  Several concepts on the measure of observability, reachability, and
robustness are defined and illustrated for both linear and nonlinear control
systems. Defined by using computational dynamic optimization, these concepts
are applicable to a wide spectrum of problems. Some questions addressed include
the observability based on user-information, the determination of strong
observability vs. weak observability, partial observability of complex systems,
the computation of $L^2$-gain for nonlinear control systems, and the measure of
reachability in the presence of state constraints. Examples on dynamic systems
defined by both ordinary and partial differential equations are shown.
