Zhongjing Ma, Suli Zou

Optimal Control Theory

The Variational Method

• Gebundenes Buch

Produktbeschreibung

This book focuses on how to implement optimal control problems via the variational method. It studies how to implement the extrema of functional by applying the variational method and covers the extrema of functional with different boundary conditions, involving multiple functions and with certain constraints etc. It gives the necessary and sufficient condition for the (continuous-time) optimal control solution via the variational method, solves the optimal control problems with different boundary conditions, analyzes the linear quadratic regulator & tracking problems respectively in detail, and provides the solution of optimal control problems with state constraints by applying the Pontryagin's minimum principle which is developed based upon the calculus of variations. And the developed results are applied to implement several classes of popular optimal control problems and say minimum-time, minimum-fuel and minimum-energy problems and so on.

As another key branch of optimal control methods, it also presents how to solve the optimal control problems via dynamic programming and discusses the relationship between the variational method and dynamic programming for comparison.

Concerning the system involving individual agents, it is also worth to study how to implement the decentralized solution for the underlying optimal control problems in the framework of differential games. The equilibrium is implemented by applying both Pontryagin's minimum principle and dynamic programming.

The book also analyzes the discrete-time version for all the above materials as well since the discrete-time optimal control problems are very popular in many fields.

Produktdetails

• Verlag: Springer / Springer Nature Singapore / Springer, Berlin
• Artikelnr. des Verlages: 978-981-33-6291-8
• Seitenzahl: 364
• Erscheinungstermin: 31. Januar 2021
• Englisch
• Abmessung: 241mm x 160mm x 26mm
• Gewicht: 711g
• ISBN-13: 9789813362918
• ISBN-10: 981336291X
• Artikelnr.: 60672820

Autorenporträt

Zhongjing Ma received his B.Eng. degree in Automatic Control from Nankai University, Tianjin, China, in 1997, and M. Eng. and Ph.D. degrees from McGill University, Montreal, QC, Canada, in 2005 and 2009, respectively. From January 2009 to September 2010, he was a Postdoctoral Research Fellow under Prof. Duncan Callaway and Prof. Ian Hiskens at the University of Michigan, Ann Arbor. He then joined the School of Automation at the University of Beijing Institute of Technology, China, in September 2010, as an Associate Professor. He is currently the Director of the Institute of Electrical Engineering. He is an IEEE senior member. His research interests include optimal control, optimization, auction mechanism design, game theory, decentralized optimization of large-scale systems, and their applications in electrical power systems. He has published more than 50 technical articles in journals such as IEEE Trans. on Automatic Control, Automatica; IEEE Trans. on Control Systems Technology; IEEE Trans. on Systems, Man, and Cybernetics: Systems; Control Engineering Practice; IET Generation, Transmission & Distribution; International Journal of Control; International Journal of Systems Science; and IEEE CDC. Suli Zou received her B.S. degree in Electrical Engineering and Automation and her Ph.D. degree in Control Theory and Control Engineering from the Beijing Institute of Technology, China, in 2011 and 2017, respectively. She is currently a Postdoctoral Researcher at the Automatic Control Lab, ETH Zürich, Switzerland. From September 2019, she joins BIT as an Associate Professor. Her current research interests include decentralized optimization, game theory and auction mechanism design, particularly their applications to smart grids, demand response and charging coordination of electric vehicles, dynamic and stochastic games, distributed optimization in distribution systems with high penetration of renewables, and learning methods for grid power management. She has published more than 30 technical articles in journals such as IEEE Trans. on Automatic Control, Automatica; IEEE Trans. on Control Systems Technology; IEEE Trans. on Systems, Man, and Cybernetics: Systems; Control Engineering Practice; IET Generation, Transmission & Distribution; International Journal of Control; International Journal of Systems Science; and IEEE CDC.

Inhaltsangabe

Introduction.- Extrema of Functional via Variational Method.- Optimal Control via Variational Method.- Pontryagin's Minimum Principle.- Dynamic Programming.- Differential Games.- Discrete-time Optimal Control Problems.