In this paper, a novel limit-cycle navigation method is proposed for a fast mobile robot using the limit-cycle characteristics of a 2nd-order nonlinear function.
Specifically, the extended Kalman filter, ensemble Kalman filter and particle filter are used to track the limit cycle oscillations of a Duffing oscillator using noisy observational data.
So it is necessary to use non-linear analysis: the center manifold approach and the rational approximants are used to obtain the limit cycle of the non-linear system and to study the behaviour of the system in the unstable region.
The equivalent linearization method based on the first order asymptotic solution of the KBM method and the method based on the second order asymptotic solution of the KBM method are used to analyze the limit cycle flutter of the wing with store system.
Often the only information used is the frequency and amplitude of the limit cycle, which then using the describing function analysis provides estimates for the ultimate gain and frequency of the process.
Then the control of the limit cycle using a time-delayed displacement feedback is investigated.
For the in silico data of varying quality used in Figures 2, 3- 4, we used the known limit cycle x t) to generate data points x ^ i (t j ) at each of M sampling points.
The detection stage uses spatial memory to identify the limit cycle.
Finally, the centre manifold approach is used to obtain equations for the limit cycle amplitudes.
Using the computer algebra system Mathematica, the limit cycle configurations of { ( 8 ), 3 } and { ( 3 ), 6 } are obtained under synchronous perturbation at degenerate singular point and infinity.
