The application of analytical methods to the study of Pareto - optimal control systems

Nauka i Obrazovanie

I. K. Romanova¹ 

[1] Bauman Moscow State Technical University;

关键词: multiobjective optimization;    Pareto - optimal solutions;    comonotonicity and contramonotonicit;    synthesis of control systems;    missiles;   

DOI  :  10.7463/0414.0704897

来源: DOAJ

【 摘 要 】

The subject of research articles - - methods of multicriteria optimization and their application for parametric synthesis of double-circuit control systems in conditions of inconsistency of individual criteria. The basis for solving multicriteria problems is a fundamental principle of a multi-criteria choice - the principle of the Edgeworth - Pareto. Getting Pareto - optimal variants due to inconsistency of individual criteria does not mean reaching a final decision. Set these options only offers the designer (DM).

An important issue when using traditional numerical methods is their computational cost. An example is the use of methods of sounding the parameter space, including with use of uniform grids and uniformly distributed sequences. Very complex computational task is the application of computer methods of approximation bounds of Pareto.

The purpose of this work is the development of a fairly simple search methods of Pareto - optimal solutions for the case of the criteria set out in the analytical form.

The proposed solution is based on the study of the properties of the analytical dependences of criteria. The case is not covered so far in the literature, namely, the topology of the task, in which no touch of indifference curves (lines) level. It is shown that for such tasks may be earmarked for compromise solutions. Prepositional use of the angular position of antigradient to the indifference curves in the parameter space relative to the coordinate axes. Formulated propositions on the characteristics of comonotonicity and contramonotonicity and angular characteristics of antigradient to determine Pareto optimal solutions. Considers the General algorithm of calculation: determine the scope of permissible values of parameters; investigates properties comonotonicity and contraventanas; to build an equal level (indifference curves); determined touch type: single sided (task is not strictly multicriteria) or bilateral (objective relates to the Pareto); for Pareto - tasks in the presence touch formed the system of algebraic equations whose solution yields the equation of the line Pareto in the parameter space. Display space criteria provides the required Pareto - border; in the absence touch analyzes the property of monotonicity. Analysis of derivatives enables you to define two borders in the parameter space (abscissa and the ordinate axis or at the borders, their parallel).

The obtained analytical results are applied to the problem of parametric synthesis of control systems. In the framework of the given structure of double-circuit system suitable made use of a system of differential equations instead of the traditional structural schemes. The formula that shows the change dynamic coefficients of unmanaged system after applying the correction. The choice of direct quality criteria, calculated according to the transition process, made the decision problem is most visible and effective. As quality criteria selected rise time and overshoot. As parameters used the gains of the sensors of angular velocity and linear accelerations. Isolated in the space of parameters of stability and oscillatory. Given the author's conclusion formulas for gradients of direct quality criteria - and rise time overshoot. Built fields antigradient and the level lines of the criteria. The analysis of the properties of contramonotonicity all of the criteria specified parameters. In accordance with the claims put forward by tradeoff line in the space of parameters and displaying them in the form of lines of Pareto on space criteria. The use of traditional means of sensing space parameters showed the reliability of the obtained analytical manner. The calculation results for the synthesis of double-circuit motion control systems of flying devices can be used for selection of possible directions of improvement of conflicting criteria. The proposed method is able to replace traditional methods of synthesis of the systems under consideration on the basis of methods of frequency characteristics. The results allow to assess the limits of parametric correction within the existing structure.

【 授权许可】

Unknown