Improving tractability of real-time control schemes via simplified S-lemma

G. Banjac, J. Zhen, D. den Hertog and J. Lygeros

@article{Banjac2020:arxiv,
  author = {G. Banjac and J. Zhen and D. den Hertog and J. Lygeros},
  title = {Improving tractability of real-time control schemes via simplified {S}-lemma},
  year = {2020}
}

Various control schemes rely on a solution of a convex optimization problem involving a particular robust quadratic constraint, which can be reformulated as a linear matrix inequality using the well-known S-lemma. However, the computational effort required to solve the resulting semidefinite program may be prohibitively large for real-time applications requiring a repeated solution of such a problem. We use some recent advances in robust optimization that allow us to reformulate such a robust constraint as a set of linear and second-order cone constraints, which are computationally better suited to real-time applications. A numerical example demonstrates a huge speedup that can be obtained using the proposed reformulation.