Fractional optimal control problems (FOCPs) are a generalization of the conventional optimal control problems of integer order in the sense that the dynamics are governed by fractional systems. FOCPs arise in many fields such as mathematics, engineering, biology, economics, finance and management. It is often impossible to obtain analytical solutions of nonlinear FOCPs in general. Thus, establishing optimization theory and finding effective numerical methods for nonlinear FOCPs have become an active research topic. In this book, we will investigate the optimality theories and numerical solution methods of a variety of nonlinear FOCPs including delay nonlinear FOCP, free final time nonlinear FOCP, robust nonlinear FOCP, nonlinear FOCPs with Atangan-Baleanu derivatives and nonlinear FOCPs with conformable derivatives. Numerical solution of fractional optimal control has been an emerging research topic which has attracted much attention in the past few years from both researchers and practitioners, as advances in this area will be very useful for solving real-world optimal control problems which cannot be solved using conventional methods. The objective of this book is to present systematically various fractional optimal control problems of practical importance. By bringing forward fresh novel methods and innovative tools, we are to provide a state-of-the-art and comprehensive systematic treatment of nonlinear fractional optimal control problems, mostly from our previous research results. This can not only develop fractional systems, optimal control theory, and optimization algorithms but also serve as a reference for applied and computational of optimal control problems. The book will be attractive to researchers in various fields of mathematics, control theory and engineering and practitioners who wants to solve their real-life fractional optimal control problems. Graduate students in related fields will also find this book useful for their training and research.
1 Introduction.- 2 Fractional IntegralsandDerivatives.- 3
Fractional-OrderSystems.- 4 ConstrainedMathematicalProgramming.- 5
FractionalOptimalControlProblems.- 6 DelayFractionalOptimalControlProblems.-
7 FreeFinal-TimeDelayFractionalOptimalControl Problems.- 8
RobustFractionalOptimalControlProblems.- 9
FractionalOptimalControlProblemswithAtangana BaleanuDerivatives.- 10
FractionalOptimalControlProblemswithConformable Derivatives.
Chongyang Liu received a Ph.D. in Operational Research and Control Theory from Dalian University of Technology, China in July 2010. Currently, he is a Professor in School of Mathematics and Information Science at Shandong Technology and Business University. He visited Curtin University, Australia as research fellow in 2013, 2015 and 2019, and the Hong Kong Polytechnic University, China as research associate in 2018. Professor Lius research interests include fractional system, optimal control, and engineering optimization. He has published one book and over seventy academic papers in well-established international journals. Professor Liu now is on the editorial boards of three international journals. Song Wang received a B.Sc. degree from Wuhan University of Hydraulic and Electric Engineering, China (now Wuhan University) in 1982 and a Ph.D. degree in Numerical Analysis from Trinity College Dublin in 1989. He had been with a Dublin-based hi-tech company Tritech Ltd., The University of New South Wales, Curtin University and The University of Western Australia, before he moved back to Curtin University as the Head of Department of Mathematics & Statistics in 2014. Currently, he is a Professor at Curtin University. Professor Wangs research interests include scientific computation, numerical optimization and optimal control, optimum design and computational finance. He is a leading researcher in these areas and has published many original research papers in well-established international journals. Currently, he is an Editor-in-Chief of one and on the editorial boards of several other international journals. Zhaohua Gong received a Ph.D. in Operational Research and Control Theory from Dalian University of Technology, China in July 2009. Currently, she is a Professor in School of Mathematics and Information Science at Shandong Technology and Business University. She visited Curtin University, Australia as research associate in 2013, 2015 and 2020. Professor Gongs research interests include nonlinear system, optimal control, and numerical optimization. Professor Gong has published one book and over forty academic papers in well-established international journals.
