Generalised conjugate-gradient algorithm for control optimisation using models

The use of a simple model of a system to help optimise the control of the system is considered. It is shown that a generalisation (due to Hestenes) of the usual conjugate-gradient algorithm can be used for optimisation using models. The generalisation is derived here from the Davidon-Fletcher-Powell algorithm with non-unity initial estimate of the inverse second-derivative operator. A model is used to provide an approximation to the second-derivative operator which is potentially easier to invert than the operator for the system because the model has state dimension smaller than that for the system. Optimisations of the model are employed to generate search directions along which the control for the system is optimised. Computed results are presented for an example.