Uniform Trigonometrization Method for Optimal Control Problems with Control and State Constraints

Abstract

Application of indirect optimization methods to solve constrained optimal control problems is not a straightforward task. This study presents a new construct, the Uniform Trigonometrization Method (UTM), that enables handling problems with control bounds and state path constraints within the indirect formalism. First, three different classes of problems are discussed with 1) bang–bang and singular control arcs, where the control appears in a linear form; 2) control constraints in which the control appears in a nonlinear form; and 3) state path constraints. Accurate solutions are achieved in all classes of problems with a simpler formulation compared to the conventional indirect approach. To demonstrate the potential of the UTM, a complex aerospace problem with bounded control (angle of attack) and state path (maximum heat rate) constraints is also solved. The results demonstrate the utility of the UTM for making challenging constrained optimal control problems amenable to numerical treatment with minimal modifications to the structure of the problem.