On the Estimation of Time-varying Parameters in Continuous-time Nonlinear Systems

Finite-Time Estimation of Time-Varying Frequency Signals in Low-Inertia Power Systems

“…This is achieved by interpreting the frequency as a time-varying parameter and, inspired by ideas from [19] and [20], deriving a time-varying version of the super twisting algorithm in vector form for the estimator design. The present approach avoids the typical over-parameterization pertinent to methods based on series expansion [21], [22], [23] and does, hence, not increase the dimension of the frequency estimator. 2) To provide a set of sufficient conditions for the estimator gains, the feasibility of which guarantees exact convergence of the estimated frequency signal in finite time.…”

“…and by substituting p 1 = 2 k 2 − k 1 /A and p 2 = 1, the above expressions are equivalent to λ − and λ + defined in (10). (22) is satisfied. This condition is the one used in Theorem 1, which hence summarizes all findings of the derivations detailed in this section.…”

Parameter identification for a stochastic SEIRS epidemic model: case study influenza

“…The best known identification techniques for non-linear deterministic models and constant parameter values use Taylor series (Gunn et al 1997;Pohjanpalo 1978), similarity transformations (Chappell et al 1990;Evans et al 2002;Vajda et al 1989), or differential algebra (Audoly et al 2001;Eisenberg 2013;Eisenberg et al 2013;Ljung and Glad 1994). For time-dependent parameters, differential algebra approaches can also be used (Hadeler 2011;Mummert 2013;Pollicott et al 2012), as well as modulating functions methods (method of moment functionals) (Ungarala et al 2013).…”