Efficient robust control of first order scalar conservation laws using semi-analytical solutions

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

Research output: Contribution to journalArticlepeer-review

6 Scopus citations

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 initial density control and boundary flow control, as a Linear Program. We then show that this framework can be extended to arbitrary control problems involving the control of subsets of the initial and boundary conditions. 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/MILP. 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.
Original languageEnglish (US)
Pages (from-to)525-542
Number of pages18
JournalDiscrete and Continuous Dynamical Systems - Series S
Volume7
Issue number3
DOIs
StatePublished - Jan 28 2014

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics
  • Discrete Mathematics and Combinatorics

Fingerprint Dive into the research topics of 'Efficient robust control of first order scalar conservation laws using semi-analytical solutions'. Together they form a unique fingerprint.

Cite this