Exploiting symmetries in active set enumeration for constrained linear–quadratic optimal control

This paper studies symmetric constrained linear-quadratic optimal control problems. The parametric solution to these problems 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 examples.