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Sliding Mode Control of Fractional-order Systems
- 1st Edition - March 28, 2025
- Authors: Hamid Reza Karimi, Xin Meng, Baoping Jiang
- Language: English
- Paperback ISBN:9 7 8 - 0 - 4 4 3 - 3 1 6 9 6 - 8
- eBook ISBN:9 7 8 - 0 - 4 4 3 - 3 1 6 9 7 - 5
In the fields of dynamical systems and control theory, a fractional-order system is a dynamical system that can be modeled by a fractional differential equation containing… Read more
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Request a sales quoteIn the fields of dynamical systems and control theory, a fractional-order system is a dynamical system that can be modeled by a fractional differential equation containing derivatives of non-integer order. In control systems, sliding mode control (SMC) is a nonlinear control method that alters the dynamics of a nonlinear system by applying a discontinuous control signal (or more rigorously, a set-valued control signal) that forces the system to "slide" along a cross-section of the system's normal behavior. Sliding Mode Control of Fractional-order Systems discusses the design of several types of fractional-order systems. Sliding mode control strategy allows the exploration of the problems of projection synchronization control, finite-time stability, asymptotic stability, and formation control of fractional-order systems, which make up the shortages in the analysis and design of fractional-order systems. The book focuses on several types of fractional-order control systems, combined with the sliding-mode control (SMC) and event-triggered control, the problems of projection synchronization control, finite-time stability, asymptotic stability, and formation control for those systems are explored, which makes up the shortages in the analysis and design of fractional-order systems.
- Provides a comprehensive and clear explanation of recent developments in sliding mode control of fractional-order systems
- Unifies existing and emerging concepts concerning sliding mode control of fractional-order systems
- Provides a series of the latest results in, including but not limited to, projective synchronization control, exponential consensus control, formation control and fractional-order event-triggered control
Control engineers working on system modeling, robust control and stochastic systems, signal processing engineers working on estimation and control over communication networks
- Title of Book
- Cover image
- Title page
- Table of Contents
- Copyright
- Acknowledgments
- Chapter 1: Introduction of sliding mode control and fractional-order control systems
- 1.1. Overview of sliding mode control and its applications
- 1.2. Overview of fractional-order control systems and their applications
- 1.2.1. Variable-order fractional systems
- 1.2.2. Fractional-order coupled systems
- 1.2.3. Fractional-order multi-agent systems
- 1.2.4. Fractional-order switched systems
- 1.2.5. Fractional-order complex networked systems
- 1.3. Preview of the book
- 1.4. Notations
- Chapter 2: Theoretical foundations of fractional-order systems
- 2.1. Theory of fractional calculus
- 2.1.1. Typical functions
- 2.1.2. Typical definitions
- 2.1.3. Basic properties of fractional derivatives
- 2.2. Stability theory of fractional-order systems
- 2.2.1. Description of fractional-order control systems
- 2.2.2. Basic definitions of stability
- 2.2.3. Stability criteria
- 2.3. Some important lemmas
- 2.4. Conclusion
- Chapter 3: Finite-time projective synchronization control of variable-order fractional chaotic systems via sliding mode approach
- 3.1. Introduction
- 3.2. Problem statement
- 3.3. Main results
- 3.3.1. Sliding mode surface design and stability analysis
- 3.4. Finite-time stability analysis
- 3.5. Numerical example
- 3.6. Conclusion
- Chapter 4: Finite-time synchronization of variable-order fractional uncertain coupled systems via adaptive sliding mode control
- 4.1. Introduction
- 4.2. Problem statement
- 4.3. Main results
- 4.3.1. VOF sliding mode controller design
- 4.3.2. Adaptive VOF controller design
- 4.4. Numerical examples
- 4.5. Conclusion
- Chapter 5: Sliding mode projective synchronization for fractional-order coupled systems based on network without strong connectedness
