SOFTWARE IMPLEMENTATION OF ALGORITHMS FOR SOLVING THE SPEED-IN-ACTION PROBLEM FOR LINEAR DISCRETE-TIME SYSTEMS

The article discusses the development of software for solving the speed-in-action problem for linear systems with discrete time and first-order constraints (geometric or summary). Algorithms for constructing an optimal process are formulated and the main theoretical information necessary for their derivation is given. In particular, the discussed solution method is based on the apparatus of null-controllable sets, which was developed in previous theoretical works, and the dynamic programming method. The computational complexity of these algorithms is estimated. It is demonstrated that the solution of the speed-in-action problem can be performed in polynomial time depending on the minimum time (in the case of geometric constraints, this requires additional polyhedral approximations of null-controllable sets). A description of the computer program, all its structural elements and interface, composed using the programming language MatLab, is presented. The program uses the Quick Hull algorithm as its main tool when constructing null-controllable sets, and the interior point method for solving linear and quadratic programming problems when calculating optimal control and polyhedral approximation, respectively. The program output is provided in graphical and text formats. The operation of the software is demonstrated by the example of solving the problem of the fastest stabilization of glucose and insulin levels in blood plasma. Two mathematical models are considered: with restrictions on the volume of a singe injection of insulin and glucose and with restrictions on the total permissible volume of all injections. The first statement corresponds to geometric constraints on control, the second statement is described by summary constraints.