Recent Results on Nonlinear Delay Control Systems: In honor of Miroslav Krstic (Advances in Delays and Dynamics (4))

This volume collects recent advances in nonlinear delay systems, with an emphasis on constructive generalized Lyapunov and predictive approaches that certify stability properties. The book is written by experts in the field and includes two chapters by Miroslav Krstic, to whom this volume is dedicated. This volume is suitable for all researchers in mathematics and engineering who deal with nonlinear delay control problems and students who would like to understand the current state of the art in the control of nonlinear delay systems. Foreword 7 Preface 8 Contents 11 Stabilization of Nonlinear Delay Systems: A Tutorial on Recent Results 14 1 General Introduction 15 2 Basic Definitions and Notation 16 3 Delay in the Input Channel 17 3.1 Introduction 17 3.2 Preserving Stability Under Bounds on the Delays 18 3.3 Backstepping 22 3.4 Stabilization Under Large Input Delays Using Predictors 26 3.5 Stabilization by Sampled-Data Feedback Under Input Delays 31 4 Delay in the State 36 4.1 Stabilization Using Lyapunov-Krasovskii Functionals 36 4.2 Equivalence of Stabilization and Existence of a CLKF 37 4.3 Backstepping Under State Delays 41 4.4 Practical Input-to-State Stabilization Under State Delays 46 5 Conclusions 50 References 50 Robust Stabilization of Nonlinear Globally Lipschitz Delay Systems 55 1 Introduction 55 2 Notation 57 3 Statement of Main Results 57 4 Key Lemmas 62 5 Proof of Theorem ?? 63 6 Concluding Remarks 71 References 72 Backstepping Designs in the Presence of Non-constant Delays on the Virtual Input 73 1 Introduction 73 2 Constant Delay 74 3 Time-Varying Delay 76 4 Delay Dependent on Current State 77 5 Delay Dependent on Past State 79 6 Examples 82 7 Conclusions 87 References 87 Prediction-Based Control of Linear Systems by Compensating Input-Dependent Input Delay of Integral-Type 90 1 Introduction 90 2 Problem Statement 92 3 Control Design 96 4 Proof of Theorem---Halanay-Like Inequalities 97 4.1 Halanay Inequality for Delay Equations of Order n 1 98 4.2 Application to Dynamical Equation Defined Through the Predictor-Based Control Law 101 5 Conclusion 103 References 103 State Estimation and Control of Nonlinear Systems with Large and Variable Measurement Delays 105 1 Overview 106 2 Classification of Delay Functions 107 3 Single-Step Exponential Observer 110 4 Sufficient Conditions for Global Regulation from Delayed Output 114 5 Chain Observers 116 5.1 Chain Observers for Variable LDF Delays 117 5.2 Chain Observers for Variable Non-LDF Delays 119 6 Conclusions 121 References 121 On the Existence of the Normal Form for Nonlinear Delay Systems 123 1 Introduction 123 2 Preliminaries and Problem Statements 124 3 Recalling Results on Algebraic and Geometric Tools 129 3.1 Differential Representation 129 3.2 Left- and Right-Annihilators 130 3.3 The Action of a Bicausal Change of Coordinates 131 3.4 Extended Lie Bracket 131 3.5 Integrability 133 4 Main Results 135 4.1 Generalized Normal Form 135 4.2 Normal Form 147 5 Some Concluding Remarks 151 References 151 Compensating for Fatigue-Induced Time-Varying Delayed Muscle Response in Neuromuscular Electrical Stimulation Control 153 1 Introduction 153 2 Knee Joint Dynamics 155 3 Control Objective 158 4 Control Development 159 5 Stability Analysis 160 6 Experiments 163 7 Results 165 8 Discussion 167 References 167 Global and Local Weighted Homogeneity for Time-Delay Systems 172 1 Introduction 172 2 Preliminaries 174 3 Homogeneity 174 4 Local Homogeneity 182 5 ISS Property of Time-Delay Homogeneous Systems 184 6 Examples 186 6.1 Homogeneous Time-Delay System with Degree d=0 186 6.2 Nicholson's Blowfly Population Dynamics 187 6.3 ISS Academic Example of Degree d=0 187 7 Conclusions 