Sparse Robust Optimal Control in Continuous-Time: A Computationally Viable Approach
arXiv:2607.11827 · doi:10.1109/TAC.2026.3708411
The paper introduces a computationally tractable algorithm that solves sparse robust optimal control problems for continuous-time linear noisy systems by reformulating them as semi‑infinite programs and then solving a finite convex optimization problem exactly.
Abstract
This article presents a novel, numerically viable algorithm for solving sparse robust optimal control problems in continuous time. We consider a constrained linear noisy system governed by an ordinary differential equation (ODE), with an -type objective function in line with the sparse optimal control literature. The resulting optimal control problem is shown to admit a semi-infinite programming (SIP) formulation. Building upon this insight, we develop a new framework that enables the computation of exact solutions -- to our knowledge, the first such achievement in the context of sparse optimal control. We demonstrate that a finite and computationally viable convex optimization problem can be solved to recover, in a lossless manner, both the optimal value and the corresponding optimizers of the original SIP, while also guaranteeing satisfaction of uncountably many constraints. We also show that the parameter-dependent noisy systems and the minimum attention problem fall into our framework and can be solved efficiently via our algorithm. The efficacy of our algorithm is illustrated through a benchmark numerical example.