zhouazhou98 / pylgr

A basic Python implementation of a Legendre-Gauss-Radau pseudospectral method for computational optimal control.

PyLGR

Note: this repository is no longer maintained. The benchmark_ocp repository contains a regularly updated implementation of this code's functionality.

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pylgr is a basic Python implementation of a Legendre-Gauss-Radau (LGR) pseudospectral (PS) method for infinite horizon computational optimal control. The optimal control problem (OCP) is collocated in time at LGR points, turning it into a constrained nonlinear programming problem which we solve with sequential least squares quadratic programming (SLSQP). Rough estimates for the costates are extracted based on the covector mapping theorem.

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The code has been tested with the following dependencies:

python>=3.6
numpy>=1.19.5
scipy>=1.5.4
pytest>=7.0.1
matplotlib>=3.3.4

The code can be installed using the following command:

pip install -e .

You can then import pylgr in any python script. The main function is pylgr.solve_ocp. Documentation can be accessed by the python command help(pylgr.solve_ocp).

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The test suite can be run from the main directory with the command

pytest unit_tests -s -v

Plotting can be enabled in test_solve.py inside each individual test function.

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See the following references for details on the LGR PS approach:

Fahroo, F. and Ross, I. M. "Pseudospectral Methods for Infinite-Horizon Optimal Control Problems," Journal of Guidance, Control, and Dynamics, Vol. 31, No. 4, July–Aug. 2008, pp. 927-936. doi: 10.2514/1.33117

Ross, I. M., Gong, Q., Fahroo, F., and Kang, W., "Practical Stabilization Through Real-Time Optimal Control," Proceedings of the 2006 American Control Conference, Inst. of Electrical and Electronics Engineers, Piscataway, NJ, June 2006, pp. 14–16. doi: 10.1109/ACC.2006.1655372.