Integral operators for the reconstruction of the phase vector of dynamical systems (Q2731787)

The author considers the nonlinear analytical dynamical systems NEWLINE\[NEWLINEdx/dt=f(x(t)),\quad y=g(x(t)),\quad f\in C^\omega(U,\mathbb R^n), \quad g\in C^\omega(U,\mathbb R^1).NEWLINE\]NEWLINE The initial data are unknown. The interval of observation \([0,T]\) and the set of possible finite states \(\{x(T)\}\subseteq U\) in the phase space \(\mathbb R^n\) are given. The problem consists in the construction of the operation enabling any possible realizations of a device to determine uniquely the unknown phase vector. In function dependence terms, a description of observable functions is obtained. An analogue of the duality principle in linear systems is developed for the nonlinear case.