Indirect Methods

Indirect method of optimization based on Bryson-Ho [1].

Controls are handled in one of two ways: ICRM [2] [3] or PMP.

Path constraints are handled in one of two ways: UTM [4] [5] [6]_ [7] or epsilon-trig [4] [5]

Inequality boundary constraints are handled using UTM [8]_.

Switching conditions are handled using RASHS [9].

Base Class Reference

References

[1]Arthur E. Bryson, and Yu-Chi Ho. “Applied Optimal Control: Optimization, Estimation, and Control.” Hemisphere, New York (1975)
[2]Thomas Antony, and Michael J. Grant. “Path Constraint Regularization in Optimal Control Problems using Saturation Functions.” AIAA 2018-0018, 2018 AIAA Atmospheric Flight Mechanics Conference. 2018
[3]Antony, Thomas. “Large Scale Constrained Trajectory Optimization Using Indirect Methods.” Dissertation. Purdue University, West Lafayette, 2018
[4](1, 2) Kshitij Mall, and Michael J. Grant. “Epsilon-Trig Regularization for Bang-Bang Optimal Control Problems.” Journal of Optimization Theory and Applications, Vol. 174, No. 2, 2017, pp. 500-517
[5](1, 2) Kshitij Mall, and Michael J. Grant. “Trigonomerization of Optimal Control Problems with Bounded Controls.” AIAA 2016-3244, AIAA Atmospheric Flight Mechanics Conference, Washington D.C., 13-17 Jun. 2016
[6]Kshitij Mall, and Michael J. Grant. “Trigonomerization of Optimal Control Problems with Mixed State-Control Constraints.” Journal of Optimization Theory and Applications. [Submitted]
[7]Kshitij Mall. “Advancing Optimal Control Theory using Trigonometry for Solving Complex Aerospace Problems.” Dissertation. Purdue University, West Lafayette, 2018
[6]Nolan, Sean M., Michael J. Sparapany, and Daniel A. DeLaurentis. “Extension of Unified Trigonometrization Method to Enforce Inequality Boundary Conditions in Optimal Control Problems.” AIAA AVIATION 2020 FORUM. 2020.
[9]Harish Saranathan, and Michael J. Grant. “The Relaxed Autonomously Switched Hybrid System (RASHS) Approach to Indirect Multi-Phase Trajectory Optimization for Aerospace Vehicles.” AIAA 2018-0016, 2018 AIAA Atmospheric Flight Mechanics Conference. 2018