Regional Analysis of Time-Fractional Diffusion Processes

This monograph provides an accessible introduction to the regional analysis of fractional diffusion processes. It begins with background coverage of fractional calculus, functional analysis, distributed parameter systems and relevant basic control theory. New research problems are then defined in terms of their actuation and sensing policies within the regional analysis framework. The results presented provide insight into the control-theoretic analysis of fractional-order systems for use in real-life applications such as hard-disk drives, sleep stage identification and classification, and unmanned aerial vehicle control. The results can also be extended to complex fractional-order distributed-parameter systems and various open questions with potential for further investigation are discussed. For instance, the problem of fractional order distributed-parameter systems with mobile actuators/sensors, optimal parameter identification, optimal locations/trajectory of actuators/sensors and regional actuation/sensing configurations are of great interest.

The book’s use of illustrations and consistent examples throughout helps readers to understand the significance of the proposed fractional models and methodologies and to enhance their comprehension. The applications treated in the book run the gamut from environmental science to national security.

Academics and graduate students working with cyber-physical and distributed systems or interested in the applications of fractional calculus will find this book to be an instructive source of state-of-the-art results and inspiration for further research.

“The monograph is written using very clear and precise mathematical language. The proofs of theorems are carried out using notions of actuators connected to excitations and sensors that are responsible for state components of the dynamic system. The authors present many convincing numerical examples that illustrate the correctness and usefulness of their results.” (Kzysztof Rogowski, Mathematical Reviews, September, 2018)​

Fudong Ge  earned his a Ph.D. in College of Information Science and Technology of Donghua University, Shanghai, China. He joined the MESA Lab of the University of California, Merced from October, 2014 to October, 2015 as a China Scholarship Council Exchange Ph.D. student hosted by Prof. YangQuan Chen. Since July 2016, he has been an associate professor in the School of Computer Science, China University of Geosciences, Wuhan. He is also with Hubei Key Laboratory of Intelligent Geo-Information Processing of the China University of Geosciences. His research interests include existence, uniqueness, stability issues of the solutions of the fractional (partial) differential equations; modeling of continuous time random walks and the anomalous diffusion processes; distributed measurement and distributed control problems in generalized distributed parameter systems with applications in cyber-physical systems in general form.

YangQuan Chen earned his Ph.D. from Nanyang Technological University, Singapore, in 1998. He was a faculty of Electrical Engineering at Utah State University from 2000-2012. He joined the School of Engineering, University of California, Merced in 2012 teaching “Mechatronics”, “Engineering Service Learning” and “Unmanned Aerial Systems” for undergraduates and “Fractional Order Mechanics” and “Nonlinear Controls” for graduates. His current research interests include mechatronics for sustainability, cognitive process control, small multi-UAV based cooperative multi-spectral “personal remote sensing” and applications, applied fractional calculus in controls, modeling and complex signal processing; distributed measurement and distributed control of distributed parameter systems using mobile actuator and sensor networks. He has been the Co-Chair for IEEE RAS Technical Committee (TC) on Unmanned Aerial Vehicle and Aerial Robotics (2012-2018). He was the Mechatronics and Embedded Systems Applications (MESA) TC Chair for ASME Design Engineering Division in 2009-2010 and served as an Associated Editor for ASME Journal of Dynamics Systems, Measurements and Control (2009-2015) and IEEE Transactions on Control Systems Technology (2010-2016). Currently, he serves as the Topic Editor-in-Chief of International Journal of Advanced Robotic Systems (Field Robotics) and a Senior Editor for International Journal of Intelligent Robotic Systems. He is an Associate Editor for Fractional Calculus and Applied Analysis, Mechatronics, Control Engineering Practice, IET Control Theory and Applications, and ISA Transactions. Dr. Chen serves as the Steering Committee Chair for International Conference on Fractional Derivatives and Applications, a program chair for 2016 International Conference on Unmanned Aircraft Systems (ICUAS), and a member of the IEEE-USA's Committee on Transportation and Aerospace Policy (CTAP). He is a member of IEEE, ASME, AIAA, ASPRS, AUVSI and AMA.

Chunhai Kou received his Ph.D. degree fromShanghai Jiao Tong University, Shanghai, China, in 2002. He joined the Department of Science, Donghua University in 2004 where he teaches “Stability Analysis of Nonlinear Differential Equations”, “Basic Theory of Ordinary Differential Equations”, “Theory and Applications of Fractional Differential Equations” and “Mathematical Analysis”. His current research interests include the stability analysis of differential equations based on the Lyapunov theory; basic theory of differential inclusions; applied fractional calculus in controls; existence, uniqueness, stability issues of solutions of the fractional (partial) differential equations, the control and analysis of the general distributed parameter systems.