Foreword	7
	Preface	9
	Acknowledgments	15
	Contents	16
	Acronyms	28
	1 Nonlinear Dynamical Systems and Global Linearizing Control Methods	29
	1.1 Introduction	29
	1.2 Characteristics of the Dynamics of Nonlinear Systems	29
	1.3 Computation of Isoclines	34
	1.4 Basic Features in the Study of Nonlinear Dynamics	36
	1.4.1 The Phase Diagram	36
	1.4.2 Stability Analysis of Nonlinear Systems	37
	1.4.3 Stability Analysis of Nonlinear Models	39
	1.5 Phase Diagrams and Equilibria of Nonlinear Models	40
	1.5.1 Phase Diagrams for Linear Dynamical Systems	40
	1.5.2 Multiple Equilibria for Nonlinear Dynamical Systems	45
	1.5.3 Limit Cycles	47
	1.6 Bifurcations in Nonlinear Dynamics	49
	1.6.1 Bifurcations of Fixed Points of Nonlinear Models	49
	1.6.2 Saddle-Node Bifurcations of Fixed Points in a One-Dimensional System	49
	1.6.3 Pitchfork Bifurcation of Fixed Points	50
	1.6.4 The Hopf Bifurcation	52
	1.7 Predecessors of Differential Flatness Theory	54
	1.7.1 The Differential Geometric Approach	54
	1.7.2 Elaboration on the Frobenius Theorem	57
	1.7.3 Input--Output Linearization	58
	1.7.4 Elaborating on Input--Output Linearization	61
	1.7.5 Input-State Linearization	65
	1.7.6 Stages in the Implementation of Input-State Linearization	71
	1.7.7 Input--Output and Input-State Linearization for MIMO Systems	72
	1.7.8 Dynamic Extension	73
	2 Differential Flatness Theory and Flatness-Based Control	74
	2.1 Introduction	74
	2.2 Definition of Differentially Flat Systems	75
	2.2.1 The Background of Differential Flatness Theory	75
	2.2.2 Differential Flatness for Finite Dimensional Systems	76
	2.3 Properties of Differentially Flat Systems	84
	2.3.1 Equivalence and Differential Flatness	84
	2.3.2 Differential Flatness and Trajectory Planning	99
	2.3.3 Differential Flatness, Feedback Control and Equivalence	102
	2.4 Flatness-Based Control and State Feedback for Systems ƒ	106
	2.5 Classification of Types of Differentially Flat Systems	109
	2.5.1 Criteria About the Differential Flatness of a System	109
	2.5.2 A Sufficient Condition for Showing that a System Is Not Differentially Flat	112
	2.5.3 Liouvillian and Nondifferentially Flat Systems	113
	2.6 Elaborated Criteria for Checking Differential Flatness	114
	2.6.1 Implicit Control Systems on Manifolds of Jets	114
	2.6.2 The Lie-Backlünd Equivalence for Implicit Systems	116
	2.6.3 Conditions for Differential Flatness of Implicit Systems	117
	2.6.4 Example of Elaborated Differential Flatness Criteria to Nonlinear Systems	120
	2.7 Distributed Parameter Systems and Their Transformation ƒ	123
	2.7.1 State-Space Description of a Heat Diffusion Dynamics	123
	2.7.2 Differential Flatness of the Nonlinear Heat Diffusion PDE	126
	3 Nonlinear Adaptive Control Based on Differential Flatness Theory	129
	3.1 Introduction	129
	3.2 Flatness-Based Adaptive Neuro-Fuzzy Control for SISO Systems	130
	3.2.1 Overview	130
	3.3 Flatness-Based Adaptive Fuzzy Control for SISO Dynamical Systems	131
	3.3.1 Transformation of SISO Nonlinear Systems into a Canonical Form	131
	3.3.2 Adaptive Control Law for SISO Nonlinear Systems	132
	3.3.3 Approximators of SISO System Unknown Dynamics	133
	3.3.4 Lyapunov Stability Analysis for SISO Dynamical Systems	135
	3.3.5 Simulation Tests	137
	3.4 Flatness-Based Adaptive Fuzzy Control for MIMO Systems	142
	3.4.1 Overview	142
	3.4.2 Differential Flatness for MIMO Nonlinear Dynamical Systems	143
	3.4.3 Flatness-Based Adaptive Fuzzy Control for MIMO Nonlinear Systems	146
	3.4.4 Flatness-Based Control for a MIMO Robotic Manipulator	148
	3.4.5 Lyapunov Stability Analysis for MIMO Nonlinear Systems	153
