Robust Control for a Transportation Network With Stochastic Quadratic Constraints

Motivated by a traffic management application, this work proposes a novel robust optimal control framework for networks subject to disruptions. It minimizes deviations from a target vehicle configuration while enforcing bounds on the expected values of quadratic constraints including states and controls, and fulfilling balance equations constraints. The problem uses a recent Linear-Quadratic (LQ) framework with stochastic quadratic constraints. Validation via two case studies shows that the method, despite disruptions, maintains proximity to references and satisfies all constraints, outperforming a traditional LQ controller and a heuristic controller, both of which lack the stochastic constraints. Furthermore, offline verification checks the covariance matrices' asymptotic limits to guarantee bound compliance.