188 References 189 Sliding Mode Observer for Robust Fault Reconstruction of Time Delay Systems 191 1 Introduction 191 2 Problem Statement 193 3 Observer Design 194 3.1 Input-to-State Stability of the Error Dynamics: Singular Perturbation Approach 195 3.2 LMIs for Switching Gain Design 198 3.3 Ultimate Boundedness of the Error Dynamics 199 4 Input Fault Reconstruction in the Presence of Uncertainty 200 5 Sensor Fault Reconstruction in the Presence of Uncertainty 201 6 Example 204 6.1 Reconstruction of an Actuator Fault 204 6.2 Reconstruction of Sensor Fault 206 6.3 Comparison with a Classical Fault Reconstruction Scheme 206 7 Conclusion 207 8 Proof of Theorem ?? 208 References 210 A Lyapunov-Krasovskii Methodology for a Class of Large-Scale Systems with Neutral-type Delays in an iISS Framework 212 1 Introduction 212 2 Network Description and Problem Formulation 214 3 Translation into a Lyapunov-Krasovskii Functional 216 4 A Small-Gain Condition 220 5 Proofs of Theorems 223 5.1 Proof of Theorem ?? 223 5.2 Proof of Theorem ?? 227 6 Conclusion 228 References 229 Input-to-State Stability of Switched Systems with Time Delays 231 1 Introduction 231 2 Preliminaries 233 3 Main Results 235 3.1 Discrete Delays 239 3.2 Common Lyapunov-Razumikhin Functions 240 4 Proof of Main Theorem 240 5 Conclusions 245 References 247 A Note on Converse Lyapunov Theorems for Neutral Systems 248 1 Introduction 248 2 Notation 249 3 System-Theoretic Results for Neutral Systems 250 4 Global Stability Results for Neutral Systems 255 References 264 Hybrid Dynamical Systems with Finite Memory 265 1 Introduction 265 2 Preliminaries 266 2.1 Hybrid Systems with Memory 266 2.2 Phase Space 268 2.3 Hybrid Basic Conditions 269 2.4 Basic Existence and Continuation 270 3 Hybrid Systems with Finite Memory 271 4 Lyapunov Conditions for mathscrKL Pre-asymptotic Stability 272 4.1 Lyapunov--Krasovskii Functionals 272 4.2 Lyapunov--Razumikhin Functions 273 5 Well-Posed Hybrid Systems with Memory and Robustness of mathscrKmathscrL Stability 274 6 Conclusions 276 References 276 Control-Oriented Modeling of Fluid Networks: A Time-Delay Approach 278 1 Introduction 278 2 Isothermal Euler Equations 280 3 Time Delay Model 281 3.1 Linear Approximation 282 3.2 Nonlinear Approximation 284 4 Network Model 285 4.1 Conservation at the Nodes and Fluid Capacitance 286 4.2 State-Space Representation 287 4.3 Interconnections and Delays 288 5 Simulation Results 289 6 Conclusion 291 References 291 Finite Spectrum Assignment for Nonlinear Time-Delay Systems 293 1 Introduction 293 2 Preliminaries 294 2.1 Mathematical Definitions 294 2.2 Retarded Linear Systems 295 2.3 Retarded Nonlinear Systems 297 3 Main Results 300 3.1 Motivation 300 3.2 Synchronization-Based Predictor 301 3.3 Predictor-Based Control 302 3.4 Extended Separation Principle 302 3.5 FSA for Linearizable Systems with Input Delay 304 3.6 FSA for Nonlinear Retarded Systems 305 4 Examples 306 4.1 Linearizable System 307 4.2 FSA for Nonlinear Retarded Systems 308 5 Conclusions 310 References 311 Improved Stability Criteria for Sampled-Data Systems with Input Saturation 312 1 Introduction 312 2 Problem Formulation 314 3 Preliminary Lemmas and Theorems 316 3.1 Modified Sector Condition 316 3.2 Saturated and Sampled-Data Systems 316 3.3 Integral Inequality 317 4 Stabilization of Sampled-Data Systems with Input Saturation 318 5 Optimization Problems 323 6 Illustrative Examples 324 6.1 Example 1: Static Output Feedback Control 324 6.2 Example 2: Static Feedback Control 325 7 Conclusion 325 References 326 Inversion of State-Dependent Delay 327 1 Observation Models 327 2 Exact Inversion 329 2.1 Analytic Determination of Delay from Position 331 3 Examples 332 3.1 Graphical Determination of Delay from Position 334 3.2 Graphical Determination of Position