Digital calculation of optimum controls for time-varying linear multivariable systems. realisation of contraction-mapping algorithm

The paper considers the digital-computer implementation of the contraction-mapping algorithm, which is used to solve the integral equations defining the optimal control for time-varying multivariable systems with quadratic cost functions. A completely time-varying problem is first considered, and a general flow diagram for the digital-computer solution is given, together with a detailed description of each block of the flow diagram including an estimate of the storage-location requirements. As an illustration, an example problem is examined in detail and a complete flow diagram and the program listing of the digital-computer solution are given. Results are then presented which illustrate the digital-computer iterates and compare the actual and predicted measures of convergence.