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Alessandro Astolfi · Lorenzo Marconi (Eds.) Analysis and Design of Nonlinear Control Systems Alessandro Astolfi · Lorenzo Marconi (Eds.) Analysis and Design ofNonlinear Control Systems In Honor of Alberto Isidori With  Figures 123 Professor Alessandro Astolfi Imperial College London London SW AZ, UK and Dipartimento di Informatica, Sistemi e Produzione Universita` di Roma “Tor Vergata” Via del Politecnico   Roma, Italy E-mail: a.astolfi@imperial.ac.uk Professor Lorenzo Marconi Dipartimento Elettronica Informatica e Sistemistica C.A.SY./ D.E.I.S. – Universita` di Bologna Viale Risorgimento   Bologna, Italy E-mail: to Alberto, the Scientist, the Teacher, the Friend Preface This book is a tribute to Prof. Alberto Isidori on the occasion of his 65th birthday. Prof. Isidori’s prolific, pioneering and high-impact research activity has spanned over 35 years. Throughout his career, Prof. Isidori has developed ground-breaking results, has initiated research directions and has contributed towards the foundation of nonlinear control theory. In addition, his dedication to explain intricate issues and difficult concepts in a simple and rigorous way and to motivate young researchers has been instrumental to the intellectual growth of the nonlinear control community worldwide. The volume collects 27 contributions written by a total of 52 researchers. The principal author of each contribution has been selected among the researchers who have worked with Prof. Isidori, have influenced his research activity, or have had the privilege and honour of being his PhD students. The contributions address a significant number of control topics, including theo- retical issues, advanced applications, emerging control directions and tutorial works. The diversity of the areas covered, the number of contributors and their international standing provide evidence of the impact of Prof. Isidori in the control and systems theory communities. The book has been divided into six parts: System Analysis, Optimization Methods, Feedback Design, Regulation, Geometric Methods and Asymptotic Analysis, reflecting important control areas which have been strongly influenced and, in some cases, pioneered by Prof. Isidori. The first part “System Analysis” collects four contributions. In “Smooth Distributions Are Globally Finitely Spanned”, H.J. Sussmann focuses on the foundations of differential geometry providing a characterization of smooth distributions. Then E.D. Sontag and Y. Wang, in “Uniformly Universal In- puts”, prove the existence of universal inputs, uniformly for the observability of all analytic continuous-time systems. In “System Interconnection”, J.C. Willems reviews and sheds new light on the classical notion of intercon- X Preface nection, with special emphasis on physically consistent formalizations. Finally, in “Reduced Order Modeling of Nonlinear Control Systems”, A.J. Krener presents a method for nonlinear model reduction based on a normal form for the controllability and observability functions. The second part “Optimization Methods” consists of four contributions. In “Nonholonomic Trajectory Optimization and the Existence of Twisted Matrix Logarithms”, R.W. Brockett discusses an optimal control problem for bilinear systems as a representative example for a class of problems with a Lie group structure. Then A.B. Kurzhanski and P. Varaiya, in “The Hamilton-Jacobi Type Equations for Nonlinear Target Control and Their Approximation”, present a comparison principle for first-order PDEs, of the Hamilton-Jacobi- Bellman type, arising in nonlinear target control synthesis and reachability analysis. In “Causal Coding of Markov Sources with Continuous Alphabets”, S. Yu¨ksel and T. Ba¸sar deal with the remote control problem for linear and nonlinear systems with quantization, by studying the structure of optimal causal encoders for kth-order Markov sources. Finally, in “Pseudospectral Optimal Control and Its Convergence Theorems”, W. Kang, I.M. Ross and Q. Gong present convergence theorems for the pseudospectral methods of nonlinear optimal control with constraints. The third part “Feedback Design” comprises six contributions. In “Event Based Control”, K.J. A˚ström discusses the advantages of event-based control strategies over sampled-data theory in computer controlled systems. Then, A.P. Aguiar, J.P. Hespanha and P.V. Kokotović investigate, in “Zero Dynam- ics and Tracking Performance Limits in Nonlinear Feedback Systems”, the tracking performance achievable for nonminimum-phase nonlinear systems by exploiting the concept of zero dynamics. In “A Nonlinear Model for Com- bustion Instability: Analysis and Quenching of the Oscillations”, I.D. Lan- dau, F. Bouziani and R.R. Bitmead study a model for combustion instability in gas-fueled turbo-machinery using the Krylov-Bogoliubov method. Then, M. Cao and A.S. Morse, in “Convexification of the Range-Only