abstract = "This dissertation proposes a new methodology for
modelling and identifying non-linear systems called the
Group Method of Cartesian Programming. This new
methodology combines the ideas of nonlinear functional
networks and statistical optimization via the Group
Method of Data Handling and Particle Swarm
Optimization, respectively. The utility of Particle
Swarm Optimization is demonstrated by applying it to
the System Identification problem. In particular,
Particle Swarm Optimization is used to determine the
constants for several autoregressive moving average
(ARMA) models. The ARMA models discovered using
Particle Swarm Optimization were found to be
competitive with traditional gradient based
optimization techniques. Particle Swarm Optimization
was next integrated into the Group Method of Data
Handling methodology. It was demonstrated that it is
practical to use statistical optimization (Particle
Swarm Optimization) within a complex adaptive
functional network (The Group Method of Data Handling).
A methodology of Gaussian Regularization was developed
that has the potential to further improve the adaptive
modeling capabilities of a Complex Adaptive Functional
Network. Several applications were used to illustrate
the use of Particle Swarm Optimization and the Group
Method of Data Handling. In particular the new Group
Method of Cartesian Programming was used for optimal
sensor design. The positive results of the sensor study
lend support for further research that would implement
all of the ideas set forth in this dissertation.",