Advanced Search

Query:

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

Format:

Display: entries per page entries

Zbl 1024.93048
Bressan, A.
Singularities of stabilizing feedbacks. (English)
[J] Rend. Semin. Mat., Torino 56, No.4, 87-104 (1998). ISSN 0373-1243

The paper deals with the stabilization problem of finite-dimensional control systems in the case of discontinuous feedback controls. The study is motivated by the fact that ODEs associated with such systems might not have any Carathéodory solution. Two main directions are identified for approaching this topic: (i) the use of arbitrary feedback controls, which requires adequate definitions for the generalized solutions of discontinuous ODEs, (ii) the use of a particular class of feedback controls, which allows considering solutions in the usual Carathéodory sense. Approach (i) relies on various definitions of generalized solutions found in the literature and their possible application to feedback stabilization. Approach (ii) exploits previous works of the same author, referring to patchy vector fields [with {\it F. Ancona}, ESAIM, Control Optim. Calc. Var. 4, 445-471 (1999; Zbl 0924.34058)] and directionally continuous vector fields [with {\it G. Colombo}, Boll. Unione Mat. Ital. (7) B 4, 295-311 (1990; Zbl 0709.34003)]. Some open problems related to approach (ii) are formulated in the last section of the paper.
[Octavian Pastravanu (Iasi)]

MSC 2000:: *93D15 Stabilization of systems by feedback
34A36 Discontinuous equations
93C10 Nonlinear control systems

Keywords: stabilizing feedback; discontinuous ODE's; Carathéorody solution; patchy vector fields; directionally continuous vector fields

Citations: Zbl 0924.34058; Zbl 0709.34003

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