The optimality of KL transformation is also used in the system control area. In this area KL expansion works mostly as a data reduction technique, allowing someone to analyze the experimental data quickly and more efficiently. The results of the analysis are usually an input parameter to a control feedback.
One of the first applications of KL in system control was presented in [31] for the identification of linear Distributed Parameter Systems (DPS) with only limited a priori information about the physical process. Basic information from the system inputs and outputs was used to identify approximate spatial characteristics of the DPS. The identification procedure resulted in a pseudo-modal input/output model for the system. Approximations to the eigenfunctions were determined numerically from input/output data using Galerkin's method and KL decomposition. Application of this procedure to DPS described by both a self-adjoint and a non-self-adjoint parabolic PDE model was demonstrated. The usefulness of the identified model for an example control system design was shown.
Krischer et al [27] used KL to analyze instabilities in chemically reacting systems. Here KL allowed the identification of coherent spatial structures from the experimental data and the determination of the active degree of freedom (important spatial structures). Projection onto these ``modes'' reduced the data to a small number of time series. On the next step these time series were processed through Artifial Neural Network to get a low-dimensional nonlinear dynamic model. It predicted correctly the spatiotemporal short-term behavior and the long-term dynamics of the system (the attractor). The KL-based model was shown to be a good-data post-processing tool, which can lead to low-dimensional input-output models.
Burl ([21]) proposed the usage of KL transform in system identification. The state system identification is important for the control of the system, but often complicated in application by a plethora of sensor data. The algorithm consists of experimental data reduction using the truncated KL algorithm. These estimates form a reduced-order state vector for the system. A dynamic model later can be found using stochastic least squares system identification.
In [15] KL method was implemented to extract the most dominant spatial structure from 2-D video images of the reacting flow in order to suppress self-sustained oscillations of thermal front through controlled feedback. They point out, though, the problems of taking experimental data arising in 3-dimensional case.