Feature request: easily log the input and the output to the qpsolver

In happens quite frequently that a qpsolver fails in an unexected way as part of a controller, but it is not always easy to debug the failure as the state, input and output of the solver are not saved.

The issue does not name any files, tests, or entry points, so first trace how the controller invokes the qpsolver abstraction and how solver state, inputs, and outputs are represented. Done means providing a clear way to capture and inspect that information when a solver fails unexpectedly.

Written by the indexing model from the issue text.