	3.4.6 Simulation Tests	159
	4 Nonlinear Kalman Filtering Based on Differential Flatness Theory	166
	4.1 Introduction	166
	4.2 The Derivative-Free Nonlinear Kalman Filter	167
	4.2.1 Overview	167
	4.2.2 Extended Kalman Filtering for Nonlinear Dynamical Systems	168
	4.2.3 Derivative-Free Kalman Filtering to SISO Nonlinear Systems	174
	4.2.4 Simulation Tests	177
	4.2.5 Derivative-Free Kalman Filtering for MIMO Nonlinear Systems	188
	4.2.6 Simulation Tests	191
	4.3 The Derivative-Free Distributed Nonlinear Kalman Filter	197
	4.3.1 Overview	197
	4.3.2 Overview of the Extended Information Filter	198
	4.3.3 Distributed Filtering for Sensorless Control	202
	4.3.4 Simulation Tests	204
	5 Differential Flatness Theory and Industrial Robotics	207
	5.1 Overview	207
	5.2 Adaptive Fuzzy Control of Underactuated MIMO Robots	209
	5.2.1 Overview	209
	5.2.2 Dynamic Model of the Closed-Chain 2-DOF Robotic System	210
	5.2.3 Linearization of the Closed-Chain 2-DOF Robotic System Using Lie Algebra Theory	216
	5.2.4 Differential Flatness of the Underactuated Manipulator	219
	5.2.5 Flatness-Based Adaptive Fuzzy Control for the Underactuated Robot	222
	5.2.6 Simulation Tests	222
	5.3 Observer-Based Adaptive Fuzzy Control of MIMO Robots	223
	5.3.1 Overview	223
	5.3.2 Estimation of the Robot's State Vector	225
	5.3.3 Application of Flatness-Based Adaptive Fuzzy Control	227
	5.3.4 Dynamics of the Observation Error	228
	5.3.5 Approximation of the System's Unknown Dynamics	229
	5.3.6 Lyapunov Stability Analysis	230
	5.3.7 The Role of Riccati Equation Coefficients in Observer-Based Adaptive Fuzzy Control	236
	5.3.8 Simulation Tests	238
	5.4 State Estimation-Based Control of Underactuated Robots	242
	5.4.1 Overview	242
	5.4.2 Derivative-Free Nonlinear Kalman Filter for the Closed-Chain 2-DOF Robotic System	243
	5.4.3 Simulation Tests	246
	5.5 Distributed Filtering Under External Disturbances	247
	5.5.1 Overview	247
	5.5.2 Dynamics and Control of the Robot	249
	5.5.3 Simulation Tests	251
	5.6 Distributed Nonlinear Filtering Under Measurement Delays	254
	5.6.1 Networked Control Under Communication Disturbances	254
	5.6.2 Networked Kalman Filtering for an Autonomous System	255
	5.6.3 Smoothing Estimation in Case of Delayed Measurements	256
	5.6.4 Distributed Filtering-Based Fusion of the Robot's State Estimates	259
	5.6.5 Simulation Tests	260
	6 Differential Flatness Theory in Mobile Robotics and Autonomous Vehicles	263
	6.1 Outline	263
	6.2 State Estimation-Based Control of Autonomous Vehicles	265
	6.2.1 Localization and Autonomous Navigation of Ground Vehicles	265
	6.2.2 Application of Derivative-Free Kalman Filtering to MIMO UGV Models	266
	6.2.3 Controller Design for UGVs	268
	6.2.4 Derivative-Free Kalman Filtering for UGVs	271
	6.2.5 Simulation Tests	272
	6.2.6 Derivative-Free Kalman Filter-Based Navigation of the Autonomous Vehicle	276
	6.3 State Estimation-Based Control and Synchronization of Cooperating Vehicles	285
	6.3.1 Overview	285
	6.3.2 Distributed Kalman Filtering for Unmanned Ground Vehicles	287
	6.3.3 Simulation Tests	288
	6.4 Distributed Fault Diagnosis for Autonomous Vehicles	289
	6.4.1 Integrity Testing in Navigation Sensors of AGVs	289
	6.4.2 Sensor Fusion for AGV Navigation	291
	6.4.3 Canonical Form for the AGV Model	294
	6.4.4 Derivative-Free Extended Information Filtering for UGVs	294
	6.4.5 Simulation Tests	295
	6.5 Velocity Control of 4-Wheel Vehicles	296
	6.5.1 Overview	297
	6.5.2 Dynamic Model of the Vehicle	300
	6.5.3 Flatness-Based Controller for the 3-DOF Vehicle Model	304
