Backstepping Control of Linear 2 × 2 Hyperbolic Systems with Dynamic Boundary Conditions. Issue 1 (July 2017)

• Record Type: Journal Article
• Authors: Deutscher, J.; Gehring, N.; Kern, R.
• Is Part Of: IFAC-PapersOnLine. Volume 50:Issue 1(2017)
• Page Start: 4522
• Page End: 4527
• Publication Date: 2017-07
• Subjects: Distributed-parameter systems -- hyperbolic systems -- backstepping -- boundary control -- coupled PDE-ODE systems; Automatic control -- Periodicals; 629.805
• DOI: 10.1016/j.ifacol.2017.08.724
• Languages: English
• ISSNs: 2405-8963

Abstract

Abstract: In this paper the boundary control of linear 2 × 2 hyperbolic systems with spatially-varying coefficients and dynamic boundary conditions is considered. This leads to the stabilization problem for a bidirectionally coupled PDE-ODE system. For its solution a two-step backstepping approach is developed, that yields the usual kernel equations and additional decoupling equations of simple form. The latter can be traced back to a Volterra integral equation of the second kind, which is directly solvable with a successive approximation. The results of the paper are illustrated for a heavy rope with load.