Nonlinear control in the year 2000. Vol. 1. Papers from the 2nd workshop of the nonlinear control network, Paris, France, June 5--9, 2000 (Q5934762)

This book is the first of a pair of volumes providing a written version of talks delivered at a workshop of the ``Nonlinear Control Network'' held in Paris in the summer of 2000. The goal is to present recent developments in nonlinear control and to suggest perspectives for the future. The authors present many times the results of their research published elsewhere. The main editors feel somewhat uncomfortable in providing a classification and the publications are not ordered by theme but alphabetically according to the names of the authors (volume one from \(A\) to \(K\)) but since there are often several authors per paper, the rule is not clear. One may follow a distinction theory-applications; however the boundary is not always sharp and applications may have contacts with different theoretical developments. There is a strong representation of the differential geometric control area in particular in connection with optimal control and Hamiltonian dynamics. This amounts to more than the quarter of the titles of this volume and is certainly not representative of the proportion published in the control journals (even when restricting to the nonlinear domain). The publication of C. Byrnes which presents original ideas related to stabilization to sets and bifurcation of the zero dynamics relying on the qualitative dynamics methods is quite isolated. Eight publications are devoted to stability and stabilization (not including the one of C. Byrnes). Five publications treat the topic of observability. A group consists of areas related to design (QFT (1), PID (1), sampled-data systems (1), discretization and sliding mode (1), adaptive control (3)) and another of applications (6) (robotics, distributed architecture for teleoperation over the internet, controllability of numerical eigenvalue algorithms (but the application aspects motivate and the treatment is theoretical), induction machines (2), power generator). Finally, only two publications use functional analysis (Diffusive representation of nonlinear fractional systems, Eigenstructure of nonlinear Hankel operators). These distinctions seem to minimize the overlaps but a few publications have connections with two domains like the one on flatness for DC drives, the one on state detection and stability and finally the one which develops an observer view for synchronization. The differential geometric aspects focus on sub-Riemannian geometry (with studies involving sub-analyticity and regularity, the properties of curves (Jacobi curves, curves on the Lie group SE(3), complexity aspects) and also on optimal control (symmetries including the publication of J. Baras on their impact on the PDEs for nonlinear filtering and their relation to the dynamic programming equations, singular situations). One publication deals with controllability on Lie groups. Contents: Tarek Ahmed-Ali, Frédéric Mazenc and Françoise Lamnabhi-Lagarrigue, Disturbance attenuation for discrete-time feedfoward nonlinear systems (1--17); Alessandro Astolfi and Laura Menini, Further results on decoupling with stability for Hamiltonian systems (19--51); Georges Bastin, Issues in modelling and control of mass balance systems (53--74); Nils Berglund and Klaus R. Schneider, Control of dynamic bifurcations (75--93); Pierre-Alexandre Bliman, Extension of Popov criterion to time-varying nonlinearities: LMI, frequential and graphical conditions (95--114); Fritz Colonius and Marco Spadini, Uniqueness of control sets for perturbations of linear systems (115--135); Ludovic Faubourg and Jean-Baptiste Pomet, Design of control Lyapunov functions for ``Jurdjevic-Quinn'' systems (137--150); Francisco Gordillo, Gerardo Escobar and Javier Aracil, Bifurcation analysis of a power factor precompensator (151--164); Lars Grüne, Stabilization by sampled and discrete feedback with positive sampling rate (165--182); Erjen Lefeber, Anders Robertsson and Henk Nijmeijer, Linear controllers for tracking chained-form systems (183--199); Luc Moreau and Dirk Aeyels, Asymptotic methods in stability analysis and control (201--213); Pascal Morin and Claude Samson, Robust point-stabilization of nonlinear affine control systems (215--237); Romeo Ortega, Arjan J. van der Schaft and Bernhard M. Maschke, Stabilization of port-controlled Hamiltonian systems via energy balancing (239--260); Pierre Rouchon and Joachim Rudolph, Invariant tracking and stabilization: problem formulation and examples (261--273); Kurt Schlacher and Andreas Kugi, Control of mechanical structures by piezoelectric actuators and sensors (275--292); Stefano Stramigioli, A novel impedance grasping strategy as a generalized Hamiltonian system (293--324); Héctor J. Sussmann, A nonsmooth hybrid maximum principle (325--354); John Tsinias and John Spiliotis, A converse Lyapunov theorem for robust exponential stochastic stability (355--374); Bart Wams, Miguel Ayala Botto, Ton van den Boom and José Sá da Costa, LMIs for robust stable neural model-based control (375--387). The articles of this volume will indexed individually.