Finite horizon optimal control of non-linear discrete-time switched systems using adaptive dynamic programming with ε-error bound

Abstract

In this paper, we aim to solve the finite-horizon optimal control problem for a class of non-linear discrete-time switched systems using adaptive dynamic programming(ADP) algorithm. A new ε-optimal control scheme based on the iterative ADP algorithm is presented which makes the value function converge iteratively to the greatest lower bound of all value function indices within an error according to ε within finite time. Two neural networks are used as parametric structures to implement the iterative ADP algorithm with ε-error bound, which aim at approximating the value function and the control policy, respectively. And then, the optimal control policy is obtained. Finally, a simulation example is included to illustrate the applicability of the proposed method.

Keywords:

• non-linear switched system
• adaptive dynamic programming
• optimal control
• finite horizon
• neural network

Acknowledgements

This work was supported by the National Natural Science Foundation of China (50977008, 61034005, 61104010), National Basic Research Program of China (2009CB320601) and the National High Technology Research and Development Program of China (2012AA040104).

Additional information

Notes on contributors

Chunbin Qin

Chunbin Qin received the BS degree and the MS degree in school of Computer and Information Engineering from Henan University, Kaifeng, China, in 2004 and 2009, respectively. He is currently pursuing the PhD degree in Power Electronics and Power Transmission with Northeastern University, Shenyang, China. He is currently also working in Henan University as a Lecturer. His current research interests include adaptive dynamic programming, neural networks-adaptive controls, adaptive optimal controls, game theory and their industrial applications.

Huaguang Zhang

Huaguang Zhang received the BS degree and the MS degree in Control Engineering from Northeast Dianli University of China, Jilin City, China, in 1982 and 1985, respectively. He received the PhD degree in Thermal Power Engineering and Automation from Southeast University, Nanjing, China, in 1991. He joined the Department of Automatic Control, Northeastern University, Shenyang, China, in 1992, as a Post-Doctoral Fellow for two years. Since 1994, he has been a Professor and Head of the Institute of Electric Automation, School of Information Science and Engineering, Northeastern University, Shenyang, China. His main research interests are fuzzy control, stochastic system control, neural networks based control, non-linear control and their applications. He has authored and co-authored over 200 journal and conference papers, four monographs and co-invented 20 patents. Dr Zhang is an Associate Editor of Automatica, IEEE Transactions on Fuzzy Systems, IEEE Transactions on Systems, Man, and Cybernetics - Part B and Neurocomputing, respectively. He was awarded the Outstanding Youth Science Foundation Award from the National Natural Science Foundation Committee of China in 2003. He was named the Cheung Kong Scholar by the Education Ministry of China in 2005.

Yanhong Luo

Yanhong Luo received the BS degree in Automation Control, the MS degree and the PhD degree in Control Theory and Control Engineering from Northeastern University, Shenyang, China, in 2003, 2006 and 2009, respectively. She is currently working in Northeastern University as an Associate Professor. Her research interests include approximate dynamic programming, neural networks adaptive control, fuzzy control and their industrial application.

Binrui Wang

Binrui Wang received the BS degree in Mechanical Manufacturing from the Department of Mechanical Engineering at Shenyang Ligong University, China in 1999, and the MS degree in Mechanical Engineering and Automation from the School of Mechanical Engineering and Automation at Northeastern University, China in 2002, and the PhD degree in pattern recognition and intelligent system from the School of Information Science and Engineering at Northeastern University in 2005. Currently, he is an Associate Professor in the College of Mechanical and Electrical Engineering at China Jiliang University, China. He was a visiting research scholar in the Department of Automation at Zhejiang University from September 2011 to June 2012. His research interests include intelligent control algorithm and humanoid robot.