	6.5.4 Estimation of Vehicle Disturbance Forces with Kalman Filtering	307
	6.5.5 Simulation Tests	310
	6.6 Active Vehicle Suspension Control	312
	6.6.1 Overview	312
	6.6.2 Dynamic Model of Vehicle Suspension	316
	6.6.3 Flatness-Based Control for a Suspension Model	320
	6.6.4 Compensating for Model Uncertainty with the Use of the Hinfty Kalman Filter	321
	6.6.5 Robust State Estimation with the Use of Disturbance Observers	324
	6.6.6 Simulation Tests	326
	6.7 State Estimation-Based Control of Quadrotors	328
	6.7.1 Overview	328
	6.7.2 Kinematic Model of the Quadropter	334
	6.7.3 Euler-Lagrange Equations for the Quadropter	335
	6.7.4 Design of Flatness-Based Controller for the Quadrotor's Model	337
	6.7.5 Estimation of the Quadrotor's Disturbance Forces and Torques with Kalman Filtering	339
	6.7.6 Simulation Tests	342
	6.8 State Estimation-Based Control of the Underactuated Hovercraft	344
	6.8.1 Overview	344
	6.8.2 Lie Algebra-Based Control of the Underactuated Hovercraft	347
	6.8.3 Flatness-Based Control of the Underactuated Vessel	353
	6.8.4 Disturbances' Compensation with the Use of the Derivative-Free Nonlinear Kalman Filter	354
	6.8.5 Simulation Tests	356
	7 Differential Flatness Theory and Electric Power Generation	360
	7.1 Outline	360
	7.2 State Estimation-Based Control of PMSGs	361
	7.2.1 The PMSG Control Problem	361
	7.2.2 Dynamic Model of the Permanent Magnet Synchronous Generator	363
	7.2.3 Lie Algebra-Based Design of State Estimators for the PMSG	365
	7.2.4 Differential Flatness of the PMSG	370
	7.2.5 Estimation of PMSG Disturbance Input with Kalman Filtering	372
	7.2.6 Simulation Experiments	375
	7.3 State Estimation-Based Control of DFIGs	381
	7.3.1 Overview	381
	7.3.2 The Complete Sixth-Order Model of the Induction Generator	382
	7.3.3 Input--Output Linearization of the DFIG Using Lie Algebra	386
	7.3.4 Input--Output Linearization of the DFIG Using Differential Flatness Theory	390
	7.3.5 Kalman Filter-Based Disturbance Observer for the DFIG Model	394
	7.3.6 Simulation Tests	396
	7.4 Flatness-Based Control of DFIG in Cascading Loops	400
	7.4.1 Overview	400
	7.4.2 A New Proof of the Differential Flatness of the DFIG	401
	7.4.3 Control of the DFIG in Cascading Loops	403
	7.4.4 EKF Implementation for Sensorless Control of the DFIG	406
	7.4.5 Simulation Tests	408
	7.5 State Estimation-Based Control of Distributed PMSGs	411
	7.5.1 Overview	411
	7.5.2 Dynamic Model of the Distributed Power Generation Units	413
	7.5.3 Lie Algebra-Based Design of a Feedback Controller for the PMSG	414
	7.5.4 Differential Flatness of the Distributed PMSG Model	416
	7.5.5 Simulation Tests	420
	8 Differential Flatness Theory for Electric Motors and Actuators	426
	8.1 Introduction	426
	8.2 Flatness-Based Adaptive Control of DC Motors	427
	8.2.1 Overview	427
	8.2.2 Dynamics and Linearization of the DC Motor Model	428
	8.3 Flatness-Based Control of Induction Motors in Cascading Loops	432
	8.3.1 Overview	432
	8.3.2 A Cascading Loops Scheme for Control of Field-Oriented Induction Motors	433
	8.3.3 A Flatness-Based Control Approach for Induction Motors	437
	8.3.4 Implementation of the EKF for the Nonlinear Induction Motor Model	438
	8.3.5 Unscented Kalman Filtering for Induction Motor Control	439
	8.4 Simulation Results	441
	8.5 Flatness-Based Adaptive Control of Electrostatic MEMS Using Output Feedback	443
	8.5.1 Introduction	445
	8.5.2 Dynamic Model of the Electrostatic Actuator	446
	8.5.3 Linearization of the MEMS Model Using Lie Algebra	448
	8.5.4 Differential Flatness of the Electrostatic Actuator	450
	8.5.5 Adaptive Fuzzy Control of the MEMS Model Using Output Feedback	452
