ADAPTx is software for the automated modeling of dynamical processes or systems from time series data. The conceptual and computational framework is quit different from the traditional methods of system identification and time series analysis.

**The traditional approach** to modeling deals primarily with a
particular parametric model of a system and then proceeds to find the best
values for the parameters by solving a parameter optimization problem. The
procedure is repeated for a number of different parametric structures for the
model based upon some diagnostic information that is often only suggestive of
the appropriate structure to use. The result of such an approach is a tedious
iterative procedure where the analyst must more or less guess at the appropriate
model structure and then use the computer to solve the parameter optimization
problem. The high accuracy methods such as Maximum Likelihood (ML) often
require nonlinear optimization that frequently does not converge particularly
in the case of multivariable processes. The procedure can provide excellent
results when appropriate model structures are selected and when the optimization
algorithms converge, however, this is often not the case leading to unreliable
results. The procedure generally requires graduate level training of the
analyst and a significant amount of the analysts time.

**The ADAPTx approach** involves the use of Canonical Variate Analysis
(CVA). This procedure directly determines the linear functions of the ``past''
of the process with predictive information for the future evolution of the
process. These are the state variables of the system. The number of
statistically significant states is directly determined in a single CVA
computation that primarily involves a singular value decomposition (SVD). The
SVD is one of the most accurate and stable procedures in matrix computation. As
a result, the procedure is computationally reliable and automatically determines
the appropriate model state order and structure. Once the system state, state
order and structure are determined, the parameters of the linear dynamical
system are computed simply by multivariate linear regression. The overall
procedure has been shown to be very close to ML in accuracy, but avoids having
to solve a nonlinear optimization problem.

**The practical result **of the ADAPTx technology is to make possible
the routine and reliable application of time series analysis and system
identification to complex multivariable dynamical systems. The ADAPTx software
can be executed in a completely automatic mode with no input from the user. It
has be applied to wind tunnel tests of online adaptive control involving the
identification of over 100,000 system models with no failures of the algorithm.

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