About nonparametric modeling of dynamic processes

The problem of non-parametric modeling of linear dynamic processes is discussed. Discrete form of the Duhamel integral for zero initial conditions is used as the model: t / At *s (t) =Z hs (t -Ti )u (Ti )At, i=1 where h (t) is the assessment of the weight function, u(t) - input action, Дт - time-step discretization, xi = г'Дт - the value of time discretization. As an estimate of the weight function is used nonparametric regression estimator. By definition: the weighting function is a reaction to the system input action in the S-function form. In this paper, as an approximation of S-function system is used: H,t e [0, AT + At]; u(t) = { (0,t g [0, AT + At]. Input effect can be given through the width of the interval ог through height of level. These methods have different input 5 parameters, in the first case, the width of the interval is given and height of level is defined, in the second case, the height of level is fixed and the width of the interval is defined. The accuracy of the weighting function depends on these parameters, so when the input effect is defined with the width of the interval, weight function is closer to the true value than the other way. If the estimate of the weight function is used in the simulation, which is as close to the true value, then the model is effective in determining the system response to arbitrary input action. This method is applicable for modeling linear dynamic systems, without reference to the order of equation of the describing system.

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