Construction of Reachable Sets of Two-Dimensional Nonlinear Controlled System By The Pixel Method

Abstract

We describe the pixel method for the construction of reachable sets in various optimal control problems using parallel computation technology. A program has been developed for the construction of reachable sets in nonlinear controlled systems by the pixel method. Sample cases have been examined with known analytical representations for the reachable set boundary. The sample library has been expanded. For problems with gravitational-type nonlinearity we analyze the comparison of the constructed approximation with the corresponding analytical representation. The approximation accuracy is shown to depend on the selection of input parameters.