Summary: Logical Modeling Frameworks for the
Optimization of Discrete-Continuous Systems
SUBMITTED IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR
the degree of
Doctor of Philosophy
Carnegie Institute of Technology
CARNEGIE MELLON UNIVERSITY
Pittsburgh, PA, U.S.A.
Often, it is very difficult to pose a model for a system even after the system is concep-
tually understood. The reason is the mathematical languages we employ have few forms
of expression. We define more expressive languages, first for dynamical discrete-continuous
systems, and then more rigorously for mathematical programs (MP). Our approach provides
theoretical basis for designing MP software.
The first framework we define is called linear coupled component automata (LCCA).