Voronov

Description of dynamically controlled object flat trajectory with piecewise constant plots of control was obtained with use of logarithmic spiral plot. Examples of the segments of acceleration and deceleration with fixed values of normal and tangent overloads were included in the article. The usage of this approximation method for models moving along the flat trajectories allows to substitute system of differential equations with analytical dependences.  That technique leads to significant reduce in trajectory creation time.

The problem of trajectory safety ensuring for the dynamic controlled object (DCO) that moves on a plane in which circle forbidden zone exists is considered. Mathematical model of DCO motion is described. At first the case of static circle forbidden zone is considered for the formalization of the fly-around problem, intervals of non-safety courses of motion which form a zone of dangerous trajectories for the class of piecewise path segments of motion consisting of trajectory of sharp turn of the maximum curvature and linear path segment after it. Problem of evaluation of the zone of dangerous trajectories in the case of dynamic circle forbidden zone is considered on the basis of the obtained description. As a result iteration algorithm of the zone of dangerous trajectories evaluation is formed.

The problem of conflict-optimum counteraction of small groups of aircrafts in the form of two-stage procedure of ranking-allocation and conflict optimization by Nash for obtaining the stable-effective decision in the shape of matrix of conflict-optimum target setting is considered. Calculating time in the case of the exhaustive search is far from real-time, therefore the procedure of thinning of the counteraction effectiveness matrix is proposed, as a result the operating speed for the problem of counteraction of 4-by-4 aircrafts is rising twenty-fold.