for curvilinear integral actions
Constantin Udrişte · International Conference on Systems · 2009
This paper introduces a new type of dynamic programming PDEs for optimal control problems with performance criteria involving curvilinear integrals. The main novel feature of the multitime dynamic programming PDEs, relative to the standard Hamilton-Jacobi-Bellman PDEs, is that they are 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 PDEs system that may be viewed as a feedback law. In the case of performance criteria involving curvilinear integrals with quadratic integrands, the new equations lead to multitime variants of the Riccati equation. Section 1 shows how a multitime control dynamics determines the multitime Hamilton-Jacobi-Bellman PDEs via the value function. Section 2 describes a two-time dynamics with nine velocities. Section 3 describes the connection between multitime dynamic programming and the multitime maximum principle. Section 4 analyzes the linear regulator problems.