Dissipativity-based observer design for a class of coupled 1-D semi-linear parabolic PDE systems. Issue 8 (2016)

• Record Type: Journal Article
• Authors: Schaum, A.; Moreno, J.A.; Meurer, T.
• Is Part Of: IFAC-PapersOnLine. Volume 49:Issue 8(2016)
• Page Start: 98
• Page End: 103
• Publication Date: 2016
• Subjects: Observer -- dissipative distributed parameter systems; Automatic control -- Periodicals; 629.805
• DOI: 10.1016/j.ifacol.2016.07.425
• Languages: English
• ISSNs: 2405-8963

Abstract

Abstract: In the present paper the dissipativity-based observer design approach is extended to a class of 1-D semi-linear parabolic PDE systems with pointwise in-domain measurement. On the basis of a modal innovation over the set of slow eigenvalues of the linear operator and the consideration of a dissipativity (sector) condition for the nonlinearity an exponential convergence condition for the estimation error is derived in form of a linear operator inequality, which is solved on the basis of an eigenfunction expansion of the linear operator. The approach is illustrated by numerical simulations for a coupled two-state semi-linear PDE system.