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Abstract
This paper considers the minimum-energy control problem for a class of time-varying systems with multiple state and input delays. First, a state transform matrix is presented. By using the transform matrix, a system with multiple state and input delays is converted to a formal equivalent one without delay. Then, the optimal problem of the novel system is solved by using the maximum principle. Analytical expressions of the optimal control law and optimal performance are given by two formulas with respect to the state transform matrix. At last, an algorithm is given to solve the analytical expression of the state transform matrix. Simulation results show that the design algorithm is efficient and easy to implement.
Acknowledgements
This work was supported in part by the National Natural Science Foundation of China under Grant 61074092, the Natural Science Foundation of Shandong Province under Grant ZR2010FM019, and the Scientific and Technological Project of Shandong Province under Grant 2008GGB01192.
Disclosure statement
No potential conflict of interest was reported by the authors.
Additional information
Funding
Notes on contributors
Hai-Lin Liu
Hai-Lin Liu received his BSc degree from the Qufu Normal University, China, in 2008. He is pursuing his PhD degree in the College of Information Science and Engineering, Ocean University of China. His current research interests include the simulation and control of non-linear systems, and the formation control of multiple agents.
Gong-You Tang
Gong-You Tang received his BSc degree from the Shandong Institute of Chemical Technology in Automation and Instruments in Chemical Industry, Qingdao, PR China, and PhD degree from the South China University of Technology in Automatic Control Theory and Applications, Guangzhou, PR China, in 1982 and 1991, respectively. He worked in the Department of Automation in the Qingdao Institute of Chemical Technology from 1982 to 1988, where he was a visiting scholar at the South China University of Technology in Automatic Control Theory and Applications, Guangzhou, PR China, in 1982–1984 and he was a lecturer from 1987 to 1988. Since 1991, he has joined the College of Information Science and Engineering at the Ocean University of China, where he was an associate professor from 1992 to 1995, he is currently a professor since 1995. His current research interests include analysis and control for time-delay systems, networked control systems and non-linear systems, and formation control for multiple agents.
Xue Yang
Xue Yang received her MS degree from the School of Mathematics and Information, Ludong University. She is pursuing her PhD degree in the College of Information Science and Engineering, Ocean University of China. Her main research interest is the control of non-linear systems.