Sheet and film processes, which include coating, papermaking, and polymer film extrusion processes, are of worldwide industrial importance. Existing identification and estimation techniques require much more input-output data than are usually available for poorly conditioned large-scale sheet and film processes. The objective of this project is to exploit the inherent structure of these processes to improve numerical conditioning and the robustness of model and state estimates. This is leading to the development of an automatic identification procedure, where the model and an estimate of its accuracy are iteratively improved as opportunities for increased input-output testing become available.

Although neural networks have been heavily applied in the process industries, there have existed no general techniques for analyzing the stability and performance of these systems. Polynomial-time computable analysis tools are being developed that are applicable to dynamic neural network systems with arbitrary interconnections. The application of these tools for optimization-based nonlinear control is under investigation.

Process constraints, time delays, and model uncertainties are prevalent in large-scale industrial processes. Existing algorithms for computing robustness margins do not adequately address the effect of time delay uncertainties and process constraints on the overall closed loop stability and performance. An algorithm is being developed for mapping time delay uncertainties to equivalent finite-dimensional real parametric variations that can be analyzed using available techniques. The effect of process constraints on closed loop stability and performance is addressed using improved Lyaponov function techniques.

Pattern recognition techniques are being developed for the on-line detection and isolation of faults in large-scale industrial plants. These algorithms notify the process operator when abnormal process behavior has occurred and its likely cause, based on past data histories for which similar behavior has occurred. Subspace identification and operator-theoretic statistical methods are being investigated for improving the dynamic behavior of the developed techniques.

N umerous researchers over the last few decades have proposed techniques to rigorously address model inaccuracies in multivariable systems. The purpose of this project is to draw theoretical connections between various branches of robust control theory. This is leading to relationships between modern and classical control methods, theoretical justifications of ad hoc methods for the synthesis of robust controllers, and to the removal of computational limitations posed by these methods for the analysis of robust controllers.

Robustness analysis requires that the uncertain system be written as a linear fractional transformation of the uncertain parameters. This problem is algebraically equivalent to the problem of deriving the state space realization for a multidimensional transfer function matrix. We are developing multidimensional realization algorithms which are applicable to large-scale uncertain systems, which have large numbers of uncertain parameters, states, and manipulated, measured, and controlled variables. Computationally efficient model-reduction algorithms are being developed that allow robustness analysis and synthesis to be applied to processes of large dimension.

We are developing computational approaches for designing globally optimal controllers for large-scale sheet and film processes. The resulting controllers are robust to inaccuracies in physical properties of the sheet or film and to faults and/or failures in measured and manipulated variables. One of the key ideas in these approaches is to exploit nonlocalized structural characteristics of the sheet or film.

The objective of this research is to develop approaches for the black and grey box modeling of large-scale nonlinear dynamic processes. These techniques, which involve time-scale, chemometric, and decomposition data reduction methods, incorporate a priori known causality information and are applicable also to the detection and isolation of process faults.

Numerous researchers over the last few decades have worked to develop efficient methods for computing robustness margins. We are studying how uncertainty representation affects the computational difficulty associated with robustness margin computations for large-scale systems. Computational complexity theory is used to show which robustness margins may be efficiently computed and for which uncertainty representations there does not exist any algorithm that can calculate the robustness margin in polynomial time as a function of the size of the system. This theory is key to motivating the development of polynomial time upper and lower bounding and globally convergent branch-and-bound algorithms.