	8.5.6 Lyapunov Stability Analysis	457
	8.5.7 Simulation Tests	462
	9 Differential Flatness Theory in Power Electronics	465
	9.1 Introduction	465
	9.2 Three-Phase Voltage Source Converters Control	466
	9.2.1 Overview	466
	9.2.2 Linearization of the Converter's Model Using Lie Algebra	468
	9.2.3 Differential Flatness of the Voltage Source Converter	471
	9.2.4 Kalman Filter-Based Disturbance Observer for the VSC Model	475
	9.2.5 Simulation Tests	477
	9.3 Inverters Control	480
	9.3.1 Overview	480
	9.3.2 Dynamic Model of the Inverter	481
	9.3.3 Lie Algebra-Based Control of the Inverter's Model	485
	9.3.4 Differential Flatness of the Inverter's Model	488
	9.3.5 Flatness-Based Control of the Inverter	490
	9.3.6 State and Disturbances Estimation with Nonlinear Kalman Filtering	494
	9.3.7 Simulation Tests	495
	9.4 Distributed Inverters Synchronization	497
	9.4.1 Overview	497
	9.4.2 The Synchronization Problem for Parallel Inverters	499
	9.5 State and Disturbances Estimation of Parallel Inverters with Nonlinear Kalman Filtering	504
	9.6 Simulation Tests	505
	10 Differential Flatness Theory for Internal Combustion Engines	513
	10.1 Overview	513
	10.2 Flatness-Based Control of Valves in Marine Diesel Engines	515
	10.2.1 Overview	515
	10.2.2 Dynamic Model of the Valve	516
	10.2.3 Input--Output Linearization Using Lie Algebra	520
	10.2.4 Input--Output Linearization Using Differential Flatness Theory	523
	10.2.5 Disturbances Compensation with Derivative-Free Nonlinear Kalman Filter	526
	10.2.6 Simulation Tests	528
	10.3 Flatness-Based Control of Diesel Combustion Engines	533
	10.3.1 Overview	533
	10.3.2 Dynamic Model of the Turbocharged Diesel Engine	534
	10.3.3 Nonlinear Control of the Diesel Engine Using Lie Algebra	536
	10.3.4 A Dynamic Extension-Based Feedback Control Scheme	539
	10.3.5 Nonlinear Control of the Diesel Engine Using Differential Flatness Theory	543
	10.3.6 Disturbances Compensation Using the Derivative-Free Nonlinear Kalman Filter	547
	10.3.7 Simulation Tests	549
	10.4 Adaptive Control for Diesel Combustion Engines	550
	10.4.1 Overview	550
	10.4.2 Observer-Based Adaptive Fuzzy Control for the Diesel Combustion Engine	551
	10.4.3 Application of Flatness-Based Adaptive Fuzzy Control to the MIMO Diesel Engine Model	555
	10.4.4 Lyapunov Stability Analysis	560
	10.4.5 Simulation Tests	565
	10.5 Flatness-Based Control and Kalman Filtering for the Spark-Ignited Engine	568
	10.5.1 Overview	569
	10.5.2 Dynamic Model of the SI Engine	570
	10.5.3 Feedback Linearizing Control of the SI Engine Using Lie Algebra	571
	10.5.4 Feedback Linearizing Control of the SI Engine Using Differential Flatness Theory	573
	10.5.5 Compensation of Disturbances Using the Derivative-Free Nonlinear Kalman Filter	575
	10.5.6 Simulation Tests	576
	10.6 Flatness-Based Adaptive Fuzzy Control of the Spark-Ignited Engine	579
	10.6.1 Overview	580
	10.6.2 Flatness-Based Adaptive Fuzzy Control for SI Motors	581
	10.6.3 Lyapunov Stability Analysis	584
	10.6.4 Simulation Tests	587
	10.7 Flatness-Based Control and Kalman Filtering of the Air--Fuel Ratio	588
	10.7.1 Overview	588
	10.8 Dynamic Model of the Air--Fuel Ratio System	589
	10.8.1 The Air and Fuel Flow Models	589
	10.8.2 Dynamics of the Air--Fuel Ratio System	591
	10.8.3 Differential Flatness of the Air--Fuel Ratio System	592
	10.8.4 Flatness-Based Control of the Air--Fuel Ratio System	594
	10.8.5 Compensation of Uncertainties with the Derivative-Free Nonlinear Kalman Filter	595
	10.8.6 Simulation Tests	599
	11 Differential Flatness Theory for Chaotic Dynamical Systems	600
