Appendix: Optimization Techniques
To obtain a way to control or manage a physical system, this work introduces a mathematical model that closely represents the physical system and describes and represents the real system.
Abstract
Systems engineering provides systematic methodologies for studying and analyzing the various structural and nonstructural aspects of a system and its environment by using mathematical and/or physical models. It also assists in the decisionmaking process by selecting the best alternative policies subject to all pertinent constraints by using simulation and optimization techniques. In general, to obtain a way to control or manage a physical system, we introduce a mathematical model that closely represents the physical system. A mathematical model is a set of equations that describes and represents the real system. This set of equations uncovers the various aspects of the problem, identifies the hnctional relationships between all of the system’s components and elements and its environment, establishes measures of effectiveness and constraints, and thus indicates what data should be collected to deal with the problem quantitatively. These equations could be algebraic, differential, or other, depending on the nature of the system being modeled. The mathematical model is solved, and its solution is applied to the physical system. Figure A. 1 depicts a schematic representation of the process of system modeling and optimization. The same input applied to both the real system and the mathematical model yields two different responses, namely, the system’s output and the model’s output. The closeness of these responses indicates the merit and