Multitime linear-quadratic regulator problem based on curvilinear integral
نویسندگان
چکیده
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 Riccati PDE that may be viewed as a feedback law. Section 1 recalls the theory of an optimal control problem with curvilinear 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 multitime maximum principle. Section 3 describes the linear-quadratic regulator problem via multitime Hamilton-Jacobi-Bellman PDEs. M.S.C. 2000: 49L20, 49K20, 93C20.
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