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Immersion and invariance: a new tool for stabilization and adaptive control of nonlinear systems

A new method to design asymptotically stabilizing and adaptive control laws for nonlinear systems is presented. The method relies upon the notions of system immersion and manifold invariance and does not require the knowledge of a (control) Lyapunov function. The construction of the stabilizing control laws resembles the construction used in nonlinear regulator theory to derive the (invariant) output zeroing manifold and its friend. The method is well suited in situations where we know a stabilizing controller of a nominal reduced order model, which we would like to robustify with respect to high order dynamics. This is achieved by designing a control law that immerses the full system dynamics into the reduced order one. We also show that in this new framework the adaptive control problem can be formulated from a new perspective that, under some suitable structural assumptions, allows to modify the classical certainty equivalent controller and derive parameter update laws such that stabilization is achieved. It is interesting to note that our construction does not require a linear parameterization, furthermore, viewed from a Lyapunov perspective, it provides a procedure to add cross terms between the parameter estimates and the plant states. Finally, it is shown that the proposed approach yields new stabilizing control laws for systems in feedback and feedforward form. We illustrate the method with several practical examples, including a mechanical system with flexibility modes, an electromechanical system with parasitic actuator dynamics and an adaptive nonlinearly parameterized visual servoing application.

Type of Seminar:
Public Seminar
Prof. Alessandro Astolfi
Politecnico of Milan and Imperial College, London
Jul 10, 2001   14:15

Contact Person:

Prof. W. Schaufelberger
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Biographical Sketch:
Alessandro Astolfi was born in Rome, Italy, in 1967. He graduated in electrical engineering from the University of Rome in 1991. In 1992 he joint ETH-Zurich where he obtained the PhD degree with Medal of Honour in 1995 with a thesis on discontinuous stabilization of nonholonomic systems. In 1996 he was awarded a Ph.D. from the University of Rome for his work on nonlinear robust control. Since 1996 he is with the Electrical and Electronic Engineering Dept. of Imperial College, London (UK), where he is currently Senior Lecturer. In 1998 he was appointed Associate Professor at the Dept. of Electronics and Information of the Politecnico of Milano (Italy). He has been visiting lecturer in "Nonlinear Control" in several universities, including ETH-Zurich (1995-1996); Terza University of Rome (1996); Rice University, Houston (1999); Kepler University, Linz (2000); SUPELEC, Paris (2001). His research interests are focused on mathematical control theory and control applications, with special emphasis for the problems of discontinuous stabilization, robust stabilization and robust control. He is author of 17 journal papers, of 9 book chapters and of 64 papers in refereed conference proceedings. He is co-editor of a book on " Modeling and Control of Mechanical systems". He is Associate Editor of Systems and Control Letters, the International Journal of Control and the European Journal of Control. He has also served in the IPC of various international conferences.