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Study on indefinite stochastic linear quadratic optimal control with inequality constraint. (English) Zbl 1397.93237

Summary: This paper studies the indefinite stochastic linear quadratic (LQ) optimal control problem with an inequality constraint for the terminal state. Firstly, we prove a generalized Karush-Kuhn-Tucker (KKT) theorem under hybrid constraints. Secondly, a new type of generalized Riccati equations is obtained, based on which a necessary condition (it is also a sufficient condition under stronger assumptions) for the existence of an optimal linear state feedback control is given by means of KKT theorem. Finally, we design a dynamic programming algorithm to solve the constrained indefinite stochastic LQ issue.

MSC:

93E20 Optimal stochastic control
49N10 Linear-quadratic optimal control problems
49J55 Existence of optimal solutions to problems involving randomness
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