The ADAPTx Approach

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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