Backstepping Control of Nonlinear Dynamical Systems

Contents
Contributors
Preface
	About the book
	Objectives of the book
	Organization of the book
	Book features
	Audience
	Acknowledgments
1 An introduction to backstepping control
	1.1 Introduction
	1.2 Backstepping design for a 2-D linear system
	1.3 Backstepping design for a 2-D nonlinear system
	1.4 Backstepping design for a 3-D linear system
	1.5 Backstepping design for the 3-D Vaidyanathan jerk chaotic system
	1.6 Backstepping control method
	1.7 Examples of backstepping control design
	1.8 Conclusions
	References
2 A new chaotic system without linear term, its backstepping control, and circuit design
	2.1 Introduction
	2.2 Properties of the system
	2.3 Dynamics of the system
	2.4 Backstepping control for the global stabilization of the new chaos system
	2.5 Backstepping control for the synchronization of the new chaos systems
	2.6 Circuit design
	2.7 Conclusions
	Acknowledgment
	References
3 A new chaotic jerk system with egg-shaped strange attractor, its dynamical analysis, backstepping control, and circuit simulation
	3.1 Introduction
	3.2 System details
	3.3 Backstepping control of the jerk system
	3.4 Backstepping synchronization of the jerk system
	3.5 Circuit design
	3.6 Conclusions
	References
4 A new 4-D chaotic hyperjerk system with coexisting attractors, its active backstepping control, and circuit realization
	4.1 Introduction
	4.2 System model
	4.3 Dynamic analysis of the new hyperjerk system
	4.4 Active backstepping stabilization of the new hyperjerk system
	4.5 Active backstepping synchronization of the new hyperjerk system
	4.6 Circuit simulation of the new hyperjerk system
	4.7 Conclusions
	Acknowledgment
	References
5 A new 3-D chaotic jerk system with a saddle-focus rest point at the origin, its active backstepping control, and circuit realization
	5.1 Introduction
	5.2 System model
	5.3 Dynamic analysis of the new jerk system
	5.4 Backstepping control of the jerk system
	5.5 Backstepping synchronization of the jerk system
	5.6 Electronic circuit simulation of the chaotic jerk system
	5.7 Conclusions
	Acknowledgments
	References
6 A new 5-D hyperchaotic four-wing system with multistability and hidden attractor, its backstepping control, and circuit simulation
	6.1 Introduction
	6.2 System model
	6.3 Dynamic analysis of the 5-D hyperchaotic four-wing model
		6.3.1 Rest points
		6.3.2 Multistability
	6.4 Active backstepping control for the global stabilization design of the new 5-D hyperchaotic four-wing system
	6.5 Active backstepping control for the global synchronization design of the new 5-D hyperchaotic four-wing systems
	6.6 Circuit simulation of the new 5D hyperchaotic four-wing system
	6.7 Conclusions
	References
7 A new 4-D hyperchaotic temperature variations system with multistability and strange attractor, bifurcation analysis, its active backstepping control, and circuit realization
	7.1 Introduction
	7.2 System model
	7.3 Dynamic analysis of the hyperchaotic temperature variations model
		7.3.1 Bifurcation analysis
		7.3.2 Rest points
		7.3.3 Multistability
	7.4 Active backstepping control for the global stabilization design of the new hyperchaotic temperature variations system
	7.5 Active backstepping control for the global synchronization design of the new hyperchaos temperature variation systems
	7.6 Circuit simulation of the new 4D hyperchaotic temperature variation system
	7.7 Conclusions
	References
8 A new thermally excited chaotic jerk system, its dynamical analysis, adaptive backstepping control, and circuit simulation
	8.1 Introduction
	8.2 A new jerk system with two nonlinearities
	8.3 Dynamic analysis of the new thermo-mechanical jerk model
		8.3.1 Rest points of the new jerk model
		8.3.2 Bifurcation analysis
		8.3.3 Multistability and coexisting attractors
	8.4 Adaptive backstepping control of the new thermo-mechanical jerk system
