Performance Improvement of Discrete-time Linear Control Systems Subject to Varying Sampling Rates Using the Tikhonov Regularization Method

• Published in: International journal of automation and computing Vol. 17; no. 3; pp. 453 - 463
• Main Authors: Pazos, Fernando Agustín, Zanini, Anibal, Bhaya, Amit
• Format: Journal Article
• Language: English
• Published: Beijing Institute of Automation, Chinese Academy of Sciences 01.06.2020; Springer Nature B.V
• Subjects: Automation; CAE) and Design; Closed loops; Communication; Computer Applications; Computer-Aided Engineering (CAD; Control; Control systems design; Controllability; Controllers; Design; Discrete time systems; Dynamical systems; Engineering; Error functions; Feedback control; Hilbert space; Ill posed problems; Linear control; Linear systems; Mechatronics; Regularization; Regularization methods; Research Article; Robotics; Robust control; Sampling; Stability; State feedback; varying sampling rates; networked control systems; discrete-time control systems; Tikhonov regularization; Discrete-time switched systems
• ISSN: 1476-8186; 2153-182X; 1751-8520; 2153-1838
• DOI: 10.1007/s11633-019-1205-8

Methods to stabilize discrete-time linear control systems subject to variable sampling rates, i.e., using state feedback controllers, are well known in the literature. Several recent works address the use of the Tikhonov regularization method, originally designed to attenuate the noise effects on ill-posed problems, with the aim of improving performance and stabilizing approximately controllable dynamical systems. Inspired by these works, we propose the use of a feedback controller designed using the Tikhonov method to regularize discrete-time linear systems subject to varying sampling rates. The goal is to minimize an error function, thus improving the performance of the closed loop system and reducing the possibility of instability. Illustrative examples show the effectiveness of the proposed method.