Exact solutions to robust control problems involving scalar hyperbolic conservation laws using Mixed Integer Linear Programming

Yanning Li, Edward S. Canepa, Christian G. Claudel

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

This article presents a new robust control framework for transportation problems in which the state is modeled by a first order scalar conservation law. Using an equivalent formulation based on a Hamilton-Jacobi equation, we pose the problem of controlling the state of the system on a network link, using boundary flow control, as a Linear Program. Unlike many previously investigated transportation control schemes, this method yields a globally optimal solution and is capable of handling shocks (i.e. discontinuities in the state of the system). We also demonstrate that the same framework can handle robust control problems, in which the uncontrollable components of the initial and boundary conditions are encoded in intervals on the right hand side of inequalities in the linear program. The lower bound of the interval which defines the smallest feasible solution set is used to solve the robust LP (or MILP if the objective function depends on boolean variables). Since this framework leverages the intrinsic properties of the Hamilton-Jacobi equation used to model the state of the system, it is extremely fast. Several examples are given to demonstrate the performance of the robust control solution and the trade-off between the robustness and the optimality. © 2013 IEEE.
Original languageEnglish (US)
Title of host publication2013 51st Annual Allerton Conference on Communication, Control, and Computing (Allerton)
PublisherInstitute of Electrical and Electronics Engineers (IEEE)
Pages478-485
Number of pages8
ISBN (Print)9781479934096
DOIs
StatePublished - Oct 2013

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