	8.5 Adaptive backstepping synchronization of the new thermo-mechanical jerk systems
	8.6 Electronic circuit simulation of the new thermo-mechanical chaotic jerk system
	8.7 Conclusions
	References
9 A new multistable plasma torch chaotic jerk system, its dynamical analysis, active backstepping control, and circuit design
	9.1 Introduction
	9.2 A new plasma torch chaotic jerk system with two nonlinearities
	9.3 Dynamic analysis of the new plasma torch chaotic jerk model
		9.3.1 Rest points of the new chaotic jerk model
		9.3.2 Bifurcation analysis
		9.3.3 Multistability and coexisting attractors
	9.4 Active backstepping control for the global stabilization of the new plasma torch chaotic jerk system
	9.5 Active backstepping control for the global synchronization of the new plasma torch chaotic jerk systems
	9.6 Electronic circuit simulation of the new plasma torch chaotic jerk system
	9.7 Conclusions
	References
10 Direct power control of three-phase PWM-rectifier with backstepping control
	10.1 Introduction
	10.2 Mathematical model of PWM-rectifier
		10.2.1 Vector representation
		10.2.2 A brief review of direct power control
	10.3 Principle and definitions of backstepping control
	10.4 Control of DC-voltage by backstepping
	10.5 Simulation results
	10.6 Conclusion
	References
11 Adaptive backstepping controller for DFIG-based wind energy conversion system
	11.1 Introduction
	11.2 Wind sensor-less rotor speed reference optimization
	11.3 Modeling `AC/DC/AC converter-DFIG' association
		11.3.1 DFIG-AC/DC modeling
		11.3.2 AC/DC rectifier modeling
	11.4 Controller design
		11.4.1 Control objectives
		11.4.2 Speed and stator flux norm regulator design
		11.4.3 PFC and DC voltage controller
			11.4.3.1 Controlling rectifier output current to meet PFC
			11.4.3.2 DC voltage loop
	11.5 Simulation results and discussions
	11.6 Conclusion
	References
12 Dynamic modeling, identification, and a comparative experimental study on position control of a pneumatic actuator based on Soft Switching and Backstepping-Sliding Mode controllers
	12.1 Introduction
	12.2 Related works
	12.3 Experimental setup of the PneuSys
	12.4 Dynamic modeling of the pneumatic system
		12.4.1 Cylinder dynamics
		12.4.2 Pressure dynamics
		12.4.3 State space representation of the PneuSys
	12.5 GA-based identification of the PneuSys and validation
		12.5.1 Identification of the unknown parameters
		12.5.2 Validation of the identified dynamic model
	12.6 Proposed controllers; Model-free and Model-based controllers
		12.6.1 Model-free; Soft Switching controller
		12.6.2 Model-based; Backstepping-Sliding Mode controller
	12.7 Experimental results
	12.8 Discussion
	12.9 Conclusion
	References
13 Optimal adaptive backstepping control for chaos synchronization of nonlinear dynamical systems
	13.1 Introduction
	13.2 Chaos detection and chaos synchronization
		13.2.1 Chaos detection
			13.2.1.1 Lyapunov exponent
			13.2.1.2 0-1 test for chaos in dynamical system
		13.2.2 Chaos synchronization and recurrence
	13.3 Problem statement and preliminaries
	13.4 Stability analysis of adaptive backstepping control systems
		13.4.1 Lyapunov stability theory and the invariance principle
		13.4.2 Adaptive backstepping controller design
			13.4.2.1 Principle of backstepping control method
			13.4.2.2 Adaptive backstepping control process
			13.4.2.3 Optimal backstepping controller based on genetic algorithms
	13.5 The PID controller based on genetic algorithms
	13.6 Simulation examples and discussion
		13.6.1 Lorenz system description
		13.6.2 Optimal adaptive backstepping control and genetically optimized PID control for chaos synchronization of Lorenz systems
			13.6.2.1 Adaptive backstepping stabilization control for Lorenz system
			13.6.2.2 Optimal adaptive backstepping control for Lorenz system synchronization
			13.6.2.3 Genetically optimized PID control for chaos synchronization of Lorenz systems
			13.6.2.4 Discussion
	13.7 Conclusion
	References
