SENSITIVITY ANALYSIS FOR AN OPTIMAL CONTROL PROBLEM OF PRODUCTION SYSTEM BASED ON NONLINEAR CONSERVATION LAW

Abstract

Dynamics of a production system having large number of items can be represented through hyperbolic conservation law. Due to nonlinear dependence on the work in progress, the resulting partial differential equation becomes nonlinear. Further, occurrence of yield loss during the process makes it nonhomogeneous. In this paper an optimal control problem has been studied incorporating hyperbolic conservation law as a constraint. One of the few ways to control the output of production system is by adjusting the influx in the system. Moreover, yield loss can also be controlled in a time dependent manner. It is well known that the solutions of nonlinear conservation laws may develop discontinuities known as shock waves that forbid the use of classical variational techniques. This paper studies sensitivity analysis with the presence of shocks. Adjoint technique has been implemented to evaluate gradients of cost functionals.