TY - JOUR

T1 - Efficient robust control of first order scalar conservation laws using semi-analytical solutions

AU - Li, Yanning

AU - Canepa, Edward S.

AU - Claudel, Christian G.

N1 - KAUST Repository Item: Exported on 2020-10-01

PY - 2014/1/28

Y1 - 2014/1/28

N2 - 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.

AB - 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.

UR - http://hdl.handle.net/10754/563317

UR - http://aimsciences.org//article/doi/10.3934/dcdss.2014.7.525

UR - http://www.scopus.com/inward/record.url?scp=84897688459&partnerID=8YFLogxK

U2 - 10.3934/dcdss.2014.7.525

DO - 10.3934/dcdss.2014.7.525

M3 - Article

VL - 7

SP - 525

EP - 542

JO - Discrete and Continuous Dynamical Systems - Series S

JF - Discrete and Continuous Dynamical Systems - Series S

SN - 1937-1632

IS - 3

ER -