14 Backstepping controller for nonlinear active suspension system
	14.1 Introduction
	14.2 Plant model and problem statement
		14.2.1 Nonlinear active suspension system
		14.2.2 Problem statement
	14.3 Backstepping controller synthesis
		14.3.1 Backstepping controller
		14.3.2 Fuzzy PD controller
		14.3.3 Conventional PD controller
		14.3.4 Tuning of gains of controllers
			14.3.4.1 Grey Wolf optimizing algorithm
			14.3.4.2 Cost function
	14.4 Results and discussions
		14.4.1 Bump road surface
			14.4.1.1 Sprung mass uncertainty
			14.4.1.2 Uncertainty in height of bump
		14.4.2 Multiple bumps road profile
	14.5 Conclusions
	References
15 Single-link flexible joint manipulator control using backstepping technique
	15.1 Introduction
	15.2 Single-link flexible joint manipulator model
	15.3 Controller design using backstepping technique
	15.4 Optimization algorithms
		15.4.1 Jaya algorithm
		15.4.2 Teaching learning based optimization algorithm
		15.4.3 Genetic algorithm
	15.5 Results and discussions
	15.6 Conclusion
	References
16 Backstepping control and synchronization of chaotic time delayed systems
	16.1 Introduction
	16.2 Related work
	16.3 Backstepping stabilization of time delayed systems
	16.4 Backstepping synchronization of time delayed chaotic systems
	16.5 Numerical examples
		16.5.1 Example 1: Stabilization of the time delayed Lorenz chaotic system
		16.5.2 Example 2: Synchronization of the time delayed Rössler chaotic system
	16.6 Discussion
	16.7 Conclusion
	References
17 Multi-switching synchronization of nonlinear hyperchaotic systems via backstepping control
	17.1 Introduction
	17.2 Problem formulation
	17.3 System description
		17.3.1 Chaotic attractor of the system
		17.3.2 Dissipation and existence of chaotic attractor
		17.3.3 Symmetry and invariance
		17.3.4 Poincaré map
	17.4 Simulation results and discussions
		17.4.1 Switch 1
			17.4.1.1 Design of η1 and η2
			17.4.1.2 Design of η3 and η4
			17.4.1.3 Numerical simulations
		17.4.2 Switch 2
			17.4.2.1 Design of η2 and η3
			17.4.2.2 Design of η1 and η4
			17.4.2.3 Numerical simulations
		17.4.3 Switch 3
			17.4.3.1 Design of η1 and η2
			17.4.3.2 Design of η3 and η4
			17.4.3.3 Numerical simulations
	17.5 Conclusion
	References
18 A 5-D hyperchaotic dynamo system with multistability, its dynamical analysis, active backstepping control, and circuit simulation
	18.1 Introduction
	18.2 System model
	18.3 Dynamic analysis of the 5-D hyperchaotic dynamo model
		18.3.1 Rest points
		18.3.2 Multistability
	18.4 Active backstepping control for the global stabilization design of the new 5-D hyperchaotic dynamo system
	18.5 Active backstepping control for the global synchronization design of the new 5-D hyperchaotic dynamo systems
	18.6 Circuit simulation of the new 5D hyperchaotic system
	18.7 Conclusions
	References
19 Design and implementation of a backstepping controller for nonholonomic two-wheeled inverted pendulum mobile robots
	19.1 Introduction
	19.2 Distributed controller design based on backstepping approach
	19.3 Discrete event modeling and control net representation
	19.4 Implementation issues on a multi-task processing architecture
	19.5 Conclusion
	References
20 A novel chaotic system with a closed curve of four quarter-circles of equilibrium points: dynamics, active backstepping control, and electronic circuit implementation
	20.1 Introduction
	20.2 A new chaotic system with closed-curve equilibrium
	20.3 Dynamic analysis of the new chaotic system with a closed-curve equilibrium
		20.3.1 Lyapunov exponents analysis
		20.3.2 Multistability and coexisting attractors
	20.4 Active backstepping control for the global stabilization of the new chaos system with a closed-curve equilibrium
	20.5 Active backstepping control for the synchronization of the new chaos systems
	20.6 Circuit design for the new chaotic system with a closed-curve equilibrium
	20.7 Conclusions
	Acknowledgment
	References
Index