Asynchronous switching and sparse discretization with time scaling for control vector parameterization optimal control

Abstract

This work introduces a novel approach for solving open-loop Optimal Control Problems (OCPs) using multiple time grids, sparse discretization and a time scaling transformation. Control Vector Parameterization (CVP) method parameterizes control variables to create a finite-dimensional problem. The Variable Time Nodes Control Vector Parameterization (VTNCVP) discretization strategy allows each control component an independent time grid, offering enhanced input design flexibility and potentially yielding improved outcomes. A novel time scaling technique for OCPs with multiple time grids is presented that is easier to comprehend than existing methods and can circumvent some numerical difficulties. Additionally, Multiple Grid (MG)–Sparse Variable Time Nodes (MG-SVTN) is presented. This novel discretization strategy employs asynchronous switching with user-specified numbers of subdivisions for input controls, potentially yielding comparable objective function values to VTNCVP while reducing the dimensionality of decision variables. Two example problems with path constraints are solved using the methods.