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% Progress Report % Drew Allen McNeely % June 28, 2021

Reproducing the Automatica Paper

Finite-horizon covariance control for discrete-time stochastic linear systems subject to input constraints

Work so far

  • Read the paper thoroughly and rederived chunks of it by hand for better understanding
  • Attempting to code the general vector state version of the controller using CVXPY as the convex optimizer
  • Running into a snag with Disciplined Convex Programming

Output from CVX

cvxpy.error.DCPError:
Problem does not follow DCP rules. Specifically:
The objective is not DCP.
Its following subexpressions are not:
...

Testing in pdb

Output from pdb

Source of issues

The issue is in the convexity of the composition of the components of the cost function. As in the paper, $\mathrm{trace}(\mathcal{A}\mathcal{A}^T)$ is convex, but $\mathcal{A}\mathcal{A}^T$ is not necessarily convex in $\mathcal{A}$.

I am currently trying to rederive the performance index to be able to utilize one of the built-in CVX atoms. Another avenue I am exploring is in looking at the code that Boyd himself uses for his paper.

Future Plans

  • Translate the Boyd code into Python and see if I can adapt it to the Automatica paper while getting it to run correctly
  • Expand the codebase to include the separation based paper
  • Run the numbers from the illustrative example in the Automatica paper through the code