Linearization and Reduction: Two Approaches to the Formation of Models of Dynamic Systems

摘要

We considered one of the central problems of technical objects modeling - the formation of models of nonlinear dynamic systems. We also carried out a comparative analysis of two major approaches: linearization and reduction. The advantages and disadvantages of each approach and the problems of their use were noted. We proposed a number of approaches to improving linearization procedures, including reduction of the problem of reducing the estimation error to the solution of the Riccati equation and direct application of optimization formulas, for example, Newton's method. It is also proposed to introduce a different optimization criterion in comparison with the generally accepted one, namely, the norm of the difference between the vectors of the dynamic state of the object obtained by exact and approximate solutions. It is proposed to use in the calculation of the base for comparison, i.e. determining the exact values when modeling the right-hand side of the nonlinear model of the system is not the current iterations, but the known exact nonlinear solution. We noted the need for comparative calculations at the initial and equilibrium points. The application of linearization technologies in solving the problem of reduction of nonlinear systems is considered. The influence of linearization errors on the accuracy of the results of the reduction of nonlinear systems is estimated. The ratio of reduction and linearization as two interconnected technologies is analyzied.