Unified Trigonometrization Method for Solving Optimal Control Problems in Atmospheric Flight Mechanics
Kshitij Mall, Ehsan Taheri
Abstract
Application of indirect optimization methods to solve constrained optimal control problems (OCPs) is a challenging task. This study demonstrates the utility of a new construct, the Unified Trigonometrization Method (UTM), which alleviates some of the issues associated with OCPs that consist of control bounds and state path constraints. Three different classes of OCPs are treated: 1) problems with control affine form whose solutions consist of bang-bang and singular control arcs, 2) problems with constrained non-linear control solutions, and 3) problems with state path constraints. For the considered problems, we have been able to achieve accurate results using a simpler formulation in comparison with the conventional indirect approach. To demonstrate the utility of the UTM in the atmospheric flight mechanics domain, a benchmark problem from each of the three classes of OCPs is solved including the Goddard rocket problem, the Mars aerocapture problem, and a hypersonic problem with a constraint on the maximum heat rate. The solutions obtained using the UTM are compared with a general-purpose direct optimal control solver. These comparisons demonstrate the effectiveness of the UTM framework for solving challenging constrained OCPs with minimal modifications to the structure of the original problem.