	11.1 Introduction	600
	11.2 Flatness-Based Control of Chaotic Dynamical Systems	601
	11.2.1 Overview	601
	11.2.2 Differential Flatness of Chaotic Dynamical Systems	602
	11.2.3 Flatness-Based Adaptive Fuzzy Control for Chaotic Systems	606
	11.2.4 Design of the Feedback Controller	606
	11.2.5 Approximators of Unknown System Dynamics	608
	11.2.6 Lyapunov Stability Analysis	609
	11.2.7 Nonlinear Feedback Control of Chaotic Systems Based on Fuzzy Local Linearization	612
	11.2.8 Simulation Tests	614
	11.3 Differential Flatness Theory for Chaos-Based Communication Systems	616
	11.3.1 Overview	617
	11.3.2 Structure of the Chaotic Communication System	619
	11.3.3 Differential Flatness Theory	621
	11.3.4 Estimation in Chaotic Modulators with Nonlinear Kalman Filter	622
	11.3.5 Channel Equalization and Synchronization Using Dual Kalman Filtering	623
	11.3.6 Simulation Tests	626
	12 Differential Flatness Theory for Distributed Parameter Systems	633
	12.1 Introduction	633
	12.2 Pointwise Flatness-Based Control of Distributed Parameter Systems	635
	12.2.1 Overview	635
	12.2.2 Nonlinear 1D Wave-Type Partial Differential Equations	636
	12.2.3 Sine-Gordon Nonlinear PDE in the Model of the Josephson Junction	637
	12.2.4 Current Equation in a Josepshon Transmission Line	638
	12.2.5 State-Space Description of the Nonlinear Wave Dynamics	639
	12.2.6 Solution of the Control and Estimation Problem for Nonlinear Wave Dynamics	642
	12.2.7 Simulation Tests	645
	12.3 Control of Heat Diffusion in Arc Welding Using Differential Flatness Theory and Nonlinear Kalman Filtering	647
	12.3.1 Overview	647
	12.4 Dynamic Model of the Arc Welding Process	651
	12.5 State-Space Description of the Nonlinear Heat Diffusion Dynamics	653
	12.6 Solution of the Control and Estimation Problem for Nonlinear Heat Diffusion	655
	12.6.1 Solution of the Control Problem	655
	12.6.2 Solution of the Estimation Problem	657
	12.7 Simulation Tests	659
	12.8 Fault Detection and Isolation in Distributed Parameter Systems	660
	12.8.1 Overview	660
	12.8.2 Estimation of Nonlinear Wave Dynamics	663
	12.8.3 Equivalence Between Kalman Filters and Regressor Models	665
	12.8.4 Change Detection with the Local Statistical Approach	666
	12.8.5 Simulation Tests	671
	12.9 Application to Condition Monitoring of Civil and Mechanical Structures	676
	12.9.1 Overview	676
	12.9.2 Dynamical Model of the Building---Mechanical Structure	677
	12.10 Differential Flatness of the Multi-DOF Building's Structure	679
	12.10.1 Damage Detection with the Use of Statistical Criteria	682
	12.10.2 Disturbances Estimation with the Derivative-Free Nonlinear Kalman Filter	684
	12.10.3 Simulation Tests	686
	13 Differential Flatness Theory in the Background of Other Control Methods	691
	13.1 Differential Flatness Theory in the Background of Backstepping Control	691
	13.1.1 Overview	691
	13.1.2 Flatness-Based Control Through Transformation into the Canonical Form	693
	13.1.3 A New Approach to Flatness-Based Control for Nonlinear Dynamical Systems	694
	13.1.4 Closed-Loop Dynamics	697
	13.1.5 Comparison to Backstepping Control	699
	13.1.6 Simulation Tests	700
	13.2 Differential Flatness and Optimal Control	706
	13.3 Boundary Control of Nonlinear PDE Dynamics Using ƒ	707
	13.3.1 Overview	707
	13.3.2 Transformation of the PDE Model into a Set of Nonlinear ODEs	708
	13.3.3 Differential Flatness of the Nonlinear PDE Model	711
	13.3.4 Computation of a Boundary Conditions-Based Feedback Control Law	713
	13.3.5 Closed-Loop Dynamics	715
	13.3.6 Simulation Tests	717
	References	720
	Index	750