A partial state collocation method for covariance optimal control

An overview is presented for two methods of incorporating the covariance in an optimal control problem. Including the covariance in the optimal control problem can be beneficial in the field of navigation where it is desirable to design trajectories which either minimize navigation error or maximize observability for instrument calibration. The full state collocation method uses Legendre Gauss Radau collocation to discretize the deterministic states and controls as well as the unique elements of the covariance matrix. The problem is then transcribed to a nonlinear progamming problem (NLP) and is solved with an NLP solver. This method, however, results in problems with many constraints and variables, which is computationally expensive. The partial state collocation method, the main focus of this thesis, collocates the deterministic states and controls but uses a shooting method to incorporate the covariance matrix. The problem is then transcribed to a nonlinear programming problem, which has fewer constraints and variables than the full state collocation method. Both of these methods are demonstrated by solving for the trajectory that minimizes the final position uncertainty for a spacecraft reentering Earth's atmosphere. The problem is tested with different sized covariance matrices, which shows how the time it takes to solve the problem increases as the covariance matrix increases in size. The partial state collocation method is generally faster and converges in fewer NLP iterations than the full state collocation method. As the covariance matrix increases in size, the time it takes to solve the problem increases at a smaller rate for the partial state collocation method.

Department dc:contributor.department

Massachusetts Institute of Technology. Department of Aeronautics and Astronautics.

Grantor dc:publisher

Massachusetts Institute of Technology

Year dc:date.issued

2018

Author dc:creator

• Kapolka, Tyler J. (Tyler Joseph)

Advisor dc:contributor.advisor

• Steven R. Hall and Matthew J. Weinstein.

• Aeronautics and Astronautics.

Statement dc:rights

• MIT theses are protected by copyright. They may be viewed, downloaded, or printed from this source but further reproduction or distribution in any format is prohibited without written permission.

Licence dc:rights.uri

• http://dspace.mit.edu/handle/1721.1/7582

Language dc:language.iso

eng

Handle dc:identifier.uri

http://hdl.handle.net/1721.1/119908

OAI identifier oai:identifier

oai:dspace.mit.edu:1721.1/119908