On the Construction of Suboptimal Trajectories for a Linear Control System with State Constraints on Part of Variables

The article considers the problem of controlling a linear system of differential equations under state constraints and pointwise restrictions on control parameters. Such problems are often found in applications from robotics, in the field of controlling autonomous movement on a plane or in space. As a rule, it is not possible to obtain an exact mathematical solution to such problems, and traditional numerical methods may be ineffective due to the slow speed of work. In recent years, methods for approximate solution of control problems with state constraints using random graphs have become widespread. They have shown high efficiency in the case of trivial dynamics of a controlled object, when it is possible to move without inertia along broken lines. At the same time, problems with so-called kinodynamic constraints (when dynamics are described by nontrivial differential equations) have remained unsolved until recently. Significant progress in this area has been achieved by combining the ideas of constructing random graphs and ellipsoidal estimation techniques developed earlier by academician A. B. Kurzhansky and his students. This article continues the research in this area. The authors propose a new modification of the previously developed methods, which will increase it’s effectiveness and make it suitable for solving specific applied problems. The improvement of the method’s characteristics was achieved by allocating the variables responsible for state constraints and separately processing such variables and the remaining part of the state vector.