ИСТИНА

The solution of a wide range of optimal control problems involves constructing reachable sets and their analogs. The pixel method of constructive description and determination of the reachable sets for a given controlled system is described and implemented. For the initial set we build the characteristic matrix in the following way: all the set is covered up with the grid. The size of this grid depends on our implementation. If the element from the initial set reaches the grid node, the corresponding position of the characteristic matrix is 1, otherwise it is 0. Then at every step we work with characteristic matrix. We go from one moment of time to another with time steps and we solve the Cauchy problem every time. In the pixel method parallel computing is applied to characteristic matrix work, because the work with every pixel element goes independently in parallel way. Presented algorythm is used to solve the problem of construction of reachable sets numerically. CUDA (Compute Unified Device Architecture) technology allows to use Graphics Processing for parallel processing Units. CUDA is a complex of software and hardware tools. CUDA is a parallel computing platform and a programming model. It dramatically increases the computing performance by increasing the power of the graphics processing units (GPU). The effectiveness of the approach is demonstrated on several examples. Based on realistic numerical values for control examples we conclude that the computed reachable sets are in fact full thrust. The approach may be applied to multidimensional problems.