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Optimistic value model of indefinite LQ optimal control for discrete-time uncertain systems. (English) Zbl 1391.49066
Summary: Uncertainty theory is a branch of mathematics which provides a new tool to deal with the human uncertainty. Based on uncertainty theory, this paper proposes an optimistic value model of discrete-time linear quadratic (LQ) optimal control, whereas the state and control weighting matrices in the cost function are indefinite, the system dynamics are disturbed by uncertain noises. With the aid of the Bellman’s principle of optimality in dynamic programming, we first present a recurrence equation. Then, a necessary condition for the state feedback control of the indefinite LQ problem is derived by using the recurrence equation. Moreover, a sufficient condition of well-posedness for the indefinite LQ optimal control is given. Finally, a numerical example is presented by using the obtained results.

MSC:
49N10 Linear-quadratic optimal control problems
93C55 Discrete-time control/observation systems
93C41 Control/observation systems with incomplete information
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