Multitime linear-quadratic regulator problem based on curvilinear integral
Constantin Udrişte, Ionel Ţevy · Balkan Journal of Geometry and its Applications (BJGA) · 2009
This paper interrelates the performance criteria involving path independent curvilinear integrals, the multitime maximum principle, the multitime Hamilton-Jacobi-Bellman PDEs and the multitime dynamic programming, to study the linear-quadratic regulator problems and to characterize the optimal control by means of multitime variant of the Ric- cati PDE that may be viewed as a feedback law. Section 1 recalls the theory of an optimal control problem with curvi- linear integral cost functional, the notion of maximum value function and the multitime Hamilton-Jacobi-Bellman PDEs. It explains also the connections between dynamic programming and the multitime maximum principle. Section 2 solves the linear-quadratic regulator problem via mul- titime maximum principle. Section 3 describes the linear-quadratic regu- lator problem via multitime Hamilton-Jacobi-Bellman PDEs.