An Algorithm for Obtaining Bang–Bang Control Laws

Bang-bang control problems have long been of interest to control engineers. Much of the theoretical study of these problems has been limited to linear systems and the results are usually problem-specific. This paper presents a new computational method for solving control problems when it is desired that the control action be bang-bang. A gradient-based algorithm is developed where the switching times are updated to minimize the final state missed distance. The algorithm explains how a change in a switching time propagates through the other switching times and affects the final state. The algorithm is applicable to linear and nonlinear problems, including multi-input systems.