| List of Contributors | p. XV |
| Introduction to Nonlinear Optimal Control | p. 1 |
| Introduction | p. 1 |
| Optimal Control and Maximum Principle | p. 2 |
| Preliminaries | p. 2 |
| The Weak Maximum Principle | p. 3 |
| The Maximization Condition | p. 6 |
| Maximum Principle, Fixed Time | p. 6 |
| Maximum Principle, General Case | p. 12 |
| Maximum Principle and Shooting Problem | p. 14 |
| Introduction to the Micro-analysis of the Extremal Solutions | p. 14 |
| Affine Control Systems | p. 15 |
| More Second-order Conditions | p. 15 |
| High-order Maximum Principle | p. 15 |
| Intrinsic Second-order Derivative and Conjugate Times | p. 21 |
| Examples | p. 37 |
| Time-optimal Transfer Between Keplerian Orbits | p. 40 |
| Model and Basic Properties | p. 40 |
| Maximum Principle and Extremal Solutions | p. 42 |
| Numerical Resolution | p. 44 |
| Introduction to Optimal Control with State Constraints | p. 48 |
| The Geometric Framework | p. 50 |
| Necessary Optimality Conditions for Boundary Arcs | p. 51 |
| Junction and Reflection Conditions | p. 53 |
| Proof of the Necessary Conditions in the Riemannian Case | p. 54 |
| Notes and sources | p. 59 |
| References | p. 60 |
| Observer Design for Nonlinear Systems | p. 61 |
| Introduction | p. 61 |
| Main Problem and Definitions | p. 63 |
| Problem Formulation | p. 63 |
| Conditions for a Solution | p. 65 |
| Some "Basic" Designs | p. 73 |
| Observer designs for Linear Structures | p. 73 |
| Observer Designs for Nonlinear Structures | p. 76 |
| Some "Advanced" Designs | p. 80 |
| Interconnection-based Design | p. 80 |
| Transformation-based Design | p. 84 |
| Conclusion | p. 87 |
| References | p. 87 |
| Sampled-data Control of Nonlinear Systems | p. 91 |
| Introduction | p. 91 |
| Mathematical Preliminaries | p. 95 |
| Zero-order-hold Equivalent Models | p. 96 |
| Motivating" Counter-examples | p. 98 |
| Preliminary Results on Stability and Stabilization | p. 101 |
| Framework for Controller Design | p. 103 |
| Global Exponential Stabilization | p. 104 |
| Semiglobal Practical Stability | p. 108 |
| Controller Design within the Framework | p. 110 |
| Emulation | p. 111 |
| Continuous-time Controller Redesign | p. 113 |
| Discrete-time Interconnection and Damping Assignment - Passivity-based Control (IDA-PBC) | p. 115 |
| Backstepping via the Euler Model | p. 121 |
| Design Examples | p. 126 |
| Jet Engine System | p. 126 |
| Inverted Pendulum | p. 127 |
| Overview of Related Literature | p. 130 |
| Open Problems | p. 133 |
| References | p. 134 |
| Stability Analysis of Time-delay Systems: A Lyapunov Approach | p. 139 |
| Introduction | p. 139 |
| Basic Concepts of Time-delay Systems | p. 141 |
| Systems of Retarded Type | p. 141 |
| Pointwise Delays | p. 142 |
| Linear Systems | p. 142 |
| Characteristic Quasipolynomials | p. 143 |
| Stability | p. 143 |
| Some Simple Lyapunov-Krasovskii Functionals | p. 145 |
| Delay-independent Stability | p. 145 |
| Delay-dependent Stability Using Model Transformation | p. 148 |
| Implicit Model Transformation | p. 149 |
| Complete Quadratic Lyapunov-Krasovskii Functional | p. 151 |
| Analytical Expression | p. 151 |
| Discretization | p. 153 |
| A Comparison of Lyapunov-Krasovskii Functionals | p. 155 |
| Dealing with Time-varying Delays | p. 156 |
| Razumikhin Theorem | p. 159 |
| Coupled Difference-Differential Equations | p. 161 |
| Introducation | p. 161 |
| Fundamental Solutions | p. 163 |
| Lyapunov-Krasovskii functional | p. 166 |
