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

Content Provider	IEEE Xplore Digital Library
Author	Yanning Li Canepa, E. Claudel, C.
Copyright Year	2013
Description	Author affiliation: Dept. of Electr. Eng., King Abdullah Univ. of Sci. & Technol. (KAUST), Thuwal, Saudi Arabia (Canepa, E.; Claudel, C.) \|\| Dept. of Mech. Eng., King Abdullah Univ. of Sci. & Technol. (KAUST), Thuwal, Saudi Arabia (Yanning Li)
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.
Sponsorship	IEEE Cont. Syst. Soc.
Starting Page	478
Ending Page	485
File Size	2302563
Page Count	8
File Format	PDF
e-ISBN	9781479934102
DOI	10.1109/Allerton.2013.6736563
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2013-10-02
Publisher Place	USA
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Robust control Uncertainty Optimal control Boundary conditions Linear programming Mathematical model Equations
Content Type	Text
Resource Type	Article

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4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
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