Paper:

# Discrete-Time Uncertain LQ Optimal Control with Indefinite Control Weight Costs

## Yuefen Chen^{*,†} and Liubao Deng^{**}

^{*}College of Mathematics and Information Science, Xinyang Normal University

Xinyang 464000, China

^{**}School of Finance, Anhui University of Finance and Economics

Bengbu 233030, China

^{†}Corresponding author

This paper deals with a discrete-time uncertain linear quadratic (LQ) optimal control, where the control weight costs are indefinite . Based on Bellman’s principle of optimality, the recurrence equation of the uncertain LQ optimal control is proposed. Then, by using the recurrence equation, a necessary condition of the optimal state feedback control for the LQ problem is obtained. Moreover, a sufficient condition of well-posedness for the LQ problem is presented. Furthermore, an algorithm to compute the optimal control and optimal value is provided. Finally, a numerical example to illustrate that the LQ problem is still well-posedness with indefinite control weight costs.

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