Control of the Lorenz Chaos by the Exact Linearization

Chen Liqun; Lin Yanzhu

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Article Navigation > Applied Mathematics and Mechanics > 1998 > 19(1): 62-69

Chen Liqun, Lin Yanzhu. Control of the Lorenz Chaos by the Exact Linearization[J]. Applied Mathematics and Mechanics, 1998, 19(1): 62-69.

Citation:

Chen Liqun, Lin Yanzhu. Control of the Lorenz Chaos by the Exact Linearization[J]. Applied Mathematics and Mechanics, 1998, 19(1): 62-69.

Citation:

Chen Liqun, Lin Yanzhu. Control of the Lorenz Chaos by the Exact Linearization[J]. Applied Mathematics and Mechanics, 1998, 19(1): 62-69.

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Control of the Lorenz Chaos by the Exact Linearization

Department of Engineering Mechanics Shanghai Jiaotong University, Shanghai 200030, P. R. China

Received Date: 1996-05-13
Rev Recd Date: 1997-05-21
Publish Date: 1998-01-15

Abstract

Abstract

Controlling chaos in the Lorenz system with a controllable Rayleigh number is investigated by the sate space exact linearization method. Based on proving the exact linearizability, the nonlinear feedback is utilized to design the transformation changing the original chaotic system into a linear controllable one so that the control is realized. A numerical example of control is prsented.
- Rayleigh number,
- Lorenz system,
- chaos

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References(25)

References

[1]	T.Shinbrot,C.Grebogi,E.Ott and J.A.Yorke,Using small perturbation to control chaos,Nature,363(1993),411-474.
[2]	G.Chen and X.Dong,From chaos to order:perspectives and methodologies in controlling chaotic non-linear dynamical systems,Int.J.Bifur.Chaos,3(1993),1363-1490.
[3]	M.J.Ogorzalek,Taming chaos:control,IEEE Tran.Circ.Syst.I.,40(1993),700-706.
[4]	B.Blazejcyzk,T.Kapitaniak,J.Wojewoda and J.Brindly,Controlling chaos in mechanical systems,Appl.Mech.Rev.,46(1993),385-395.
[5]	张辉、吴淇泰,混沌运动的控制,力学进展,25(1995),392-399.
[6]	陈立群、刘延柱,控制混沌的原理和应用,物理,25(1996),278-282.
[7]	E.N.Lorenz,Deterministic non-periodic flow,J.Atmos.Sci.,20(1963),130-141.
[8]	A.Isidori,Non linear Control Systems,Springer-Verlag(1989),156-172.
[9]	C.Sparrow,The Lorenz Equation Bifurcations,Chaos,and Strange Attractors,Springer-Verlag(1982).
[10]	J.L.Breeden and A.Hubler,Reconstructing equations of motion from eqperimental data with unob-served variables,Phys.Rev.A,42(1990),5817-5826.
[11]	E.A.Jackson,Control of dynamic flows with attractors,Phys.Rev.A,44(1991),4839-4853.
[12]	D.Gligorlski,D.Dimovski and V.Urumov,Control in multidimensional chaotic systems by small perturbations,P hys.Rev.E,51(1995),1690-1694.
[13]	R.Mettin,A.Hubler and A.Scheeline,parametric entrainment control of chaotic systems,Phys.Rev.E,51(1995),4065-4075.
[14]	E.A.Jackson and I.Grosu,An open-plus-closed-loop(OPLC) control of complex dynamic systems,Phys.D,85(1995),1-9.
[15]	Chen Liqun and Liu Yanzhu,Parametric open-plus-closed-loop control of chaos in continuous dynamical systems,Act a,Mechanics Solida Sinica,10(4)(1997).
[16]	T.L.Vincent,J.Yu,Control of a chaotic system,Dyn.Contr.,1(1991),35-52.
[17]	Z.Qu,G.Hu and B.Ma,Controlling chaos via continuous feedack,Phys.Lett.A,178(1993),265-270.
[18]	J.Alvarez-Gallegos,Nonlinear regulation of a Lorenz system by feedback linearization techniques,Dyn.Contr.,4(1994),277-289.
[19]	C.J.Wan and D.Bernstein,Nonlinear feedback control with global stabilization,Dyn.Contr.,5(1995),321-346.
[20]	20 T.W.Carr and I.B.Schwartz,Controlling unstable steady states using system parameter variation and control duration,Phys.Rev.E,50(1994),3410-3415.
[21]	M.Stampfle,controlling chaos through iteration sequences and interpolation techniques,Int.J.Bifur.Chaos,4(1994),1697-1701.
[22]	T.T.Martley and F.Mossayebi,A classical approach to controlling the Lorenz equations,Int.J.Bifur.Chaos,2(1992),881-887.
[23]	T.B.Fowler,Application of stochastic control techniques to chaotic nonlinear systems,IEEE Tran.Auto.Contr.,34(1989),201-205.
[24]	T.H.Yeap and N.U.Ahmed,Feedback control of chaotic systems,Dyn.Contr.,4(1994),97-110.
[25]	K.Ogata,Modern Control Engineering,Prentice-Hall,(1990),776-795.