AN EIGENVALUE ASSIGNMENT APPROACH IN THE POLICY DESIGN OF SYSTEM DYNAMICS MODELS

Abstract

Over the past two decades the system dynamics methodology has developed into an effective tool for building mathematical models of diverse socio-economic-technological systems. The methodology involves identifying the basic interactions between the variables of the systems, in the form of feedback loops. By using the notions of flows, accumulations and delays, flow diagrams were then set up from the influence diagrams. A numerical integration procedure, DYNAMO, is then used to simulate the behaviour of the systems by tracing the values of the major system variables over time. Although system dynamics has been shown to be a strong methodology, its potential for success of application has been realised only partially due to the followings: 1) very little attention has been paid to the important issue of policy design: 2) sufficient rigour in model building has not been achieved despite the availability of powerful applicable results in feedback theory and modern system theory. System structures based on state-space models can provide readily applicable concepts of stability and controllability of system dynamics models. The objective of this research project is to present system dynamics in the setting of system theory and control engineering. The application of eigenvalue assignment method on linear system is well established. The feasibility of using the proposed eigenvalue assignment method to aid in the synthesis of System Dynamics models is demonstrated in this thesis. The equivalence between the system dynamics difference equations and the multivariable state space representations were also shown. A working eigenvalue assignment algorithm, using state variable feedback is developed and presented. A computer program in Fortran code was written based on the developed algorithm. The application of the algorithm generates improved control policies which stabilises the system dynamics. The research conducted in this project would hopefully open up new avenues of application of system and control theory in the modelling and simulation of socioeconomic-technological systems. The research would establish a sound theoretical basis for system dynamics modelling and simulation.