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.