Mathematical algorithms for optimisation of large scale systems

This research is concerned with the problem of optimisation of steady state large scale systems using mathematical models. Algorithms for on-line optimisation of interconnected industrial processes are investigated. The research is concerned with two different kinds of algorithms which are based on the structure of the model used and the way of incorporating the real process information in order to compensate for model-reality differences. The first class of algorithms are developed from the price method with global feedback information which is mainly based on the normal Lagrangian function. Two existing algorithms are examined: The double iterative price correction mechanism and the augmented interaction balance method. Both methods use a double iterative coordination strategy and global feedback measurements from the real process. They are based respectively on the normal and the augmented Lagrangian functions. Hence, the first algorithm can only be recommended for application to convex problems. An algorithm, namely the augmented price correction mechanism, has been developed to extend the applicability of the previous price correction mechanism to non-convex problems. It is also applicable to convex problems with the advantage of reducing the number of times that information is required from the real process. The second class of algorithms is known as integrated system optimisation and parameter estimation (ISOPE) • The model used contains uncertain parameters and the algorithm solves the optimisation and parameter estimation tasks repeatedly until no furthur improvement is obtained. Developed ISOPE algorithms are involved in this research to cover the problems with output dependent constraints. Simulation results show superiority of the double iterative algorithm over that of single loop method in considerably reducing the number of times that information is required from the real process and hence saving on-line computing time. It is hoped that this work will provide useful information for implementing and furthur developing on-line steady state optimisation techniques