10 research outputs found
Use of synchronization and adaptive control in parameter estimation from a time series
A technique is introduced for estimating unknown parameters when time series
of only one variable from a multivariate nonlinear dynamical system is given.
The technique employs a combination of two different control methods, a linear
feedback for synchronizing system variables and an adaptive control. The
technique is shown to work even when the unknown parameter appears in the
evolution equations of the variables other than the one for which the time
series is given. The technique not only esablishes that explicit detailed
information about all system variables and parameters is contained in a scalar
time series, but also gives a way to exract it out under suitable conditions.
Illustrations are presented and effect of noise is studied.Comment: Revised for simultaneous estimation of many parameters. 24 pages of
RevTex, 12 figures in postscript files. To appear in PR(E
Dynamic algorithm for parameter estimation and its applications
We consider a dynamic method, based on synchronization and adaptive control, to estimate unknown parameters of a nonlinear dynamical system from a given scalar chaotic time series. We present an important extension of the method when the time series of a scalar function of the variables of the underlying dynamical system is given. We find that it is possible to obtain synchronization as well as parameter estimation using such a time series. We then consider a general quadratic flow in three dimensions and discuss the applicability of our method of parameter estimation in this case. In practical situations one expects only a finite time series of a system variable to be known. We show that the finite time series can be repeatedly used to estimate unknown parameters with an accuracy that improves and then saturates to a constant value with repeated use of the time series. Finally, we suggest an important application of the parameter estimation method. We propose that the method can be used to confirm the correctness of a trial function modeling an external unknown perturbation to a known system. We show that our method produces exact synchronization with the given time series only when the trial function has a form identical to that of the perturbation
Dynamics of stick-slip in peeling of an adhesive tape
We investigate the dynamics of peeling of an adhesive tape subjected to a
constant pull speed. We derive the equations of motion for the angular speed of
the roller tape, the peel angle and the pull force used in earlier
investigations using a Lagrangian. Due to the constraint between the pull
force, peel angle and the peel force, it falls into the category of
differential-algebraic equations requiring an appropriate algorithm for its
numerical solution. Using such a scheme, we show that stick-slip jumps emerge
in a purely dynamical manner. Our detailed numerical study shows that these set
of equations exhibit rich dynamics hitherto not reported. In particular, our
analysis shows that inertia has considerable influence on the nature of the
dynamics. Following studies in the Portevin-Le Chatelier effect, we suggest a
phenomenological peel force function which includes the influence of the pull
speed. This reproduces the decreasing nature of the rupture force with the pull
speed observed in experiments. This rich dynamics is made transparent by using
a set of approximations valid in different regimes of the parameter space. The
approximate solutions capture major features of the exact numerical solutions
and also produce reasonably accurate values for the various quantities of
interest.Comment: 12 pages, 9 figures. Minor modifications as suggested by refere