High-order relaxation approaches for adjoint-based optimal control problems governed by nonlinear hyperbolic systems of conservation laws

Abstract

High-order relaxation approaches for adjoint-based optimal control problems governed by nonlinear hyperbolic systems of conservation laws Abstract: A computational investigation of optimal control problems which are constrained by hyperbolic systems of conservation laws is presented. The general framework is to employ the adjoint-based optimization to minimize the cost functional of matching-type between the optimal and the target solution. Extension of the numerical schemes to second-order accuracy for systems for the forward and backward problem are applied. In addition a comparative study of two relaxation approaches as solvers for hyperbolic systems is undertaken. In particular optimal control of the 1-D Riemann problem of Euler equations of gas dynamics is studied. The initial values are used as control parameters. The numerical ow obtained by optimal initial conditions matches accurately with observations.

Jin–Xin relaxation method for solving a traffic flow problem in one dimension

“…Mathematical models may be solved either analytically or numerically [5][6][7]. Many equations are difficult to solve analytically, so we have to solve it numerically [8][9][10]. Some examples of models given by partial differential equations are the traffic flow model for busy streets [11], blood flow model for an elastic artery [12], models for gas [13] and hydraulic dynamics [14][15][16], elasticity in heterogeneous media [17], etc.…”