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
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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