Design solutions selection while developing a system of unmanned flying vehicles in conditions of multi-target uncertainty

Аuthors

Malenkov A. A.

Central Research Institute of Machine Building, TSNIIMash, 4, Pionerskaya str., Korolev, Moscow region, 141070, Russia

e-mail: malenkov.anton@mail.ru

Abstract

The article is devoted to the design solutions selection while developing a system of unmanned aerial vehicles in conditions of uncertainty. The presented article such system is assumed as a party of cruise missiles (CM) targeted at hitting an enemy naval ship grouping.

Besides solving the problem of cruise missiles optimal distribution over the target assignments this work solves the problem of ensuring stability at large. Here, the stability means achieving the probability of hitting the targets, no less than the specified one, for all possible values of uncontrolled factors.

By stability in the article is meant the achievement of the probability of defeat of target tasks not lower than given for all possible values of uncontrollable factors. Thus, the problem is set as:

where d is the vector of design parameters, E(ω) is the distribution function, and P is the probability of failure.

The distribution function E(ω) is constructed with engagement of statistical synthesis operations. A regularity criterion was adopted as a criterion of stability:

where Κ_¡  is the Lipschitz constant in the i-th row of the statistical sample of the N volume, Κ_¡pos is the specified value of the Lipschitz constant.

To ensure stable design solution, the contracting mapping is necessary, i.e. the Lipschitz constant should be less than one. With this, the less the Lipschitz constant value, the higher the degree of the design solution stability.

At each step of the statistical sample, two variants of design parameters are set. They are necessary for stability condition calculatiщn. The model values of the Lipschitz constant are restored in the class of trigonometric polynomials:

The problem of CM system optimal ranging is being solved at the already obtained stable vector of the design solution (the set of design parameters) y^ust.

The presented work solved the problem of CM system of optimal ranging, which maintains six target problems. The initial thrust-to-weight ratio and the wing area are assumed as design parameters. The target’s required payload mass, coordinates, speed and course are assumed as uncontrolled parameters.

Three nominal sizes of CMs were considered in the framework of the set problem:

Depending on the uncontrolled factors values, two variants of the cruise missiles optimal ranging were solved, and two distribution functions Ε(ω) were constructed. It is shown that the probability of the system performing the target task appeared to be the same and equals to Ρ – 0,9.

Further, the problem of a design solution selection stable to uncontrolled factors was solved. The stability conditions gave the following design parameters:

Thus, a cruise missile with such parameters solves all the target problems with uncontrolled factors given in the work, i.e. the cruise missile system includes cruise missiles of the same type, and the probability of accomplishing the target problem by the system is 0.9.

Keywords:

multifactor uncertainty, statistical sampling, Lipschitz constant, regularity criterion, stable design solution

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