Finite-dimensional observer-based controller for linear 1-D heat equation: an LMI approach⁎Supported by Israel Science Foundation (grant no. 673/19) and by C. and H. Manderman Chair at Tel Aviv University. Issue 2 (2020)

• Record Type: Journal Article
• Authors: Katz, R.; Fridman, E.
• Is Part Of: IFAC-PapersOnLine. Volume 53:Issue 2(2020)
• Page Start: 7611
• Page End: 7616
• Publication Date: 2020
• Subjects: Distributed parameter systems -- heat equation -- observer-based control -- modal decomposition -- Lyapunov method; Automatic control -- Periodicals; 629.805
• DOI: 10.1016/j.ifacol.2020.12.1360
• Languages: English
• ISSNs: 2405-8963

Abstract

Abstract: The objective of the present paper is finite-dimensional observer-based control of 1-D linear heat equation with constructive and easily implementable design conditions. We propose a modal decomposition approach in the cases of bounded observation and control operators (i.e, non-local sensing and actuation). The dimension of the controller is equal to the number of modes which decay slower than a given decay rate δ > 0. The observer may have a larger dimension N. The observer and controller gains are found separately of each other. We suggest a direct Lyapunov approach to the full-order closed-loop system and provide linear matrix inequalities (LMIs) for finding N and the exponential decay rate of the closed-loop system. Different from some existing qualitative methods, we prove that the LMIs are always feasible for large enough N leading to easily verifiable conditions. A numerical example demonstrates the efficiency of our method that gives non-conservative bounds on N and δ .