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Taming Heterogeneity and Complexity of Embedded Control

Book Description

This book gathers together a selection of papers presented at the Joint CTS-HYCON Workshop on Nonlinear and Hybrid Control held at the Paris Sorbonne, France, 10-12 July 2006. The main objective of the Workshop was to promote the exchange of ideas and experiences and reinforce scientific contacts in the large multidisciplinary area of the control of nonlinear and hybrid systems.

Table of Contents

  1. Cover
  2. Title Page
  3. Copyright
  4. Preface
  5. Chapter 1: Ellipsoidal Output-Feedback Sets for H∞ Control of a Class of Stochastic Hybrid Systems with State-Dependent Noise
    1. 1. Introduction
    2. 2. Dynamical Model of the AFTCSMP with Wiener Process
    3. 3. Definitions
    4. 4. Stochastic Stabilization
    5. 5. The H∞ Control Problem
    6. 6. Computational Issues and Examples
    7. 7. Conclusion
    8. 8. References
  6. Chapter 2: A Contribution to the Study of Periodic Systems in the Behavioral Approach
    1. 1. Introduction
    2. 2. Periodic behavioral systems
    3. 3. P-periodic kernel representations - PPKR
    4. 4. P-periodic image representations - PPIR
    5. 5. Controllability
    6. 6. Autonomicity
    7. 7. Free variables
    8. 8. Conclusions
    9. 9. Acknowledgements
    10. 10. References10s
  7. Chapter 3: Iteratively Improving Moving Horizon Observers for Repetitive Processes
    1. 1. Introduction
    2. 2. Problem Setup
    3. 3. Basic Idea
    4. 4. Stability
    5. 5. Application Example
    6. 6. Epilogue
    7. 7. References
  8. Chapter 4: Exponential Stability of Dynamic Equations on Time Scales
    1. 1. Introduction
    2. 2. Calculus on Time Scales
    3. 3. Exponential Stability for Linear Equations
    4. 4. Set of Exponential Stability
    5. 5. Stability For Time Invariant System
    6. 6. Exponential Stability For Time Varying Systems
    7. 7. Conclusions
    8. 8. References
  9. Chapter 5: Jurdjevic-Quinn Conditions and Discontinuous Bounded Damping Control
    1. 1. Introduction
    2. 2. Smooth Jurdjevic-Quinn control
    3. 3. Discontinuous control, main result
    4. 4. Proofs
    5. 5. Conclusion
    6. 6. Acknowledgements
    7. 7. References
  10. Chapter 6: Smooth Approximations of Single-Input Optimal Orbital Transfer using Continuation and Averaging Techniques
    1. 1. Introduction
    2. 2. The time-minimal control problem
    3. 3. Continuation methods
    4. 4. Averaging method
    5. 5. Acknowledgements
    6. 6. References
  11. Chapter 7: Achieving Stability in Non-holonomic Systems by Means of Switched Control Laws.
    1. 1. Introduction
    2. 2. Basic notions and useful notations
    3. 3. Switching-based stability
    4. 4. An application: the Artstein’s circle
    5. 5. Simulations
    6. 6. Conclusions
    7. 7. Acknowledgments
    8. 8. Appendix
    9. B. References
  12. Chapter 8: Stability of Equilibria for Hybrid Models of Genetic Regulatory Networks
    1. 1. Introduction
    2. 2. Piecewise-linear Models of Genetic Regulatory Networks
    3. 3. Equilibria and Stability
    4. 4. Graph of the Qualitative Dynamics
    5. 5. Criteria for Stability of Singular Equilibria
    6. 6. Discussion
    7. 7. Acknowledgments
    8. 8. References
  13. Chapter 9: Tools for Semiglobal Practical Stability Analysis of Cascaded Systems and Applications
    1. 1. Introduction
    2. 2. Stability definitions
    3. 3. Lyapunov sufficient conditions
    4. 4. Stability for cascades
    5. 5. Converse results
    6. 6. Applications
    7. 7. Conclusion
    8. 8. Acknowledgements
    9. 9. References
  14. Chapter 10: A Rigorous Numerical Algorithm for Controllability
    1. 1. Introduction
    2. 2. Interval Krawczyk Method
    3. 3. Searching for the switching times
    4. 4. Algorithm is Reachable
    5. 5. Examples
    6. 6. References
  15. Chapter 11: Dead-locks and Break of Symmetry in Robot Coordination
    1. 1. Introduction
    2. 2. Coordinated dynamics
    3. 3. Cooperative controls
    4. 4. Problem P1: two robots with symmetrical initial/final positions
    5. 5. Problem P2: break of symmetry
    6. 6. Conclusions
    7. 7. References
  16. Chapter 12: Iterative Nonlinear Model Predictive Control: A Review
    1. 1. Introduction
    2. 2. Controller synthesis
    3. 3. Examples
    4. 4. Applications
    5. 5. Conclusions
    6. 6. Acknowledgements
    7. 7. References
  17. Chapter 13: Transient Stabilization and Voltage Regulation of a Synchronous Generator
    1. 1. Introduction
    2. 2. Problem Statement
    3. 3. Nonlinear Control Design
