Robust stability condition of an adaptive control for a class of uncertain discrete-time SISO system

Article type: Research Article

Authors: Jiang, Xuecheng^{a; *} | He, Dongwei^b

Affiliations: [a] Department of Electronic, Minjiang University, Fuzhou, Fujian, China | [b] Department of Electronic Information, Fujian University of Technology, Fuzhou, Fujian, China

Correspondence: [*] Corresponding author: Jiang Xuecheng, Deptartment of Electronic, Minjiang University, Fuzhou 350208, Fujian, China. %****␣jcm-20-jcm204209_temp.tex␣Line␣25␣**** Tel.: +86 139 6082 5927; E-mail: [email protected].

Abstract: For a class of uncertain discrete-time linear single-input and single-output (SISO) system with control inputs without disturbances, an adaptive control strategy is proposed, which includes a compensation controller based on normalized least mean square (LMS) parameter identification algorithm and a state feedback controller. Then the state feedback controller is designed on base of the discrete-time algebraic Riccati equation (DARE) of nominal parameter system. But the performance of the control system will deteriorate by relying solely on this state feedback controller when the system parameters change. So designing a feed-forward compensation controller based on the parameter error makes the original design still valid after the parameters change. And sufficient stability condition and error bound of uncertain parameters that satisfy the DARE of uncertain linear systems is also derived in detail.

Keywords: Adaptive control, discrete-time uncertain linear systems, Riccati function, error bound of uncertain parameters, least mean square

DOI: 10.3233/JCM-204209

Journal: Journal of Computational Methods in Sciences and Engineering, vol. 20, no. 4, pp. 1155-1162, 2020