On nonlinear controllability and series expansions for Lagrangian systems with dissipative forces

• Published in: IEEE transactions on automatic control Vol. 47; no. 8; pp. 1396 - 1401
• Main Authors: Cortes, J., Martinez, S., Bullo, F.
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.08.2002; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Applied sciences; Charge coupled devices; Charge-coupled image sensors; Computer science; control theory; systems; Control of mechanical systems; Control system analysis; Control theory. Systems; Controllability; Dissipation; Exact sciences and technology; Formalism; Fundamental areas of phenomenology (including applications); Geometry; Homogeneity; Lagrangian functions; Mathematical analysis; Motion estimation; Nonlinearity; Physics; Robot sensing systems; Robot vision systems; Robotics and automation; Series expansion; Shape; Solid dynamics (ballistics, collision, multibody system, stabilization...); Solid mechanics; Vectors (mathematics); Series expansion; Controllability; Control; Non linear system; Mechanical system
• ISSN: 0018-9286; 1558-2523
• DOI: 10.1109/TAC.2002.801187

This paper presents series expansions and nonlinear controllability results for Lagrangian systems subject to dissipative forces. The treatment relies on the assumption of dissipative forces of linear isotropic nature. The approach is based on the affine connection formalism for Lagrangian control systems, and on the homogeneity property of all relevant vector fields.