    4. 4. Simulation Results
    5. 5. Conclusions
    6. 6. Acknowledgements
    7. 7. Bibliography
  18. Chapter 14: A Current-based Approach to Wave Reflection Suppression in AC Drives Fed through Long Cables
    1. Introduction
    2. 1. Preliminaries and background
    3. 2. Proposed topology: current-injection compensation scheme
    4. 3. Proposed compensators
    5. 4. Overall system representation
    6. 5. Towards a practically feasible implementation of current-injections based compensators
    7. 6. Active compensators proposed implementations: simulation and experimental results
    8. 7. Conclusions
    9. 8. Acknowledgements
    10. 9. References
  19. Chapter 15: Stabilizability of Affine Switching Systems: A Kalman-like Approach
    1. 1. Introduction
    2. 2. Preliminaries and basic definitions
    3. 3. Invariant hybrid subspaces
    4. 4. State space reductions based on stabilizability
    5. 5. Conclusions
    6. 6. Aknowledgement
    7. 7. References
  20. Chapter 16: Observability of Hybrid Automata by Abstraction
    1. 1. Introduction
    2. 2. Basic definitions
    3. 3. Observability of Timed Automata
    4. 4. Abstraction of Hybrid Automata
    5. 5. Conclusions
    6. 6. References
  21. Chapter 17: New Convenient Formula for Impedance Change Calculation in Non-destructive Testing Problems by Control of Eddy Currents
    1. 1. Introduction
    2. 2. Proof of the new convenient formula
    3. 3. Conclusion
    4. 4. References
  22. Chapter 18: Dynamic Optimization of Nonlinear Bioreactors
    1. 1. Introduction
    2. 2. NDOT toolbox features
    3. 3. Case studies
    4. 4. Results
    5. 5. Conclusions
    6. 6. Acknowledgements
    7. 7. References
  23. Chapter 19: About Stability Analysis for Discrete Time Systems with Time Varying Delays
    1. 1. Introduction
    2. 2. Context
    3. 3. The Krasovskii-Lyapunov inspired approach
    4. 4. The switched system transformation approach
    5. 5. Theoretical link between the two approaches
    6. 6. Numerical example
    7. 7. Conclusion
    8. 8. References
  24. Chapter 20: Real-time Implementation of Rotor Flux and Speed Control of Induction Motors using Online Rotor Resistance and Load Torque Adaptation
    1. 1. Introduction
    2. 2. Model description and problem statements
    3. 3. Summary of basic equations used for the rotor speed and flux control
    4. 4. Rotor speed and flux adaptive control design
    5. 5. Experimental results
    6. 6. Conclusion and future works
    7. 7. Acknowledgments
    8. A. Proof of the convergence of the rotor resistance estimate
    9. B. Induction motor data
    10. C. References
  25. Chapter 21: The On-line Diagnosis of Time Petri Nets Based on Partial Orders
    1. 1. Introduction
    2. 2. Notation and definitions
    3. 3. Diagnosis of TPNs
    4. 4. The analysis of TPNs based on partial orders
    5. 5. The Extended Linear Complementarity Problem
    6. 6. The method based on constraint propagation
    7. 7. The on-line diagnosis
    8. 8. Conclusions
    9. 9. Acknowledgements
    10. 10. References
  26. Chapter 22: Optimization Methods for the Sphere Packing Problem on Grassmannians
    1. 1. Introduction
    2. 2. Riemannian gradient descent
    3. 3. Optimal packings on Grassmannians
    4. 4. Nonsmooth optimal packing algorithm
    5. 5. A smoothed variant of the algorithm
    6. 6. Numerical simulations
    7. 7. References
  27. Chapter 23: Analytical Solution of the Problem on a Magnetohydrodynamic Flow in the Initial Part of a Plane Channel in a Transverse Magnetic Field in Oseen Approximation
    1. 1. Introduction
    2. 2. Formulation of the problem and its solution
    3. 3. Conclusions
    4. 4. References
  28. Chapter 24: A Formation Control Algorithm using Voronoi Regions
    1. 1. Introduction
    2. 2. Problem definition
    3. 3. Coordination algorithm
    4. 4. Properties of the algorithm
    5. 5. Simulations
    6. 6. Conclusions
    7. 7. References
  29. Chapter 25: Output Delay Systems Tracking Using System Centre Approach and Sliding Mode Control
    1. 1. Introduction
    2. 2. Problem Formulation
    3. 3. Padé Approximations and Time Delay Systems
    4. 4. System Centre Method and Sliding Mode Control
    5. 5. Numerical Example and Simulations
    6. 6. Feedback by y and Describing Function
    7. 7. Conclusion
    8. 8. References
  30. Chapter 26: State-Linearization of Positive Nonlinear Systems; Applications to Lotka-Volterra Controlled Dynamics
    1. 1. Introduction
    2. 2. Positive Linear Systems
    3. 3. Positive Nonlinear Systems
    4. 4. Linearization of Positive Nonlinear Systems
