Model Formulation

Note

In-depth information about the theoretical underlying and the calculation methods will be described in a book chapter releasing in the near future.

This library supports systems whose state variable vector \(x = (x_1, x_2, ..., x_n)\) evolution in time \(t\) is described by the ODEs:

(1)\[\begin{split}\begin{alignat}{3} &\dot{x}(t) &&= f(t, x, u, p)\\ &x(t_0) &&= x_0 \end{alignat}\end{split}\]

Here \(x_0 (t_0)\) is an initial condition, \(u\) is a vector of an external inputs, and \(p\) are the estimated parameters of the system. The observable (measured value) of the system \(y\) at a time \(t_i\) is described as

(2)\[\begin{alignat}{3} &y (t_i) &&= g(t_i, x (t_i), u, p) + \epsilon (t_i), \end{alignat}\]

where the function \(g\) is the model output, and \(\epsilon\) is the measurement noise.