Model-free control of Lorenz chaos using an approximate optimal control strategy

Communications in Nonlinear Science and Numerical Simulation

Volumn 17, Issue 12, 2012, Pages 4891-4900

  Li, Shuai ^a   Li, Yangming ^b   Liu, Bu ^c   Murray, Timmy ^c  

^a Stevens Institute of Technology   (United States)

^b INSTITUTE OF INTELLIGENT MACHINES   (China)

^c University of Massachusetts Amherst   (United States)

Author keywords

Bellman equation; Lorenz chaotic system; Model free control; Principle of optimality

Indexed keywords

CHAOTIC SYSTEMS; CONTROL THEORY; DYNAMIC PROGRAMMING; OPTIMAL CONTROL SYSTEMS;

BELLMAN EQUATIONS; CONTROL LAWS; CONTROL PERSPECTIVE; INPUT AND OUTPUTS; LORENZ CHAOTIC SYSTEM; MATHEMATICS MODEL; MODEL-FREE CONTROL; OPTIMAL CONTROL STRATEGY; OPTIMAL CONTROLS; PRINCIPLE OF OPTIMALITY;

ITERATIVE METHODS;

EID: 84864411077     PISSN: 10075704     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cnsns.2012.05.024     Document Type: Article

References (49)

1. Lorenz E.N. Deterministic nonperiodic flow. J Atmos Sci 1963, 20.
2. Virgin L.N., Dowell E.H., Conner M.D. On the evolution of deterministic non-periodic behavior of an airfoil. Int J Nonlinear Mech 1998, 34(3):499-514.
3. Oxley Les, George Donald A R Economics on the edge of chaos: some pitfalls of linearizing complex systems. Environ Model Software 2007, 22(5):580-589.
4. Kennedy M.P. Three steps to chaos. ii. a chua's circuit primer. IEEE Trans. Circuits Syst I: Fundamental Theor Appl 1993, 40(10):657-674. oct.
5. Weiss J.N., Garfinkel A., Spano M.L., Ditto W.L. Chaos and chaos control in biology. J clinical investgat 1994, 93(4):1355-1360. April.
6. Scholl E. Handbook of chaos control. 2nd ed. 2007.
7. Boccaletti S., Grebogi C., Lai Y.C., Mancini H., Maza D. The control of chaos: theory and applications. Phys Rep 2000, 329:103-197.
8. Fradkov A.L., Evans R.J. Control of chaos: methods and applications in engineering. Ann Rev Control 2005, 29(1):33-56.
9. Pyragas K. Continuous control of chaos by self-controlling feedback. Phys Lett A 1992, 170(6):421-428.
10. Abarbanel H. Analysis of observed chaotic data 1996, Springer.
11. Lu J., Zhang S. Controlling Chen's chaotic attractor using backstepping design based on parameters identification. Phys Lett A 2001, 286(23):148-152.
12. Yau H.T. Design of adaptive sliding mode controller for chaos synchronization with uncertainties. Chaos Solitons Fract 2004, 22(2):341-347.
13. Yazdanpanah A, Khaki A, Yazdanpanah A. Adaptive control of chaos in nonlinear chaotic discrete-time systems. In: Proceedings of international conference on physics and control, aug. 2005. p. 913-15.
14. Ge Z.M., Li S.C., Li S.Y., Chang C.M. Pragmatical adaptive chaos control from a new double van der pol system to a new double duffing system. Appl Math Comput 2008, 203(2):513-522.
15. Oscar Calvo, Julyan HE Cartwright. Fuzzy control of chaos.
16. Bonakdar Mohammad, Samadi Mostafa, Salarieh Hassan, Alasty Aria Stabilizing periodic orbits of chaotic systems using fuzzy control of poincar map. Chaos Solitons Fract 2008, 36(3):682-693.
17. Park Chang-Woo, Lee Chang-Hoon, Park Mignon Design of an adaptive fuzzy model based controller for chaotic dynamics in lorenz systems with uncertainty. Inf Sci Inf Comput Sci 2002, 147(1-4):245-266. october.
18. Kim Jae-Hun, Park Chang-Woo, Kim Euntai, Park Mignon Fuzzy adaptive synchronization of uncertain chaotic systems. Phys Lett A 2005, 334(4):295-305.
19. Hirasawa K., Murata J., Jinglu Hu, ChunZhi Jin Chaos control on universal learning networks. IEEE Trans Syst Man Cybernet Part C: Appl Rev 2000, 30(1):95-104.
20. Poznyak A.S., Yu Wen, Sanchez E.N. Identification and control of unknown chaotic systems via dynamic neural networks. IEEE Trans Circuits Syst I: Fundamental Theor Appl 1999, 46(12):1491-1495. dec.
21. Park J.B., Yoo S.J., Choi Y.H. Stable predictive control of chaotic systems using self-recurrent wavelet neural network. Int J Control Automat Syst 2005, 3(1):43-55. mar.
