in Wiley InterScience (www.interscience.wiley.com).The problem of feedback control of spatially distributed processes described by highly dissipative partial differential equations (PDEs) is considered. Typically, this problem is addressed through model reduction, where finite dimensional approximations to the original infinite dimensional PDE system are derived and used for controller design. The key step in this approach is the computation of basis functions that are subsequently utilized to obtain finite dimensional ordinary differential equation (ODE) models using the method of weighted residuals. A common approach to this task is the Karhunen-Loe`ve expansion combined with the method of snapshots. To circumvent the issue of a priori availability of a sufficiently large ensemble of PDE solution data, the focus is on the recursive computation of eigenfunctions as additional data from the process becomes available. Initially, an ensemble of eigenfunctions is constructed based on a relatively small number of snapshots, and the covariance matrix is computed. The dominant eigenspace of this matrix is then utilized to compute the empirical eigenfunctions required for model reduction. This dominant eigenspace is recomputed with the addition of each snapshot with possible increase or decrease in its dimensionality; due to its small dimensionality the computational burden is relatively small. The proposed approach is applied to representative examples of dissipative PDEs, with both linear and nonlinear spatial differential operators, to demonstrate its effectiveness of the proposed methodology.

We address the problem of tracking and stabilization of dissipative distributed parameter systems, by designing static output feedback controllers using adaptive proper orthogonal decomposition methodology (APOD). Initially, an ensemble of eigenfunctions is constructed based on a relatively small data ensemble which is then recursively updated as additional process data becomes available periodically. The proposed APOD methodology relaxes the need for a representative ensemble of snapshots (in the sense that it contains the global dynamics of the process). An accurate reduced-order model (ROM) is constructed and periodically refined based on these updated eigenfunctions. Using the ROM and continuous measurements available from the restricted number of sensors, a static output feedback controller is subsequently designed. This controller is successfully used to achieve the desired control objective of stabilization and tracking in the Kuramoto−Sivashinksy and FitzHugh−Nagumo equations.

in Wiley Online Library (wileyonlinelibrary.com).We address the problem of control of spatially distributed processes in the presence of measurement constraints. Specifically, we assume the availability of sensors that measure part of the state spatial profile. The measurements are utilized for the derivation and on-demand update of reduced order models (ROM) based on an extension of the adaptive proper orthogonal decomposition (APOD) method using a snapshot reconstruction technique. The proposed Gappy-APOD methodology constructs locally accurate low-dimensional ROM thus resulting in a computationally efficient alternative to using a large-dimensional ROM with global validity. Based on the low-dimensional ROM and continuous measurements available from point sensors a Lyapunov-based static output feedback controller is subsequently designed. The proposed controller design method is illustrated on an unstable process modeled by the Kuramoto-Sivashinsky equation, when the designed controller successfully stabilizes the process even in the presence of model uncertainty. V V C 2012 American Institute of Chemical Engineers AIChE J, 59: 747-760, 2013

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The problem of online system identification and control of microscopic processes is considered. Traditionally, such processes are numerically simulated employing atomistic simulations. The unavailability of closed-form models to describe the evolution makes the controller design task challenging. A methodology is developed in which subspace algorithms for bilinear system identification are coupled with feedback linearization techniques with objective the online identification and control of microscopic processes. We illustrate the applicability of the proposed methodology on a Kinetic Monte Carlo (KMC) realization of a simplified surface reaction scheme that describes the dynamics of CO oxidation by O 2 on a Pt catalytic surface. The proposed controller successfully forces the process from one stationary state to another state.