Necessary and sufficient condition for generalized passivity, passification and application to multivariable adaptive systems

• Main Author: Hsu, Liu
• Publication Date: 2011
• Other Authors: Teixeira, Marcelo Carvalho Minhoto [UNESP], Costa, Ramon Romankevicius, Assunção, Edvaldo [UNESP]
• Format: Conference object
• Language: eng
• Source: Repositório Institucional da UNESP
• Download full: http://dx.doi.org/10.3182/20110828-6-IT-1002.03348; http://hdl.handle.net/11449/72904
• topic: Adaptive control; Generalized passivity; Multivariable systems; WSPR condition; Adaptive Control; Adaptive controllers; Factorization approach; Input vector; Input/output; Linear multivariable systems; Multi variables; Multivariable adaptive control; Overparameterization; Passification; Servoing problem; SPR systems; Strictly positive real; Sufficient conditions; Symmetry conditions; System output; Adaptive control systems; Visual servoing

Recently, a generalized passivity concept for linear multivariable systems was obtained which allows circumventing the restrictiveness of the usual passivity concept. The latter is associated with the classical SPR (Strictly Positive Real) condition whereas the new concept of passivity is associated with the so called WSPR condition and its advantage in multivariable systems is that it does not require a restrictive symmetry condition of SPR systems. As a result, it allows the design of multivariable adaptive control that, unlike some existing factorization approaches, does not imply in additional overparameterization of the adaptive controller. In this paper, we complete a previously established WSPR sufficient condition and prove that it is also necessary. We also propose some methods of passification by either premultiplying the system output tracking error vector or the system input vector by an adequate passifying matrix multiplier, so that the resulting input/output transfer function becomes WSPR. The efficiency of our proposals are illustrated by simulation utilizing a well known robotics adaptive visual servoing problem. © 2011 IFAC.