High-performance LQR control for continuous time systems with redundant control inputs

Abstract

This paper investigates the linear quadratic regulator (LQR) problem for continuous-time linear systems with redundant control inputs. The LQR control problem has been widely studied, but due to technical difficulties, there is little advance in the study of adding input redundancies. To address this problem, a convergent matrix series, the limit of a monotonically decreasing sequence, is first presented as an upper bound of the symmetric positive definite solution of a class of continuous algebraic Riccati equations (CAREs). Compared with the existing studies on this topic, the obtained bounds are more precise. Moreover, by utilising these upper bounds in the LQR problem of adding input redundancies, a class of sufficient conditions is presented to decrease the quadratic performance index. Finally, the corresponding numerical examples are given to illustrate the effectiveness of our results and compare them with the existing results. Meanwhile, some simulation experiments show that systems with redundant control inputs have good control performance.

Keywords:

• Continuous algebraic Riccati equation
• feedback matrix
• redundant optimal control
• upper matrix bound

Disclosure statement

No potential conflict of interest was reported by the author(s).

Data availability statement

All data included in this study are available upon request by contact with the corresponding author.

Additional information

Funding

The work is supported partly by National Natural Science Foundation of China (Grant No. 11971413) and Postgraduate Scientific Research Innovation Project of Hunan Province (Grant No. CX20210513).