22. Sadeghpour Mehdi, Salarieh Hassan, Vossoughi Gholamreza, Alasty Aria Multi-variable control of chaos using pso-based minimum entropy control. Commun Nonlinear Sci Numer Simulat 2011, 16(6):2397-2404.
23. Sadeghpour Mehdi, Salarieh Hassan, Alasty Aria Minimum entropy control of chaos via online particle swarm optimization method. Appl Math Model 2012, 36(8):3931-3940.
24. Richter Hendrik An evolutionary algorithm for controlling chaos: The use of multiobjective fitness functions. Lecture notes in computer science 2002, vol. 2439:308-317. Springer. J. Guervos, P. Adamidis, H. Beyer (Eds.).
25. Zelinka Ivan, Senkerik Roman, Navratil Eduard Investigation on evolutionary optimization of chaos control. Chaos Solitons Fract 2009, 40(1):111-129.
26. Modabbernia M.R., Sahab A.R., Pastaki A.G. Synchronization chaos using ogbm with genetic algorithm. Int J Math Comput Simulat 2001, 5(2):102-109.
27. Zelinka Ivan, Chen Guanrong, Celikovsky Sergej, Zelinka Ivan, Celikovsky Sergej, Richter Hendrik, Chen Guanrong Chaos synthesis by evolutionary algorithms. Evolutionary algorithms and chaotic systems, studies in computational intelligence 2010, vol. 267:345-382. Springer Berlin/Heidelberg.
28. Zelinka Ivan Real-time deterministic chaos control by means of selected evolutionary techniques. Eng Appl Artificial Intell 2009, 22(2):283-297.
29. Senkerik Roman, Zelinka Ivan, Oplatkova Zuzana Comparison of differential evolution and soma in the task of chaos control optimization - extended study: complex target cf. Proceedings of the eleventh conference on congress on evolutionary computation, CEC'09 2009, 2825-2832. IEEE Press, Piscataway, NJ, USA.
30. Bertsekas Dimitri P Dynamic programming and optimal control 2007, Athena Scientific, vol. II. 3rd ed.
31. Murray J.J., Cox C.J., Lendaris G.G., Saeks R. Adaptive dynamic programming. IEEE Trans Syst Man Cybernet 2002, 32:140-153.
32. Lewis F.L., Vrabie D. Reinforcement learning and adaptive dynamic programming for feedback control. IEEE Circuits Syst Mag 2009, 9:32-50.
33. Si J, Barto A, Powell W, Wunsch D. Handbook of learning and approximate dynamic programming. 2004.
34. Morari M., Lee J.H. Model predictive control: past, present and future. Comput Chem Eng 1999, 23:667-682.
35. Allgower F., Findeisen R., K Nagy Z. Nonlinearmodel predictive control: from theory to application. J Chinese Institute Chem Eng 2004, 35(3):299-315.
36. Skaf J., Boyd S., Zeevi A. Shrinking-horizon dynamic programming. Int J Robust Nonlinear Control pages 2010, 1993-2002.
37. Qin S.J., Badgwell T.A. A survey of industrial model predictive control technology. Control Eng Practice 2003, 733-764.
38. Mayne D.Q., Michalska H. Receding horizon control of nonlinear systems. IEEE Trans Automat Control 1990, 35(7):814-824.
39. Bertsekas D.P. Dynamic programming and optimal control 2005, Athena Scientific, Nov. 3rd ed.
40. Kirk A, Sims B. Handbook of metric fixed point theory. 2001.
41. Khalil H. Nonlinear systems 2002, Prentice Hall, January.
42. Ott E., Grebogi C., Yorke J.A. Controlling chaos. Phys Rev Lett 1990, 64:1196-1199. Mar.
43. Kemih K., Filali S., Benslama M., Kimouche M. Passivity-based control of chaotic Lu system. Int J Innovative comput inform control 2006, 2(2):331-337.
44. Donglian Qi, Guangzhou Zhao, Yunzhong Song. Passive control of Chen chaotic system. In: Fifth world congress on intelligent control and automation, WCICA, vol. 2. June 2004. p. 1284-86.
45. Wang C, Ge SS. Singularity-free adaptive backstepping control of uncertain lorenz system. In: Proceedings of the American control conference, vol. 5. 2000. p. 3143-3147.
46. Mascolo S., Grassi G. Passivity-based control of chaotic Lu system. Int J Bifurcation Chaos 1999, 9(7):1425-1434.
47. Fuh C.C., Tung P.C. Controlling chaos using differential geometric method. Phys Rev Lett 1995, 75:2952-2955. Oct.
48. Bishop C.M. Pattern recognition and machine learning 2006, vol. 4. Springer.
49. Leshno Moshe, Schocken Shimon Multilayer feedforward networks with a nonpolynomial activation function can approximate any function. Neural Networks 1993, 6:861-867.