| Further Comments | p. 167 |
| Conclusions | p. 168 |
| References | p. 169 |
| Controllability of Partial Differential Equations | p. 171 |
| Semigroup Theory, and Cauchy Problems in Banach Spaces | p. 171 |
| Definitions | p. 171 |
| The Cauchy Problem | p. 173 |
| The Nonhomogeneous Initial-value Problem | p. 176 |
| Controllability and Observability in Banach Spaces | p. 177 |
| A Short Overview on Controllability of Finite-dimensional Linear Control Systems | p. 177 |
| Controllability of Linear Partial Differential Equations in Banach Spaces | p. 178 |
| Semidiscrete Approximations of Infinite-dimensional Linear Control Systems in Hilbert Spaces | p. 187 |
| Introduction | p. 187 |
| Uniform Controllability of Semidiscrete Approximations of Parabolic Control Systems | p. 189 |
| References | p. 196 |
| Stability, Told by Its Developers | p. 199 |
| Introduction | p. 199 |
| About the Chapter | p. 199 |
| Stability, Generally Speaking | p. 201 |
| Lagrange's Stability | p. 203 |
| Modern Interpretations of Lagrange-Dirichlet Stability | p. 207 |
| Lyapunov's Stability | p. 209 |
| Lyapunov's Methods to Test for Stability | p. 215 |
| Asymptotic Stability | p. 219 |
| Globalisation of Asymptotic Stability | p. 222 |
| Global, i.e. in the Large or in the Whole? | p. 223 |
| Asymptotic Stability in the Large | p. 224 |
| Asymptotic Stability in the Whole | p. 226 |
| An Illustrative Example | p. 229 |
| On the Trace of "Krasovskii-La Salle's Theorem" | p. 232 |
| Autonomous Systems | p. 232 |
| Time-varying Periodic Systems | p. 234 |
| Uniformity | p. 236 |
| Uniform Stability | p. 237 |
| Uniform Global Stability | p. 238 |
| Uniform Asymptotic Stability | p. 239 |
| Uniform Asymptotic Stability in the Large | p. 241 |
| Uniform Asymptotic Stability in the Whole | p. 242 |
| Stability with Respect to Perturbations | p. 245 |
| Further Bibliographical Remarks | p. 251 |
| Conclusions | p. 254 |
| References | p. 255 |
| Structural Properties of Linear Systems - Part II: Structure at Infinity | p. 259 |
| Introduction | p. 259 |
| Differential Polynomials and Non-commutative Formal Series | p. 259 |
| Differential Polynomials: A Short Review | p. 259 |
| Local Complete Rings | p. 260 |
| Formal Power Series | p. 260 |
| A Canonical Cogenerator | p. 261 |
| Matrices over S | p. 262 |
| Formal Laurent Series | p. 264 |
| Transmission Poles and Zeros at Infinity | p. 265 |
| Transfer Matrix of an Input-Output System | p. 265 |
| Structure at Infinity of a Transfer Matrix | p. 266 |
| Impulsive Systems and Behaviors | p. 268 |
| Temporal Systems | p. 268 |
| A Key Isomorphism | p. 270 |
| Impulsive Behavior | p. 271 |
| Impulsive System | p. 272 |
| Generalization of the Notion of Temporal System | p. 275 |
| Poles and Zeros at Infinity | p. 277 |
| Uncontrollable Poles at Infinity | p. 278 |
| System Poles at Infinity | p. 278 |
| Hidden Modes at Infinity | p. 279 |
| Invariant Zeros at Infinity | p. 281 |
| System Zeros at Infinity | p. 281 |
| Relations between the Various Poles and Zeros at Infinity | p. 281 |
| Concluding Remarks | p. 282 |
| Errata and addenda for [7] | p. 282 |
| References | p. 283 |
| A On the Literature's Two Different Definitions of Uniform Global Asymptotic Stability for Nonlinear Systems | p. 285 |
| Different UGAS Definitions | p. 285 |
| A Locally Lipschitz (Uniform-in-time) System that is ULS and UGA but not UGB | p. 286 |
| References | p. 288 |
| Table of Contents provided by Ingram. All Rights Reserved. |
