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This paper proposes a new nonlinear detection observer for the detection of component faults and their subsequent accommodation for a class of nonlinear distributed processes. Specifically, the proposed results constitute a significant extension to previous precursory work that utilized a linear observer for both detection and diagnosis of component faults for the same class of nonlinear distributed...
This work addresses the problem of tracking and stabilization of FitzHugh-Nagumo equation (FHN) subject to Neumann boundary conditions via static output feedback control using adaptive model reduction methodology and specifically the adaptive proper orthogonal decomposition (APOD) approach. Initially, an ensemble of eigenfunctions is constructed based on a relatively small data ensemble using method...
The problem of receding horizon control for a class of nonlinear distributed processes is investigated. The main focus of the manuscript lies in the development of a computationally efficient method to identify the optimal control action with respect to predefined performance criteria. An optimal control problem is formulated and is solved using standard, gradient-based, search algorithms. Employing...
The problem of robust 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 PDE system are derived. A common approach to this task is the Karhunen-Loeve expansion combined with the method of snapshots...
This paper proposes a nonlinear detection observer for the component fault detection and accommodation of nonlinear distributed processes. Specifically, the proposed results constitute an extension to previous work which utilized a linear observer for both detection and diagnosis of component faults for the same class of nonlinear distributed processes. An advantage of the proposed nonlinear observer...
We consider optimal operating conditions of a gallium arsenide/aluminum arsenide (GaAs/AlAs) deposition process with objectives of uniform deposition of the film heterostructure across the wafer surface at the macroscopic scale and the interfacial uniformity of the GaAs/AlAs heterostructure at the microscopic scale. We use a finite element solver to determine macroscale solutions and kinetic Monte...
This article focuses on dynamic output feedback and robust control of quasi linear parabolic partial differential equations (PDE) systems with time-varying uncertain variables. Especially processes that are described by dissipative PDEs are considered. The states of the process required for designing controllers are dynamically estimated from limited number of noisy process measurements employing...
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...
The problem of feedback control of distributed processes is considered. Typically this problem is addressed through model reduction where finite dimensional approximations to the original infinite dimensional system are derived. The key step in this approach is the computation of basis functions that are subsequently utilized to obtain finite dimensional ODE models using the method of weighted residuals...
In the current work we present an integrated actuator placement and fault tolerant controller design based on the concept of spatial H2 norm and combined with a fault tolerant controller design concepts for DPS presented in earlier work by the authors. Specifically, a nonlinear optimization problem is formulated to identify and rank spatially independent actuator groups that may control a distributed...
The present work focuses on a class of nonlinear distributed processes with component faults. An adaptive detection observer with a time varying threshold is proposed that provides additional robustness with respect to false declarations of faults and minimizes the detection time. Additionally, an adaptive diagnostic observer is proposed that is subsequently utilized in an automated control reconfiguration...
This work focuses on scheduling the optimal treatment strategy for patients at the early stage of HIV infection. Unlike patients with an established HIV infection, complete eradication of the infection is still possible at this stage. Treatment has the ability to further increase the probability of eradication. However, high dosages of drugs should be avoided, if possible, because of toxicity effects...
The problem of dynamic optimization for multi- scale systems comprising of coupled continuum and discrete descriptions is considered. The solution of such problems is challenging owing to large computational requirements of the multiscale process model. This problem is addressed by developing a reduced multiscale model. This is achieved by combining order reduction techniques for dissipative partial-differential...
This work focuses on the analysis of HIV infection dynamics during the initial stages of infection when the viral load is low and random fluctuations may have a significant effect on the dynamics of the disease. The ability of deterministic models to accurately describe the expected behavior of such processes is limited. Stochastic simulations, which are not hampered by this limitation, are used to...
The problem of feedback control of microstructure during thin film growth is addressed. The issue of the non-availability of closed form dynamic models for the evolution of microstructure is addressed by deriving a low-order state-space model that approximates the underlying kinetic Monte Carlo model. Initially a finite set of "coarse" observables is identified from spatial correlation functions...
We identify a minimum set of "coarse" spatially invariant parameters that accurately describe the dominant behavior of the deposition surface during thin-film growth under adsorption and surface diffusion. We demonstrate, through kMC simulations, that different deposition surfaces constructed through a stochastic reconstruction procedure, with identical values for these parameters, exhibit...
The problem of efficient formulations for the optimization of stochastic dynamical systems modeled by timestep-per based descriptions is investigated. The issue of computational requirements for the system evolution is circumvented by extending the notion of in situ adaptive tabulation to stochastic systems. Conditions are outlined that allow unbiased estimation of the mapping gradient matrix and,...
Understanding the metabolic function of microorganisms has recently received a lot of attention due to its importance in fields such as health and industry. Metabolism in microorganisms is a sophisticated process comprised of several thousands of different components with intricate interactions between them. This characteristic is translated into complex dynamical behavior that such systems can exhibit...
The issue of optimal sensor placement in the presence of disturbance is investigated for a class of transport-reaction processes, mathematically modeled by linear parabolic partial differential equations. Specifically, using modal decomposition to discretize the spatial coordinate, the optimal sensor location is computed through the solution of a nonlinear optimization problem in appropriate L2 space...
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