FINITE-ELEMENT AND CONJUGATE GRADIENT METHODS FOR A NON-LINEAR OPTIMAL HEAT-TRANSFER CONTROL PROBLEM

The boundary control problem of optimal heating of an infinitely long slab with tempertue‐dependent thermal conductivity, subjected to a convection and radiation boundary condition, is analysed by numerical methods. In order to reformulate the optimal control problem of distributed parameter systems as a mathematical programming problem of finite dimension, a space, co‐ordinate is discretized by use of the finite element method, while the Runge–Kutta method is utilized for time integrations. Finally, the performance index of the optimal control problem is minimized by the conjugate gradient method of optimization. Copyright © 1979 John Wiley & Sons, Ltd