JACIII Vol.20 No.4 pp. 633-639
doi: 10.20965/jaciii.2016.p0633


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

January 10, 2016
May 6, 2016
Online released:
July 19, 2016
July 19, 2016
uncertain LQ optimal control, indefinite control weight costs, well-posedness

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.

  1. [1] R. E. Kalman, “Contributions to the theory of optimal control,” Boletin de la Sociedad Matematica Mexicana, Vol.5, No.2, pp. 102-119, 1960.
  2. [2] X. Su, L. Wu, P. Shi, et al., “A novel approach to output feedback control of fuzzy stochastic systems,” Automatica, Vol.50, No.12, pp. 3268-3275, 2014.
  3. [3] R. Chaichaowarat and W. Wannasuphoprasit, “Linear quadratic optimal regulator for steady state drifting of rear wheel drive vehicle,” J. of Robotics and Mechatronics, Vol.27, pp. 225-234, 2015.
  4. [4] W. M. Wonham, “On a matrix Riccati equation of stochastic control,” SIAM J. on Control and Optimization, Vol.6, No.4, pp. 681-697, 1968.
  5. [5] Y. Hu and X. Y. Zhou, “Constrained stochastic LQ control with random coefficients, and application to portfolio selection,” SIAM J. on Control and Optimization, Vol.44, No.2, pp. 444-466, 2005.
  6. [6] M. Athens, “Special issues on linear-quadratic-gaussian problem,” IEEE Trans. on Automatic Control, Vol.AC-16, pp. 527-869, 1971.
  7. [7] B. Liu, “Uncertainty Theory,” 2nd Ed., Springer-Verlag, Berlin, 2007.
  8. [8] Y. Zhu, “Uncertain optimal control with application to a portfolio selection model,” Cybernetics and Systems, Vol.41, No.7, pp. 535-547, 2010.
  9. [9] L. Sheng, Y. Zhu, and T. Hamalaonen, “An uncertain optimal control with Hurwicz criterion,” Applied Mathematics and Computation, Vol.224, pp. 412-421, 2013.
  10. [10] Y. Chen and B. Li, “Multi-dimension uncertain linear quadratic optimal control with cross term,” J. of Advanced Computational Intelligence and Intelligent Informatics (JACIII), Vol.19, No.5, pp. 670-675, 2015.
  11. [11] H. Yan and Y. Zhu, “Bang-bang control model for uncertain switched systems,” Applied Mathematical Modelling, Vol.39, No.10-11, pp. 2994-3002, 2015.
  12. [12] B. Liu, “Some research problems in uncertainy theory,” J. of Uncertain Systems, Vol.3, No.1, pp. 3-10, 2009.
  13. [13] B. Liu, Uncertainty Theory: A Branch of Mathematics for Modeling Human Uncertainty, Springer-Verlag, Berlin, 2010.
  14. [14] Y. Zhu, “Functions of uncertain variables and uncertain programming,” J. of Uncertain Systems, Vol.6, No.4, pp. 278-288, 2012.
  15. [15] M. Athans, “The matrix minimum principle,” Information and Control, Vol.11, pp. 592-606, 1968.

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Last updated on Mar. 28, 2017