    5. 5. Positively Invariant Population Dynamics Models in R2
    6. 6. Concluding Remarks
    7. 7. References
  31. Chapter 27: Energy Transfer via Point Interaction Controls
    1. 1. Introduction
    2. 2. The Main Result
    3. 3. A Sketch of the Proof
    4. 4. A Further Remark
    5. 5. Acknowledgement
    6. 6. References
  32. Chapter 28: Further Remarks on Stability Crossing Curves of Distributed Delay Systems
    1. 1. Introduction and motivating examples
    2. 2. Notions and assumptions
    3. 3. Preliminary results and prerequisites
    4. 4. Maximum delay deviation problem
    5. 5. Illustrative examples
    6. 6. Concluding remarks
    7. 7. Acknowledgements
    8. 8. References
  33. Chapter 29: A New Adaptive Controller for Systems with Multilinear Parameterization
    1. 1. Introduction
    2. 2. A new adaptive controller for systems with multilinear parameterization
    3. 3. Simulations
    4. 4. Conclusions
    5. 5. Acknowledgements
    6. 6. References
  34. Chapter 30: Hybrid Model Predictive Control Applied on Sewer Networks: The Barcelona Case Study
    1. 1. Introduction
    2. 2. Hybrid MPC on Sewer Networks
    3. 3. Hybrid MPC Problem Formulation
    4. 4. Implementation and Results
    5. 5. Conclusions and further work
    6. 6. Acknowledgements
    7. 7. References
  35. Chapter 31: Realization Theory of Nonlinear Hybrid System
    1. 1. Introduction
    2. 2. Notation and terminology
    3. 3. Algebraic preliminaries
    4. 4. Moore-automata
    5. 5. Nonlinear Hybrid Systems
    6. 6. Input-Output Maps of Hybrid Systems
    7. 7. Formal Realization Problem For Hybrid Systems
    8. 8. Main Result
    9. 9. Conclusions
  36. Chapter 32: Adaptive Sliding Mode Observer Based Uncertain Chaotic Masking Communication
    1. 1. Introduction
    2. 2. Chaos and Cryptography
    3. 3. Proposed Chaotic Cryptosystem via Adaptive Sliding mode Observer Design
    4. 4. Simulation Example
    5. 5. Conclusions
    6. 6. References
  37. Chapter 33: Navier-Stokes Equation on a Plane Bounded Domain: Continuity Properties for Controllability
    1. 1. Introduction
    2. 2. Linear Operators. The Spaces
    3. 3. Existence, Uniqueness and Continuity
    4. 4. Change of Variables. Relaxation
    5. 5. Realization onto the Projection
    6. 6. Saturating sets
    7. 7. Controllability: a sufficient condition
    8. 8. References
  38. Chapter 34: Hybrid Predictive Control of a Simulated Chemical Plant
    1. 1. Introduction
    2. 2. Model of the plant
    3. 3. Hybrid model predictive control
    4. 4. Control results
    5. 5. Conclusions
    6. 6. References
  39. Chapter 35: Robust Identification in Nonlinear Dynamic Process Models
    1. 1. Introduction
    2. 2. Problem statement
    3. 3. Methods
    4. 4. Case study
    5. 5. Conclusions
    6. 6. References
  40. Chapter 36: Generic Families and Generic Bifurcations of Control-Affine Systems
    1. 1. Introduction
    2. 2. Notations
    3. 3. Non-degeneracy conditions
    4. 4. Classification results
    5. 5. Bifurcations
    6. 6. Proofs of the classification theorems
    7. 7. References
  41. Chapter 37: Sliding Control and Optimization in a Full Bridge Boost Converter
    1. 1. Introduction
    2. 2. Problem statement
    3. 3. Sliding control
    4. 4. Tracking a sinusoidal reference
    5. 5. Optimization
    6. 6. Simulation
    7. 7. Conclusions
    8. 8. References
  42. Chapter 38: Feedback Stabilization of the Periodic Operation of an Hybrid Chemical Plant
    1. 1. Introduction
    2. 2. Hybrid chemical plant with parallel production lines, shared resources and a continuous output
    3. 3. Feedback stabilization
    4. 4. Application of the feedback control and of a rescheduling strategy on the hybrid chemical plant
    5. 5. Conclusions and future work
    6. 6. Acknowledgements
    7. 7. References
  43. Chapter 39: Fast Tracking of Poiseuille Trajectories in Navier Stokes 2D Channel Flow
    1. 1. Introduction
    2. 2. Channel flow model
    3. 3. Trajectory generation and control objective
    4. 4. Main results
    5. 5. Mathematical preliminaries
    6. 6. Proof of theorem 4.1
    7. 7. Proof of theorem 4.2
    8. 8. Acknowledgements
    9. 9. References
  44. Chapter 40: Some Remarks on Interconnection and Damping Assignment Passivity-Based Control of Mechanical Systems
    1. 1. Introduction
    2. 2. Background on IDA–PBC and Problem Formulation
    3. 3. Generating an Homogeneous Kinetic Energy PDE
    4. 4. Solving the Original PDEs
    5. 5. Examples
    6. 6. Conclusions
    7. 7. References
  45. List of Authors