A note on the application of the matrix Riccati equation to the optimal control of distributed parameter systems

Numerical results from an investigation of the Optimal control of a parabolic distributed parameter system are presented. The results from a matrix Riccati formulation are contrasted with those using a variable metric method. Spurious oscillations in the optimal control given by the Riccati algorithm are shown to stem from the use of Simpson's rule to approximate the integrals. It is concluded that the trapezoidal rule is to be preferred.