- 5.1. Introduction
- 5.2. Problem statement
- 5.3. Main results
- 5.3.1. Sliding surface design
- 5.3.2. Mittag-Leffler stability analysis
- 5.3.3. Reachability of a sliding surface
- 5.4. Numerical example
- 5.5. Conclusion
- Chapter 6: An event-triggered sliding mode control mechanism to exponential consensus of fractional-order descriptor nonlinear multi-agent systems
- 6.1. Introduction
- 6.2. Problem statement
- 6.2.1. Graph theory
- 6.2.2. Model description
- 6.3. Main results
- 6.3.1. Event-triggered SMC strategy
- 6.3.2. Reachability analysis
- 6.3.3. Discussion of Zeno behavior
- 6.4. Numerical examples
- 6.5. Conclusion
- Chapter 7: Leader–follower sliding mode formation control of fractional-order multi-agent systems: a dynamic event-triggered mechanism
- 7.1. Introduction
- 7.2. Problem statement
- 7.2.1. Graph theory
- 7.2.2. Fractional-order multi-agent dynamics
- 7.2.3. Dynamic event-triggered mechanism
- 7.3. Main results
- 7.3.1. Dynamic event-triggered SMC strategy
- 7.3.2. Reachability analysis
- 7.3.3. Discussion of Zeno behavior
- 7.4. Simulation results
- 7.5. Conclusion
- Chapter 8: An event-triggered mechanism to observer-based sliding mode control of fractional-order uncertain switched systems
- 8.1. Introduction
- 8.2. Problem statement
- 8.3. Main results
- 8.3.1. Fractional-order state observer design
- 8.3.2. Event-triggered SMC strategy
- 8.3.3. Reachability analysis
- 8.3.4. Discussion on Zeno behavior
- 8.4. Numerical examples
- 8.5. Conclusion
- Chapter 9: Nonfragile sliding mode control of fractional-order complex networked systems via combination event-triggered approach
- 9.1. Introduction
- 9.2. Problem statement
- 9.3. Main results
- 9.3.1. Nonfragile fractional-order observer design
- 9.3.2. Event-triggered SMC strategy
- 9.3.3. Reachability analysis
- 9.3.4. Discussion of Zeno behavior
- 9.4. Numerical example
- 9.5. Conclusion
- Index
- No. of pages: 240
- Language: English
- Edition: 1
- Published: March 28, 2025
- Imprint: Academic Press
- Paperback ISBN: 9780443316968
- eBook ISBN: 9780443316975
HK
Hamid Reza Karimi
Dr. Karimi received the B.Sc. (First Hons.) degree in power systems from the Sharif University of Technology, Tehran, Iran, in 1998, and the M.Sc. and Ph.D. (First Hons.) degrees in control systems engineering from the University of Tehran, Tehran, in 2001 and 2005, respectively. His research interests are in the areas of control systems/theory, mechatronics, networked control systems, intelligent control systems, signal processing, vibration control, ground vehicles, structural control, wind turbine control and cutting processes. He is an Editorial Board Member for some international journals and several Technical Committee. Prof. Karimi has been presented a number of national and international awards, including Alexander-von-Humboldt Research Fellowship Award (in Germany), JSPS Research Award (in Japan), DAAD Research Award (in Germany), August-Wilhelm-Scheer Award (in Germany) and been invited as visiting professor at a number of universities in Germany, France, Italy, Poland, Spain, China, Korea, Japan, India.
Affiliations and expertise
Professor of Applied Mechanics, Department of Mechanical Engineering, Politecnico di Milano, Milan, ItalyXM
Xin Meng
Xin Meng joined the School of Physical and Mathematical Sciences, Nanjing Tech University, Nanjing, China in 2023. Dr Meng’s research interests are in the areas of sliding mode control, fractional-order systems, event-triggered control, etc. He has published more than 10 papers, and some of them are published in top journals, such as ISA Trans., Neurocomputing, etc. He also serves as an active reviewer for more than 10 international journal.
Affiliations and expertise
Nanjing Tech University, ChinaBJ
Baoping Jiang
Dr Jiang is based at the Department of Electronic and Information Engineering, Suzhou University of Science and Technology, Suzhou, China, where he is an associate professor. Drs Jiang’s research interests are in the areas of stochastic systems, networked control systems, sliding mode control and stability theory, etc. He has published more than 60 papers.
Affiliations and expertise
Suzhou University of Science and Technology, China