Reference : Estimation and approximation in nonlinear dynamic systems using quasilinearization
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Physical, chemical, mathematical & earth Sciences : Mathematics
http://hdl.handle.net/2268/167925
Estimation and approximation in nonlinear dynamic systems using quasilinearization
English
Frasso, Gianluca mailto [Université de Liège - ULiège > Institut des sciences humaines et sociales > Méthodes quantitatives en sciences sociales >]
Jaeger, Jonathan [Nestlé > Research Center, Lausanne, Switzerland > > >]
Lambert, Philippe mailto [Université de Liège - ULiège > Institut des sciences humaines et sociales > Méthodes quantitatives en sciences sociales >]
30-Apr-2014
19
No
[en] Nonlinear differential equations ; Penalized splines ; Quasilinearization ; State conditions
[en] Nonlinear (systems of) ordinary differential equations (ODEs) are common tools in the analysis of complex one-dimensional dynamic systems. In this paper we propose a smoothing approach regularized by a quasilinearized ODE-based penalty in order to approximate the state functions and estimate the parameters defining nonlinear differential systems from noisy data. Within the quasilinearized spline based framework, the estimation process reduces to a conditionally linear problem for the optimization of the spline coefficients. Furthermore, standard ODE compliance parameter(s) selection criteria are easily applicable and conditions on the state function(s) can be eventually imposed using soft or hard constraints. The approach is illustrated on real and simulated data.
http://hdl.handle.net/2268/167925
http://arxiv.org/abs/1404.7370

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