A numerical method for the approximation of reachable sets of linear control systems

In this article, a numerical method for the approximation of reachable sets of linear control systems is discussed. First a continuous system is transformed into a discrete one with Runge-Kutta methods. Then based on Benson's outer approximation algorithm for solving multiobjective optimization problems, we propose a variant of Benson's algorithm to sandwich the reachable set of the discrete system with an inner approximation and an outer approximation. By specifying an approximation error, the quality of the approximations measured in Hausdorff distance can be directly controlled. Furthermore, we use an illustrative example to demonstrate the working of the algorithm. Finally, computational experiments illustrate the superior performance of our proposed algorithm compared to a recent algorithm in the literature.