On recovering the parameters and velocity state of the Duffing's oscillator

On the Parameters Estimation of the Duffing System by Systems Synchronization

“…We summarize our previous discussion in the following proposition: Proposition 1: Under assumptions A1 and A2, the synchronization and the parameters estimation problem among systems (1) and (4), is achieved for any strictly positive constants k 1 and k 2 .…”

“…A similar work, with similar tools, is presented in [18,3]. Finally, we mention the previous works of [1], [13,11] where the authors solve only the estimation problem by using some algebraic properties that some chaotic systems satisfy. In this paper we deal with the synchronization and identification of the Duffing mechanical oscillator (DMO).…”

“…where the set of constants {k 1 , k 2 }, and p the estimate of p, will be determined later. In general, the nonlinear coupled systems (1) and (4) are known as the master and the slave systems, respectively. We want y → x, as t → ∞, when p = p. In other words, we need to find another set of differential equations for vector p of (4), such that (y, p) → (x, p), as long as t → ∞.…”

Finite-time parameters estimation of the Chua system

“…When the state of the system is not fully measurable, then the identification problem becomes more difficult due to the necessity to estimate, besides the parameters, also the hidden state variables from the sole input/output measurements. To solve this problem, in [5] an efficient approach for the estimation of the non-available state variables for the Duffings chaotic system is proposed by obtaining an integral output parametrization of the hidden state variables. In this context, the kernel-based method designs a class of Bivariate Causal Non-asymptotic Kernel (BC-NK) to form the Volterra integral operator, providing a finite-time parameter estimation for continuous-time linear systems, annihilating the effects of the unknown initial conditions and avoiding the need for output derivatives computations.…”

Reconstructing and Identifying the Rossler's System by Using a High Gain Observer

“…Also, we recommend the papers [2,8,9,12,[13][14][15]. Another approach is based on control theoretical ideas, such as inverse system design and system identification, as devices to recover parameters and unknown or difficult-to-measure states [4,[16][17][18][19].…”