Optimal control problems can in many cases become complicated and difficult to solve. One particular class of difficult control problems to solve are singular control problems. Standard methods for solving optimal control are discussed showing why those methods are difficult to apply to singular control problems. Then standard methods for solving singular control problems are discussed including why the standard methods can be difficult and often impossible to apply without having to resort to numerical techniques. Finally, an alternative method to solving a class of singular optimal control problems is given for a specific class of problems.
College and Department
Physical and Mathematical Sciences; Mathematics
BYU ScholarsArchive Citation
Dewaal, Nicholas, "The Importance of the Riemann-Hilbert Problem to Solve a Class of Optimal Control Problems" (2007). All Theses and Dissertations. 882.
control theory, riemann-hilbert problem, singular control, optimal control, Hamilton-Jacobi-Bellman equation, variation