Station Keep- ing Problem”, solve the three landmarks station keeping problem in the plane, by adopting concepts inherited from switched adaptive control. In “Control of Hydraulic Devices, an Internal Model Approach”, K. Schlacher and K. Ze- hetleitner study the problem of controlling, by output feedback, nonlinear hydraulic devices to suppress periodic disturbances in steel rolling. Finally, in “Hybrid Zero Dynamics of Planar Bipedal Walking”, J.W. Grizzle and E.R. Westervelt deal with the problem of designing stable periodic walking motions in bipedal robots by extending the concept of zero dynamics to hybrid systems. Six contributions compose the fourth part “Regulation”. In “Hybrid Sys- tems: Limit Sets and Zero Dynamics with a View Toward Output Regula- tion”, C. Cai, R. Goebel, R.G. Sanfelice and A.R. Teel investigate concepts such as limit sets and zero dynamics for hybrid systems and discuss their use in hybrid output regulation problems. Then, L. Marconi and L. Praly, in “Essential and Redundant Internal Models in Nonlinear Output Regu- Preface XI lation”, develop a few issues on the problem of semiglobal output regulation for nonlinear systems and, in particular, discuss the design of internal model-based regulators. In “Two Global Regulators for Systems with Meas- urable Nonlinearities and Unknown Sinusoidal Disturbances”, R. Marino, G.L. Santosuosso and P. Tomei deal with the problem of global regulation for a class of possibly nonminimum-phase nonlinear systems in the pres- ence of uncertainties on the system and the exosystem. Then A. Serrani, in “A Taxonomy for Time-Varying Immersions in Periodic Internal-Model Con- trol”, frames in the context of nonlinear output regulation the problem of classifying immersion mappings according to the observability properties of the steady-state generator system. In “Paving the Way Towards the Control of Wireless Telecommunication Networks”, F. Delli Priscoli and A. Pietra- bissa show how linear control methodologies can be used for the development of resource management procedures in communication networks. Finally, in “Nonlinear Synchronization of Coupled Oscillators: the Polynomial Case”, J.-S. Kim and F. Allgo¨wer present a feedback method to achieve synchronization of coupled identical oscillators which are described by polynomial vector fields. The fifth part “Geometric Methods” contains three chapters. In “Distur- bance Decoupling for Open Quantum Systems: Quantum Internal Model Prin- ciple”, N. Ganesan and T.J. Tarn explore the use of classical disturbance decoupling techniques to eliminate decoherence in quantum control systems. Then S. Monaco and D. Normand-Cyrot, in “Controller and Observer Nor- mal Forms in Discrete-Time”, study the problem of simplifying discrete-time nonlinear systems through feedback transformations and the use of output injection. Finally, in “A Geometric Approach to Dynamic Feedback Lineariza- tion”, S. Battilotti and C. Califano characterize, from a geometric perspective, dynamically feedback linearizable systems and provide an algorithm for the computation of the linearizing dynamic controller. The last part “Asymptotic Analysis” contains four contributions. In “The Steady-State Response of a Nonlinear Control System, Lyapunov Stable At- tractors, and Forced Oscillations”, C.I. Byrnes and D.S. Gilliam discuss the notion of steady-state response for nonlinear systems and its use in the study of forced oscillations. Then, in “Model Reduction by Moment Matching for Linear and Nonlinear Systems”, A. Astolfi develops a theory of model reduction for nonlinear systems introducing a nonlinear enhancement of the notion of moment and exploiting the theory of the steady-state response of nonlinear systems. In “Adaptive Control of Nonlinear Systems with Unknown Parameters by Output Feedback: a Non-Identifier-Based Method”, H. Lei and W. Lin solve the output feedback stabilization problem for a class of nonlinear systems with uncertain parameters. Finally, C. De Persis, in ‘Hy- brid Feedback Stabilization of Nonlinear Systems with Quantization Noise and Large Delays”, illustrates the design of hybrid stabilizing controllers for nonlinear feedforward systems over finite-bandwidth networks with large delays. XII Preface The editors would like to thank all authors who have contributed to this exceptional book. We are also grateful to Michelle Hammond for her help in the preparation of the volume. We complete the preface with a personal consideration. There are very few events in the life of a person that shape it in a unique way. For both of us, the encounter with Prof. Isidori has been one such event. It has determined the place we live and/or work, has directed our careers, inspired our work, set an example and influenced the way we work. It is for us a great honour to celebrate Alberto’s contributions to science and to our lives. London, Rome, Bologna Alessandro Astolfi June 2007 Lorenzo Marconi