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Passivity-Based Control of Lagrangian and Hamiltonian Systems : From Asymptotic Inversion to Energy-balancing

Motivated by the need to develop a performance theory for nonlinear control systems we have explored in the last few years the connections between energy balancing and stabilization. Energy-balance is intimately related with passivity, which we have extensively studied within the context of Euler-Lagrange (EL) systems. It turns out, however, that in general (beyond regulation problems in mechanics) their interplay is best revealed using the Hamiltonian formulation. Indeed, we will show in this talk that, in applications where we have to "shape" the kinetic energy, the energy interpretation of passivity-based control of EL systems is lost. Although in these cases the methodology based on the EL description still provides us with "passifying" controllers, the EL structure is not preserved in closed-loop and the stabilization mechanism is now akin to an asymptotic inversion, instead of energy-balancing. We prove then that adopting a Hamiltonian perspective we can -under some conditions- recover the nice features of structure invariance and stabilization via energy-balancing. Two additional benefits of the new formulation are that some obstacles for stabilization required in the EL approach - like stable invertibility - are now avoided. Furthermore, the new technique is quite systematic an amenable for symbolic computations.

Type of Seminar:
Special Series on Nonlinear Systems
Prof. Romeo Ortega
Laboratoire des Signaux et Systèmes, CNRS-ESE, Gif-sur-Yvette, France
Apr 07, 1999   13:15

ETH Zurich, Building VAW Room B1, Gloriastrasse 37-39, 8006 Zurich
Contact Person:

Prof. M.Morari
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Biographical Sketch:
Romeo Ortega was born in Mexico. He obtained his BSc in Electrical and Mechanical Engineering from the National University of Mexico, Master of Engineering from Polytechnical Institute of Leningrad, USSR, and the Docteur D`Etat from the Politechnical Institute of Grenoble, France in 1974, 1978 and 1984 respectively. He then joined the National University of Mexico, where he worked until 1989. He was a Visiting Professor at the University of Illinois in 1987-88 and at the McGill University in 1991-1992, and a Fellow of the Japan Society for Promotion of Science in 1990-1991. He has been a member of the French National Researcher Council (CNRS) since June 1992. Currently he is in the Laboratoire de Signaux et Systemes (SUPELEC) in Paris. His research interests are in the fields of nonlinear and adaptive control, with special emphasis on applications. Dr Ortega is a Fellow Member of the IEEE. He was the Chairman of the IEEE Working Group on Adaptive Control and Systems Identification and is currently Chairman of the IFAC Technical Committee on Adaptive Control and Tuning and chairman of the Automatica Paper Prize Award Committee. He is an Associate Editor of Systems and Control Letters, International Journal of Adaptive Control and Signal Processing, European Journal of Control and IEEE Transactions on Control Systems Technology.