Infinite horizon optimal control of affine nonlinear discrete switched systems using two-stage approximate dynamic programming

References

• Al-Tamimi , A , Lewis , F and Abu-Khalaf , M . 2008 . Discrete-time Nonlinear HJB Solution Using Approximate Dynamic Programming: Convergence Proof . IEEE Transactions on Systems, Man, and Cybernetics – Part B: Cybernetics , 38 : 943 – 949 .
   PubMed Web of Science ®Google Scholar
• Azhmyakov , V , Galvan-Guerra , R and Egerstedt , M . 2009 . Hybrid LQ-optimal using Dynamic Programming . Proceedings of the American Control Conference . 2009 . pp. 3617 – 3623 . St. Louis , , USA
   Google Scholar
• Beard , R . 1995 . “ Improving the Closed-loop Performance of Nonlinear Systems ” . In Ph.D. Dissertation, Rensselaer Polytechnic Institute , Troy, NY, : Electrical Engineering Department .
   Google Scholar
• Borrelli , F , Baotić , M , Bemporad , A and Morari , M . 2005 . Dynamic Programming for Constrained Optimal Control of Discrete-time Linear Hybrid Systems . Automatica , 41 : 1709 – 1721 .
   Web of Science ®Google Scholar
• Chai , T , Geng , Z , Yue , H , Wang , H and Su , C . 2009 . A Hybrid Intelligent Optimal Control Method for Complex Flotation Process . International Journal of Systems Science , 40 : 945 – 960 .
   Web of Science ®Google Scholar
• Gao , H , Lam , J and Wang , C . 2006 . Model Simplification for Switched Hybrid Systems . Systems and Control Letters , 55 : 1015 – 1021 .
   Web of Science ®Google Scholar
• Jiang , B , Yang , H and Shi , P . 2010 . Switching Fault Tolerant Control Design via Global Dissipativity . International Journal of Systems Science , 41 : 1003 – 1012 .
   Web of Science ®Google Scholar
• Lewis , F and Syrmos , V . 1995 . Optimal Control , Hoboken , NJ : Wiley .
   Google Scholar
• Lian , J , Zhao , J and Dimirovski , G . 2009 . Robust H ∞ Sliding Mode Control for a Class of Uncertain Switched Delay Systems . International Journal of Systems Science , 40 : 855 – 866 .
   Web of Science ®Google Scholar
• Lincoln , B and Rantzer , A . 2006 . Relaxing Dynamic Programming . IEEE Transactions on Automatic Control , 51 : 1249 – 1260 .
   Web of Science ®Google Scholar
• Loxton , R-C , Teo , K-L and Rehbock , V . 2009 . Computational Method for a Class of Switched System Optimal Control Problems . IEEE Transactions on Automatic Control , 54 : 2455 – 2460 .
   Web of Science ®Google Scholar
• Ni , W and Cheng , D . 2010 . Control of Switched Linear Systems with Input Saturation . International Journal of Systems Science , 41 : 1057 – 1065 .
   Web of Science ®Google Scholar
• Qin , J , Gao , H and Zheng , W . 2010 . On Average Consensus in Directed Networks of Agents with Switching Topology and Time Delay . International Journal of Systems Science , to be published
   Web of Science ®Google Scholar
• Rantzer , A . 2005 . On Approximate Dynamic Programming in Switching Systems . Proceeding of the IEEE Conference on Decision and Control and the European Control Conference . 2005 . pp. 1391 – 1396 . Spain, Seville
   Google Scholar
• Seatzu , C , Corona , D , Giua , A and Bempoard , A . 2006 . Optimal Control of Continuous Time Switched Affine Systems . IEEE Transactions on Automatic Control , 51 : 726 – 741 .
   Web of Science ®Google Scholar
• Wang , M , Zhao , J and Dimirovski , G . 2009 . Stabilisation and L 2-gain Analysis for a Class of Uncertain Switched Non-linear Systems . International Journal of Systems Science , 40 : 1077 – 1085 .
   Web of Science ®Google Scholar
• Wei , Q , Zhang , H and Dai , J . 2009 . Model-free Multiobjective Approximate Dynamic Programming for Discrete-time Nonlinear Systems with General Performance Index Functions . Neurocomputing , 72 : 1839 – 1848 .
   Web of Science ®Google Scholar
• Xu , X-P and Antsaklis , P-J . 2000 . Optimal Control of Switched Systems: New Results and Open Problems . Proceeding of the American Control Conference . 2000 . pp. 2683 – 2687 . Chicago , , Illinois
   Google Scholar
• Xu , X-P and Antsaklis , P-J . 2003 . “ Results and Perspectives on Computational Methods for Optimal Control of Switched Systems ” . In in Hybrid Systems: Computation and Control (HSCC) , 540 – 555 . Berlin : Springer .
   Google Scholar
• Yue , D and Han , Q . 2005 . Delay-dependent Exponential Stability of Stochastic Systems with Time-varying Delay, Nonlinearity, and Markovian Switching . IEEE Transactions on Automatic Control , 50 : 217 – 222 .
   Web of Science ®Google Scholar
• Zhang , W , Abate , A and Hu , J . 2009a . Efficient Suboptimal Solutions of Switched LQR Problems . Proceeding of the American Control Conference . 2009a . pp. 1084 – 1091 . St. Louis , , USA
   Google Scholar
• Zhang , L and Gao , H . 2010 . Asynchronously Switched Control of Switched Linear Systems with Average Dwell Time . Automatica , 46 : 953 – 958 .
   Web of Science ®Google Scholar
• Zhang , W , Hu , J and Abate , A . 2009b . On the Value Functions of the Discrete-time Switched LQR Problem . IEEE Transactions on Automatic Control , 54 : 2669 – 2674 .
   Web of Science ®Google Scholar
• Zhang , H , Luo , Y and Liu , D . 2009c . Neural Network-based Near-optimal Control for a Class of Discrete-time Affine Nonlinear Systems with Control Constraints . IEEE Transactions on Neural Networks , 20 : 1490 – 1503 .
   PubMed Web of Science ®Google Scholar
• Zhang , H , Wei , Q and Luo , Y . 2008 . A Novel Infinite-time Optimal Tracking Control Scheme for a Class of Discrete-time Nonlinear System Based on Greedy HDP Iteration Algorithm . IEEE Transactions on Systems, Man, and Cybernetics – Part B: Cybernetics , 38 : 937 – 942 .
   PubMed Web of Science ®Google Scholar