The Problem of Quality for Nonlinear Self-Regulating Systems with Quadratic Metric

The systems considered in this paper are characterized by differential equations of the form which are defined over a region N of Euclidean space with metric , and with ranging over some interval . The are assumed to be such that 1) and 2) there exist positive constants such that for all points in and all in . The problem of quality means the problem of determining the values of adjustable parameters in the , and in such a way as to result in a rapid return to equilibrium of the representative point in phase-space subject to a limitation on the amount of overshoot. This problem is formulated in precise terms, and a method of solution for it is indicated. As an illustration, the method is applied to a problem in regulation which was formulated by Bulgakov.