The Synthesis of Compromise-Optimal Mobile Objects Trajectories in a Conflict Environment

Introduction

In Chapter 6, we considered the problem of resolving the problematic (negative, alarm, dangerous, conflict) situations arising in different subject areas. When searching for the optimal trajectories of moving objects, we have to take into consideration that the object is usually under the influence of a conflict environment. By the latter we mean a set of subjects (mobile and fixed) arranged in a search area, oncoming of the moving object to which is not desirable. Subjects that constitute a conflict environment will be called conflicting. The terms “conflict”, “conflicting” are introduced in this case in order to emphasize the contradictory requirements to the trajectory of the mobile object movement in a conflict environment.

Thus, the desired trajectory must be characterized by the lowest path length, on one hand, and extend as far as possible from the conflicting subjects, on the other. There is a need to find a compromise solution.

Thus, the desired trajectory of the mobile object moving in a conflict environment, must as far as possible meet the following requirements:

• 1.

  Characterized by the lowest path length;

• 2.

  Take place as far as possible from the fixed conflicting subjects;

• 3.

  To ensure the greatest possible distance from the moving conflicting subjects.

The term “possible” is not accidental; it reflects the true to type of multicriteria problems inevitability of compromises.

As a rule, the conflict environment consists of conflicting subjects, the presence of which in the optimal trajectory search area is due to reasons not related to the passage of the mobile object through the zone. For example, the current configuration of the boundaries of the river banks is due to physic processes in nature and is not related to the mobile object, although it imposes on its trajectory certain requirements. Conflicting subjects of this class will be called passive.

Sometimes, however, in dealing with some specific problems of synthesis of the compromise-optimal trajectories, the object is faced with conflicting subjects that are artificially set in the search area in order to complicate its progress to the final destination point. Conflicting objects of this class will be called active. These include a system of anti-aircraft defense systems, minefields, etc.

Thus, for the correct solution of the problem of synthesis the compromise optimal trajectories of objects moving in a conflict environment must be considered and quantified (based on the properties of the conflicting subjects) the effects of the conflict environment on the mobile object trajectory.

Statement Of The Problem

We call multicriteria task of dispatcher the problem of optimal in the sense of the vector criterion I={I_k(x,u,t)}_k=1^s matched transfer of p representative points x={x_j}_j=1^p from the initial states x⁽⁰⁾={x_j⁽⁰⁾}_j=1^p∈X to predetermined final states x^(k)={x_j^(k)}_j=1^p∈X or to specified terminal areas X^(k)={X_j^(k)}_j=1^p⊂X of n-dimensional Euclidean space under the constraints defined by the vector operator inequality A(x,u,t)≤0. There x∈X is the state vector; u∈U – vector of control, belonging to the class of admissible controls U; t∈[t₀,T] – time.

This is the most overall (under consideration here) formulation of multiobjective task of dispatcher. For the classification of individual cases and the subsequent constructive solutions, with respect to the characteristic of each task must be made additional partial speculations.