On a class of the first kind Volterra equations in a problem of identification of a linear nonstationary dynamic system

This paper proposes an approach to the identification of a nonstationary linear dynamic system. Its input-output mathematical model is presented as a Volterra equation of the first kind. The problem of nonparametric identification of Volterra kernels is solved on the basis of an active experiment using test piecewise linear signals (that have a rising front). The problem statement is based on the conditions for modeling the dynamics of technical devices in the energy and power industry. The choice of an admissible family of input signals is driven by the complexity of generating piecewise-constant type signals for real energy objects. The original problem is reduced to solving Volterra integral equations of the first kind with two variable integration limits. A formula for the inversion of the integral equations under study is constructed. Sufficient conditions are obtained for the solvability of the corresponding equations with respect to Volterra kernels in the class of continuous functions.