This work establishes an abstract framework that considers the distributed filtering of spatially varying processes using a sensor network. It is assumed that the sensor network consists of groups of sensors, each of ...
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This work establishes an abstract framework that considers the distributed filtering of spatially varying processes using a sensor network. It is assumed that the sensor network consists of groups of sensors, each of which provides a number of state measurements from sensing devices that are not necessarily identical and which only transmit their information to their own sensor group. A modification to the local spatially distributed filters provides the non-adaptive case of spatially distributed consensus filters which penalize the disagreement amongst themselves in a dynamic manner. A Subsequent modification to this scheme incorporates the adaptation of the consensus gains in the disagreement terms of all local filters. Both the well-posedness of these two consensus spatially distributed filters and the convergence of the associated observation errors to zero in appropriate norms are presented. Their performance is demonstrated on three different examples of a diffusion partial differential equation with point measurements. (C) 2009 Elsevier Ltd. All rights reserved.
The synthesis of a model-based control structure for general linear dissipative distributed parameter systems (DPSs) is explored in this manuscript. Discrete-time distributed state measurements (called process snapsho...
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The synthesis of a model-based control structure for general linear dissipative distributed parameter systems (DPSs) is explored in this manuscript. Discrete-time distributed state measurements (called process snapshots) are used by a continuous-time regulator to stabilize the process. The main objective of this article is to identify a criterion to minimize the communication bandwidth between sensors and controller (snapshots acquisition frequency) using linear systems analysis and still achieve closed-loop stability. This objective is addressed by adding a modeling layer to the regulator. Theoretically, DPSs can be well described by low dimensional ordinary differential equation models when represented in functional spaces;practically, the model accuracy hinges on finding basis functions for these spaces. Adaptive proper orthogonal decomposition is used to identify statistically important basis functions and establish locally accurate reduced order models which are then used in controller design. The proposed approach is successfully applied toward thermal regulation in a tubular chemical reactor. (c) 2014 American Institute of Chemical Engineers AIChE J, 61: 434-447, 2015
This note investigates a sensitivity reduction problem by stable stabilizing controllers for a linear time-invariant multi-input multioutput distributedparameter system. The plant we consider has finitely many unstab...
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This note investigates a sensitivity reduction problem by stable stabilizing controllers for a linear time-invariant multi-input multioutput distributedparameter system. The plant we consider has finitely many unstable zeros, which are simple and blocking, but can possess infinitely many unstable poles. We obtain a necessary condition and a sufficient condition for the solvability of the problem, using the matrix Nevanlinna-Pick interpolation with boundary conditions. We also develop a necessary and sufficient condition for the solvability of the interpolation problem, and show an algorithm to obtain the solutions. Our method to solve the interpolation problem is based on the Schur-Nevanlinna algorithm.
Boundary output feedback of a class of second order distributed parameter systems is addressed. In particular, second order distributed parameter systems without distributed damping are studied. First, a uniformly exp...
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Boundary output feedback of a class of second order distributed parameter systems is addressed. In particular, second order distributed parameter systems without distributed damping are studied. First, a uniformly exponentially stable observer is designed. Then, exponentially stabilizing control laws are proposed. The existence, uniqueness and stability of solutions of the observer and the closed loop system are based on semigroup theory. (C) 2009 Elsevier B.V. All rights reserved.
In many areas of control there are gaps between the existing theory and applications. This is more so in hybrid infinite dimensional systems and in particular hybrid systems in which both the actuator and the controll...
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In many areas of control there are gaps between the existing theory and applications. This is more so in hybrid infinite dimensional systems and in particular hybrid systems in which both the actuator and the controller are switched. The main objective of this paper is to start filling in one of these gaps. We present a theoretical formulation and provide methodologies for implementing optimal and switching policies of spatially scheduled actuators for a class of distributed parameter systems (DPS). The optimization method employed is based on finite horizon LQR optimal control. Well posedness and optimality, pertaining to the switching policies of spatially scheduled actuators. are presented and proven. Tutorial examples motivated by thermal manufacturing applications along with extensive simulation results of the proposed actuator-plus-controller switching scheme are presented. (C) 2008 Elsevier Ltd. All rights reserved.
