  This paper studies symmetric constrained linear-quadratic optimal control
problems and their parametric solutions. The parametric solution of such a
problem is a piecewise-affine feedback law that can be equivalently expressed
as a set of active sets. We show symmetries of the optimal control problem
entail symmetries of the active sets, which can be used to simplify finding the
set of active sets considerably. Specifically, we improve a recently proposed
method for the dynamic-programming-based enumeration of all active sets. The
achieved reduction of the computational effort is illustrated with an example.

Optimization and Control