One of the key concerns in modern control theory is the design of steering strategies. The implementation of such strategies is done by a regulator. Presented here is a self-contained introduction to the mathematical background of this type of regulator design. The topics selected address the matter of greatest interest to the control community, at present, namely, when the design objective is the reduction of the influence of exogeneous disturbances upon the output of the system. In a first scenario the disturbance signal is regarded as a deterministic time series with known dynamics but unknown parameters. The design objective is then the asymptotic disturbance compensation. In a second scenario, no information about the disturbance signal is available apart from some bounds. Here, in an H-approach, control strategies are worked out which will prove efficient for all such disturbances. The intention of this book is to present ideas and methods on such a level that the beginning graduate student will be able to follow current research. New results are included, especially for nonlinear control systems, and as a service to the reader, an extensive appendix presents topics from linear algebra, invariant manifolds and calculus of variations, information which is hardly to be found in standard textbooks. Contents: Introduction * The problem of output regulation * Introduction * Problem statement * Output regulation via full information * Output regulation via full error feedback * A particular case * Well-posedness and robustness * The construction of a robust regulator * Disturbance attenuation via H-methods * Introduction * Problem statement * A characterization of the L2-gain of a linear system * Disturbance attenuation via full information * Disturbance attenuation via measured feedback * Full information regulators * Problem statement * Time-dependent control strategies * Examples * Time-independent control strategies * The local case * Nonlinear observers * Problem statement * Time-dependent observers * Error feedback regulators * Examples * Nonlinear H-techniques * Introduction * Construction of the saddle-point * The local scenario * Disturbance attenuation via linearization * Matrix equations * Linear matrix equations * Algebraic Riccati equations * Invariant manifolds * Existence theorem * Outflowing manifolds * Asymptotic phase * Convergence for T (1) * A special case * Dichotomies and Lyapunov functions * Hamilton-Jacobi-Bellman-Isaacs equation * Introduction * Method of characteristics * The equation of Isaacs * The Hamiltonian version of Isaacs' equation * Bibliography

It is a great honor and privilege to have this opportunity of celebrating the 65th birthday of Professor Antonio Ruberti by holding an International Conference on Systems, Models and Feedback. The conference, and this volume which contains its proceedings, is a tribute to Professor Ruberti in acknowledgement of his major contributions to System Theory, at a time in which this area was emerging and consolidat ing as an independent discipline, his role as a leader of the Italian academic community, his activity in promoting and fostering close scientific relations between Italian and U.S. scholars in Systems and Control. The format of this conference is inspired by a series of seminars initi ated exactly twenty years ago under the direction of Professor Ruberti, in Italy, and Professor R. R. Mohler, in the U.S. By bringing together many authoritative talents from both countries, these seminars were instrumental in promoting the expansion of System Theory in new areas, notably that of Nonlinear Control, and were the key to successful scientific careers for many of the younger attendants."

One of the key concerns in modern control theory is the design of steering strategies. The implementation of such strategies is done by a regulator. Presented here is a self-contained introduction to the mathematical background of this type of regulator design. The topics selected address the matter of greatest interest to the control community, at present, namely, when the design objective is the reduction of the influence of exogeneous disturbances upon the output of the system. In a first scenario the disturbance signal is regarded as a deterministic time series with known dynamics but unknown parameters. The design objective is then the asymptotic disturbance compensation. In a second scenario, no information about the disturbance signal is available apart from some bounds. Here, in an H-approach, control strategies are worked out which will prove efficient for all such disturbances. The intention of this book is to present ideas and methods on such a level that the beginning graduate student will be able to follow current research. New results are included, especially for nonlinear control systems, and as a service to the reader, an extensive appendix presents topics from linear algebra, invariant manifolds and calculus of variations, information which is hardly to be found in standard textbooks. Contents: Introduction * The problem of output regulation * Introduction * Problem statement * Output regulation via full information * Output regulation via full error feedback * A particular case * Well-posedness and robustness * The construction of a robust regulator * Disturbance attenuation via H-methods * Introduction * Problem statement * A characterization of the L2-gain of a linear system * Disturbance attenuation via full information * Disturbance attenuation via measured feedback * Full information regulators * Problem statement * Time-dependent control strategies * Examples * Time-independent control strategies * The local case * Nonlinear observers * Problem statement * Time-dependent observers * Error feedback regulators * Examples * Nonlinear H-techniques * Introduction * Construction of the saddle-point * The local scenario * Disturbance attenuation via linearization * Matrix equations * Linear matrix equations * Algebraic Riccati equations * Invariant manifolds * Existence theorem * Outflowing manifolds * Asymptotic phase * Convergence for T (1) * A special case * Dichotomies and Lyapunov functions * Hamilton-Jacobi-Bellman-Isaacs equation * Introduction * Method of characteristics * The equation of Isaacs * The Hamiltonian version of Isaacs' equation * Bibliography

This conference on nonlinear control theory was organized within a special "Nonlinear Year" of the French "Centre National de la Recherche Scientifique." This volume is a collection of invited papers giving an overview of new trends in research all over the world. It was the aim of the editors to bring together theoretical contributions by pure mathematicians and more applied communications dedicated to robotics, electrical engines, biology and computer science.

Chapter headings and selected papers: Controller Design for Nonlinear Systems. Global regulation problem for nonlinear systems (S.M. Fei, C.-B. Feng). Sliding Mode Control of Nonlinear Systems. Nonlinear sliding surface design in the presence of uncertainty (A. Loukianov "et al."). H-Infinity and Nonlinear Control. Control of nonlinear systems via feedback linearization and constrained model predictive control (W.-K. Son, O.K. Kwon). Optimization and Related Topics I. Optimization of boundary and starting controls in multi-dimensional hyperbolic systems (A.V. Arguchintsev). Optimization and Related Topics II. The optimal stabilization of plasma under uncertainty conditions (V.F. Gubarev, O.S. Yakovlev). Advanced Applications of Genetic Algorithms. Multidisciplinary optimization with evolutionary computing for control design (W. Khatib "et al."). Linear Quadratic Optimal Control. Singular optimal control problem of linear singular systems with linear-quadratic cost (Y. Chen "et al."). Control Applications of Optimization. The optimal control of processing systems by economical criteria as applied to distillation (V.P. Krivosheev, A.Y. Torgashov). Optimal Control I. Stability properties of an iterative optimal control algorithm (P.D. Roberts). Optimal Control II. Quadratic index analysis in predictive control (J.S. Senent "et al."). H-Infinity Control and Game Theoretical Approach. Game problem of approach under failure of controlling devices (A.A. Chikrii). Optimal Control Design. The Yakubovich-Kalman-Popov lemma and stability analysis of dynamic output feedback systems (R. Johansson, A. Robertsson). Nonlinear Robust Control I. Robust stability of uncertain systems with differentiable nonlinearity (A. Gaiduk). Nonlinear Robust Control II. Robust nonlinear forwarding with smooth state feedback control (W.Z. Su, M. Fu). Optimal, Robust Control I. Robust reliable "H"∞ controllers design via LMIS (D. Hu, W.-H. Chen). Optimal, Robust Control II. A dynamic games approach to disturbance attenuation control of discrete-time descriptor systems (H. Xu). Author index. Keyword index.