In the sampled-data control literature there are necessary conditions and sufficient conditions for stabilizability of distributed parameter systems by generalized sampled-data control. For finite-dimensional systems ...
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In the sampled-data control literature there are necessary conditions and sufficient conditions for stabilizability of distributed parameter systems by generalized sampled-data control. For finite-dimensional systems the necessary conditions are also known to be sufficient. We show that this equivalence extends to the infinite-dimensional case if the underlying semigroup is analytic. However, for general systems, the necessary conditions are not sufficient, nor are the sufficient conditions necessary. We prove this by a single example with a free parameter - one choice of parameter shows that the necessary conditions are too weak, and another choice shows that the sufficient conditions are tao strong. (C) 1998 Elsevier Science B.V. All rights reserved.
An optimal control problem for a class of nonlinear distributed parameter systems is posed. By using a theorem of approximation theory, necessary and sufficient conditions upon the optimal controls are derived.
An optimal control problem for a class of nonlinear distributed parameter systems is posed. By using a theorem of approximation theory, necessary and sufficient conditions upon the optimal controls are derived.
In this paper, iterative learning control (ILC) is employed in discrete spatial-temporal parabolic distributed parameter systems (DPSs), where the trial lengths vary randomly. A distributed ILC strategy is proposed, i...
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In this paper, iterative learning control (ILC) is employed in discrete spatial-temporal parabolic distributed parameter systems (DPSs), where the trial lengths vary randomly. A distributed ILC strategy is proposed, in which containing spatial variable, utilizes all past tracking information to improve current performance. Through rigorous theoretical analysis, the convergence of the system output error is proved under mathematical expectation along the iteration axis. Finally, the proposed method is applied to numerical simulation to illustrate its effectiveness.
We study the safety verification problem for a class of distributed parameter systems described by partial differential equations (PDEs), i.e., the problem of checking whether the solutions of the PDE satisfy a set of...
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We study the safety verification problem for a class of distributed parameter systems described by partial differential equations (PDEs), i.e., the problem of checking whether the solutions of the PDE satisfy a set of constraints at a particular point in time. The proposed method is based on an extension of barrier certificates to infinite-dimensional systems. In this respect, we introduce barrier functionals, which are functionals of the dependent and independent variables. Given a set of initial conditions and an unsafe set, we demonstrate that if such a functional exists satisfying two (integral) inequalities, then the solutions of the system do not enter the unsafe set. Therefore, the proposed method does not require finite dimensional approximations of the distributedparameter system. Furthermore, for PDEs with polynomial data, we solve the associated integral inequalities using semi-definite programming (SDP) based on a method that relies on a quadratic representation of the integrands of integral inequalities. The proposed method is illustrated through examples. (C) 2017 Elsevier B.V. All rights reserved.
Model predictive control (MPC) has been effectively applied in process industries since the 1990s. Models in the form of closed equation sets are normally needed for MPC, but it is often difficult to obtain such formu...
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Model predictive control (MPC) has been effectively applied in process industries since the 1990s. Models in the form of closed equation sets are normally needed for MPC, but it is often difficult to obtain such formulations for large nonlinear systems. To extend nonlinear MPC (NMPC) application to nonlinear distributed parameter systems (DPS) with unknown dynamics, a data-driven model reduction-based approach is followed. The proper orthogonal decomposition (POD) method is first applied off-line to compute a set of basis functions. Then a series of artificial neural networks (ANNs) are trained to effectively compute POD time coefficients. NMPC, using sequential quadratic programming is then applied. The novelty of our methodology lies in the application of POD's highly efficient linear decomposition for the consequent conversion of any distributed multi-dimensional space-state model to a reduced 1-dimensional model, dependent only on time, which can be handled effectively as a black-box through ANNs. Hence we construct a paradigm, which allows the application of NMPC to complex nonlinear high-dimensional systems, even input/output systems, handled by black-box solvers, with significant computational efficiency. This paradigm combines elements of gain scheduling, NMPC, model reduction and ANN for effective control of nonlinear DPS. The stabilization/destabilization of a tubular reactor with recycle is used as an illustrative example to demonstrate the efficiency of our methodology. Case studies with inequality constraints are also presented. (C) 2015 Elsevier Ltd. All rights reserved.
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