State space linearization using the concept of Brunovsky form and Lie derivative is applied to the case of a Hyperchaotic Lorentz System. It is observed that the necessary and sufficient conditions can be satisfied, the analytic form of the controller ‘u’ and the final form of the linearized equations can be obtained. Numerical simulation is used to ascertain the feasibility of the procedure in practice. It may be added that the case of an ordinary Lorentz equation is distinctively different as the controller is to be added in a different manner. The most important aspect of the present analysis is that the controller can be determined and not chosen ad hoc.

References

References
1.
Pecora
,
L. M.
, and
Carroll
,
T. L.
, 1990, “
Synchronization in Chaotic Systems
,”
Phys. Rev. Lett.
,
64
(
8
), pp.
821
824
.
2.
Ott
,
E.
,
Grebogi
,
C.
, and
Yorke
,
J. A.
, 1990, “
Controlling Chaos
,”
Phys. Rev. Lett.
,
64
, pp.
1196
1199
.
3.
Ren-hong
,
L.
, and
Wei-han
,
T.
, 1998, “
Nonlinear Control of Chaos
,”
Chin. Phys. Lett.
,
15
(
4
), p.
249
.
4.
Roy
Chowdhury
,
A.
,
Saha
,
P.
, and
Banerjee
,
S.
, 2001, “
Control of Chaos in Laser Plasma Interaction
,”
Chaos, Solitons Fractals
,
12
(
13
), pp.
2421
2426
.
5.
John
,
J. K.
, and
Amritkar
,
R. E.
, 1994, “
Synchronization of Unstable Orbits using Adaptive Control
,”
Phys. Rev. E
,
49
, pp.
4843
4848
.
6.
Huberman
,
B. A.
, and
Lumer
,
E.
, 1990, “
Dynamics of Adaptive Systems
,”
IEEE Trans. Circuits Syst.,
,
37
, pp.
547
550
.
7.
Andrievskii
,
B. R.
, and
Fradkov
,
A. L.
, 2003, “
Control of Chaos: Methods and Applications. I. Methods
,”
Autom. Remote Control (Engl. Transl.)
,,
64
, pp.
673
713
.
8.
Alvarez-Gallegos
,
J.
, 1994, “
Nonlinear Regulation of a Lorenz System by Feedback Linearization Techniques
,”
Dyn. Cont.
,
4
, pp.
277
298
.
9.
Babloyantz
,
A.
,
Krishchenko
,
A. P.
, and
Nosov
,
A.
, 1997, “
Analysis and Stabilization of Nonlinear Chaotic Systems
,”
Comput. Math. Appl.
,
34
(
2-4
), pp.
355
368
.
10.
Chen
,
L.-Q.
, and
Liu
,
Y.-Z.
, 1999, “
A Modified Exact Linearization Control for Chaotic Oscillators
,”
Nonlinear Dyn.
,
20
, pp.
309
317
.
11.
Yu
,
X.
, 1997, “
Variable Structure Control Approach for Controlling Chaos
.
Chaos, Solitons Fractals
,
8
(
9
), pp.
1577
1586
.
12.
Hou
,
M.
, and
Pugh
,
A. C.
, 1997, “
On Feedback Linearization Solution
,”
Proceedings of the 5th IEEE Mediterranean Conference on Control and Systems
, July, 1997.
13.
Brockett
,
R. W.
, 1978, “
Feedback Invariants for Nonlinear Systems
,”
Proceedings of the Seventh Triennial World Congress
, June, 1978.
14.
Slotine
,
J.-J.
and
Li
,
W.
, 1991,
Applied Nonlinear Control
,
Prentice Hall
,
New York
.
You do not currently have access to this content.