Numerical solution of the problem of determining the number and locations of state observation points in feedback control of a heating process

The problem of optimizing the number and locations of state observation points in the feedback control of heating a rod in a furnace is considered. The weighting coefficients determining the importance of each observation point in the current linear control function are also optimized. The synthesis of control functions is reduced to the problem of optimizing parameters for a pointwise loaded parabolic equation, which is solved by applying first-order optimization methods.