Numerical solution to the optimal feedback control of continuous casting process

Authors:
Bao-Zhu Guo;Bing Sun
Affiliations:
Academy of Mathematics and System Sciences, Academia Sinica, Beijing, People's Republic of China 100080;School of Computational and Applied Mathematics, University of the Witwatersrand, Johannesburg, South Africa Wits-2050
Venue:
Journal of Global Optimization
Year:
2007

Citing 9
Cited 1

Application of viscosity solutions of infinite-dimensional Hamilton-Jacobi-Bellman equations to some problems in distributed optimal control

Journal of Optimization Theory and Applications
Direct and indirect methods for trajectory optimization

Annals of Operations Research - Special issue on nonlinear methods in economic dynamics and optimal control: Gmo¨or-series No. 2
Mathematical control theory: deterministic finite dimensional systems (2nd ed.)

Mathematical control theory: deterministic finite dimensional systems (2nd ed.)
A Viscosity Approach to Infinite-Dimensional Hamilton--Jacobi Equations Arising in Optimal Control with State Constraints

SIAM Journal on Control and Optimization
Optimal Control of Continuous Casting by Nondifferentiable Multiobjective Optimization

Computational Optimization and Applications
Numerical Solution of Hamilton-Jacobi-Bellman Equations by an Upwind Finite Volume Method

Journal of Global Optimization
Numerical Comparison of Some Penalty-Based Constraint Handling Techniques in Genetic Algorithms

Journal of Global Optimization
Numerical methods for high dimensional Hamilton-Jacobi equations using radial basis functions

Journal of Computational Physics
An efficient algorithm for Hamilton–Jacobi equations in high dimension

Computing and Visualization in Science

Approximation of optimal feedback control: a dynamic programming approach

Journal of Global Optimization

Quantified Score

Hi-index	0.00

Visualization

Abstract

Using a semi-discrete model that describes the heat transfer of a continuous casting process of steel, this paper is addressed to an optimal control problem of the continuous casting process in the secondary cooling zone with water spray control. The approach is based on the Hamilton---Jacobi---Bellman equation satisfied by the value function. It is shown that the value function is the viscosity solution of the Hamilton---Jacobi---Bellman equation. The optimal feedback control is found numerically by solving the associated Hamilton---Jacobi---Bellman equation through a designed finite difference scheme. The validity of the optimality of the obtained control is experimented numerically through comparisons with different admissible controls. Detailed study of a low-carbon billet caster is presented.