A unified study of the redundant control input problem with different conditions in the stabilizable case

Abstract

This paper investigates the redundant control input problem in the sense of linear quadratic regulator optimal control. Increasing redundant control inputs leads to a decrease in the quadratic performance index. However, in some cases, this also increases the norm of the feedback matrix, resulting in actuator saturation. To solve the problem, a comparative analysis of the latest research results on the redundant control input problem under different conditions is first presented. Secondly, new tighter upper bounds of the positive (semi-)definite solution of the continuous algebraic Riccati equation (CARE) corresponding to the redundant control input problem are studied uniformly in the stabilizable case. Thirdly, based on them, a class of sufficient conditions to guarantee that the norm of the feedback matrix decreases is presented. Finally, numerical experiments demonstrate the effectiveness and superiority of our conclusions. Meanwhile, a simulation experiment demonstrates that systems with redundant control inputs can achieve good control performance.

Keywords:

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

Acknowledgments

We thank the editor for valuable discussion and three anonymous referees for insightful suggestions.

Disclosure statement

The authors declare that there are no relevant financial or non-financial competing interests to report in this paper.

Additional information

Funding

The work is supported partly by the National Natural Science Foundation of China [grant number 11971413] and Postgraduate Scientific Research Innovation Project of Hunan Province [grant number CX20210513].