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Discrete-time indefinite stochastic linear quadratic optimal control with second moment constraints. (English) Zbl 1407.93435
Summary: This paper studies the discrete-time stochastic linear quadratic (LQ) problem with a second moment constraint on the terminal state, where the weighting matrices in the cost functional are allowed to be indefinite. By means of the matrix Lagrange theorem, a new class of generalized difference Riccati equations (GDREs) is introduced. It is shown that the well-posedness, and the attainability of the LQ problem and the solvability of the GDREs are equivalent to each other.

MSC:
93E20 Optimal stochastic control
93C55 Discrete-time control/observation systems
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