Improving methods for constructing extreme control systems

Abstract

Improving methods for constructing extreme control systems

Boldyrev D.V., Koldaev A.I., Evdokimov A.A., Kocherov Y.N.

Incoming article date: 08.09.2023

A new approach to increasing the efficiency of extreme control systems by improving the method of searching for the extremum of the objective function is presented. In its multidimensional nonlinear optimization, instead of a traditional linear search along a once selected direction, an exploratory search is used, the direction of which at each step is adapted to the topology of the objective function. This makes it possible to localize an extremum as quickly as possible and significantly reduce the time of its determination. An algorithm for interpolation search for an extremum in the found interval is proposed. The objective function is modeled by a cubic spline segment based on information about its gradient vector at the boundary points of the interval, as a result of which the number of interpolation search steps is significantly reduced. The possibility of simplified nonsmooth interpolation using first-order splines in the extremum region is considered. The results of a numerical experiment confirm the high efficiency of the new method in solving various problems.

Keywords: extremal control systems, nonlinear optimization, acceleration of extremum search, quasi-Newton method, polynomial interpolation, non-smooth interpolation