Об одном методе определения параметрической чувствительности фазовых координат динамических систем

Abstract

The article presents a rational method for determining sensitivity functions of the first and second orders of phase coordinates to changes in system parameters and external effects. With this approach it is not necessary to integrate intricate chain- coupled differential equations with respect to sensitivity functions of various orders. A vector of additional variables (invariants) of the same dimension is introduced as the vector of phase coordinates. To find it, a conjugate linear inhomogeneous differential equation is obtained, which must be integrated in the inverse time. The sensitivity functions of any order can be calculated independently from each other using this vector. No assumptions reducing the accuracy of the result or restricting the capabilities of the method are made. The linearity of the equation with respect to invariants allows solving the problem in the more convenient form. Using the recurrence relation, the sensitivity functions are calculated sequentially in time from the initial point. The solution of the equation is expressed through a fundamental matrix which is computationally treated as a multiplicative integral. The results are illustrated by the example.