Methods for recovery input signals of nonlinear nonstationary dynamic systems

The problem of input signals recovery is one of the key problems in many branches of science and technology: in measurement technology for dynamic measurements; in control tasks, where the control is based on the input signal (stabilization task); in tasks of image restoration and filtering, etc., which determines the relevance of the development of methods of input signal recovery. The relevance of development of input signal recovery methods is increasing every year and becomes the most pronounced at operation of measuring and control systems in extreme and harsh operating conditions. Non-stationarity and nonlinearity in these conditions are the most pronounced, accounting of which is a prerequisite for the creation of new and improvement of existing information-measuring and control systems. The paper proposes methods for determining the input signal of nonlinear dynamic systems described by the Volterra functional series. The methods are based on the solving of a nonlinear integral equation, which is defined by a finite segment of the Volterra series. The input signal recovery is carried out under the assumption that the integral transforms of Volterra kernels possess factorization based on Borel's theorem, which leads to a nonlinear algebraic equation. Recovery methods of continuous nonlinear dynamic systems described by a finite Volterra series and their discrete analog are considered. When recovering the input signal, for continuous systems the integral Laplace transform is applied, for discrete systems the Z-transform is applied. An example of a mathematical solution to the problem of restoring a discrete one-dimensional signal is given, illustrating the efficiency and effectiveness of the developed methods. The results of studies on restoring signals of nonlinear dynamic systems will be useful to specialists engaged in theoretical research and mathematical modeling in the field of digital signal processing and vector analysis of electrical circuits.