First Integrals and Closed-form Solutions of Some Singular Optimal
Control Problems
Abstract
This article analyze singular optimal control problems (SOCP) from
different areas of engineering and applied mathematics. We use the
notion of partial Hamiltonian and we show that every singular optimal
control problem can be written in the form of current value or standard
Hamiltonian. The partial Hamiltonian approach is used to compute the
partial Hamiltonian operators and first integrals. Then these first
integrals are utilized to construct the closed-form solutions of hybrid
vehicle optimal energy management model, optimal harvesting mathematical
model and model of membrane filtration system. We explain how one can
use partial Hamiltonian approach for both finite horizon and infinite
horizon systems. This study provides a new way of solving singular
optimal control problems.