JACIII Vol.19 No.5 pp. 670-675
doi: 10.20965/jaciii.2015.p0670


Multi-Dimension Uncertain Linear Quadratic Optimal Control with Cross Term

Yuefen Chen*,** and Bo Li*

*Department of Applied Mathematics, Nanjing University of Science and Technology
Nanjing 210094, China
**College of Mathematics and Information Science, Xinyang Normal University

Xinyang 464000, China

February 26, 2015
June 30, 2015
September 20, 2015
LQ optimal control, cross term, canonical process, equation of optimality

In this paper, we consider a multi-dimension uncertain linear quadratic (LQ) optimal control with cross term. With the aid of the equation of optimality of a general multi-dimension uncertain optimal control, we present a necessary and sufficient condition for the existence of optimal linear feedback optimal control which is associated with a Riccati differential equation. Moreover, some properties of the solution for the Riccati differential equation are discussed. Furthermore, the uniqueness of the feedback optimal control for the uncertain linear quadratic optimal control with cross term is proved. Finally, as an application, an example is presented to illustrate the theory obtained.

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Last updated on Jun. 29, 2017