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HJB-POD-based feedback design for the optimal control of evolution problems. (English) Zbl 1058.35061

Summary: The numerical realization of closed loop control for distributed parameter systems is still a significant challenge and in fact infeasible unless specific structural techniques are employed. In this paper we propose the combination of model reduction techniques based on proper orthogonal decomposition (POD) with the numerical treatment of the Hamilton-Jacobi-Bellman (HJB) equation for infinite horizon optimal control problems by a modification of an algorithm originated by Gonzales and Rofman and further developed by Falcone and Ferretti. The feasibility of the proposed methodology is demonstrated numerically by means of optimal boundary feedback control for the Burgers equation with noise in the initial condition and in the forcing function.

MSC:

35F20 Nonlinear first-order PDEs
49L20 Dynamic programming in optimal control and differential games
93D15 Stabilization of systems by feedback
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