from Delay 334 3.3 Analytic Determination of Position from Delay 336 4 Iterated Functional Equations 338 5 Inversion of the Delay for Known Input 341 6 Simultaneous Observability and Input Recovery 343 References 345 Sliding Mode Observer Based-Controller Design for Nonlinear Systems with Time Varying Delay 347 1 Introduction 347 2 System Description and Preliminaries 350 3 Sliding Mode Observer Design 352 4 Stabilizing Controller Synthesis 356 5 Illustrative Example 361 6 Conclusion 364 References 364 An LMI Approach to Control of Exponentially Unstable Systems Subject to Saturation and Time-Varying Delay in the Input 366 1 Introduction 366 2 Problem Definition---Truncated Predictor Feedback Control 368 3 Preliminary Results 369 4 Stabilization of Input Delayed Systems 371 5 Maximization of the Delay Bound by Solving LMI Problems 373 6 Stabilization of Input Delayed Systems with Input Saturation 375 7 Maximization of the Delay Bound and the Domain of Attraction by Solving LMI Problems 376 8 A Numerical Example 377 8.1 Maximizing the Delay Bound 378 8.2 Enlarging the Domain of Attraction 378 9 Experimental Testing 380 10 Conclusions 382 References 382 Identifiability and Observability of Nonlinear Time-Delay Systems with Unknown Inputs 384 1 Introduction 384 2 Algebraic Framework 385 3 Notation and Preliminary Result 387 4 Identifiability 390 4.1 Dependent Outputs Over mathcalK(δ] 391 4.2 Independent Outputs Over mathcalK(δ] 392 5 Observability 394 5.1 Non-causal Observability 396 6 Illustrative Example 397 7 Conclusion 400 References 400 20 Erratum to: Recent Results on Nonlinear Delay Control Systems 403 Erratum to: M. Malisoff et’al. (eds.), Recent Results on Nonlinear Delay Control Systems, Advances in Delays and Dynamics 4, DOI 10.1007/978-3-319-18072-4 403 Index 404 Front Matter....Pages i-xv Stabilization of Nonlinear Delay Systems: A Tutorial on Recent Results....Pages 1-41 Robust Stabilization of Nonlinear Globally Lipschitz Delay Systems....Pages 43-60 Backstepping Designs in the Presence of Non-constant Delays on the Virtual Input....Pages 61-77 Prediction-Based Control of Linear Systems by Compensating Input-Dependent Input Delay of Integral-Type....Pages 79-93 State Estimation and Control of Nonlinear Systems with Large and Variable Measurement Delays....Pages 95-112 On the Existence of the Normal Form for Nonlinear Delay Systems....Pages 113-142 Compensating for Fatigue-Induced Time-Varying Delayed Muscle Response in Neuromuscular Electrical Stimulation Control....Pages 143-161 Global and Local Weighted Homogeneity for Time-Delay Systems....Pages 163-181 Sliding Mode Observer for Robust Fault Reconstruction of Time Delay Systems....Pages 183-203 A Lyapunov-Krasovskii Methodology for a Class of Large-Scale Systems with Neutral-type Delays in an iISS Framework....Pages 205-223 Input-to-State Stability of Switched Systems with Time Delays....Pages 225-241 A Note on Converse Lyapunov Theorems for Neutral Systems....Pages 243-259 Hybrid Dynamical Systems with Finite Memory....Pages 261-273 Control-Oriented Modeling of Fluid Networks: A Time-Delay Approach....Pages 275-289 Finite Spectrum Assignment for Nonlinear Time-Delay Systems....Pages 291-309 Improved Stability Criteria for Sampled-Data Systems with Input Saturation....Pages 311-325 Inversion of State-Dependent Delay....Pages 327-346 Sliding Mode Observer Based-Controller Design for Nonlinear Systems with Time Varying Delay....Pages 347-365 An LMI Approach to Control of Exponentially Unstable Systems Subject to Saturation and Time-Varying Delay in the Input....Pages 367-384 Identifiability and Observability of Nonlinear Time-Delay Systems with Unknown Inputs....Pages 385-403 Erratum to: Recent Results on Nonlinear Delay Control Systems....Pages E1-E1 Back Matter....Pages 405-407