Advanced Search

Query:

Fill in the form and click »Search«...

Format:

Display: entries per page entries

Zbl 1166.93025
Smyshlyaev, Andrey; Krstic, Miroslav
Boundary control of an anti-stable wave equation with anti-damping on the uncontrolled boundary. (English)
[J] Syst. Control Lett. 58, No. 8, 617-623 (2009). ISSN 0167-6911

Summary: Much of the boundary control of wave equations in one dimension is based on a single principle -- passivity -- under the assumption that control is applied through Neumann actuation on one boundary and the other boundary satisfies a homogeneous Dirichlet boundary condition. We have recently expanded the scope of tractable problems by allowing destabilizing anti-stiffness (a Robin type condition) on the uncontrolled boundary, where the uncontrolled system has a finite number of positive real eigenvalues. In this paper we go further and develop a methodology for the case where the uncontrolled boundary condition has anti-damping, which makes the real parts of all the eigenvalues of the uncontrolled system positive and arbitrarily high, i.e., the system is ``anti-stable'' (exponentially stable in negative time). Using a conceptually novel integral transformation, we obtain extremely simple, explicit formulae for the gain functions. For the case with only boundary sensing available (at the same end with actuation), we design backstepping observers which are dual to the backstepping controllers and have explicit output injection gains. We then combine the control and observer designs into an output-feedback compensator and prove the exponential stability of the closed-loop system.

MSC 2000:: *93D21 Adaptive and robust stabilization
93C20 Control systems governed by PDE
35L20 Second order hyperbolic equations, boundary value problems
35B37 PDE in connection with control problems

Keywords: distributed parameter systems; backstepping; boundary control; wave equation

Comment on this Item PDF MathML XML ASCII DVI PS BibTeX Online Ordering Article Journal

	Scientific prize winners of the ICM 2010
	Overhang
	Lie groups, physics and geometry. An introduction for physicists, engineers and chemists.

Advanced Search

Zentralblatt MATH Berlin [Germany]