A grid-based algorithm for constructing attainability sets with improved boundary approximation

Reachable sets provide a powerful tool for mathematical modeling. The paper proposes a new grid-based algorithm for constructing reachable sets of nonlinear control systems. The main idea of the proposed algorithm is to maximize the accuracy of boundary points computation. It also improves the accuracy of numerical solutions of some control problems. As an example, the paper describes a method for constructing an approximate solution of the time optimal control problem of the RTAC system. This system is used for benchmarking nonlinear control techniques. We implemented the proposed algorithm using the C++ programming language and the OpenMP library and performed a numerical simulation of the considered example. As a result, we constructed the time optimal control law of the RTAC system.