In this paper,the control problem of distributed parameter systems is investigated by using wireless sensor and actuator networks with the observer-based ***,a centralized observer which makes use of the measurement i...
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In this paper,the control problem of distributed parameter systems is investigated by using wireless sensor and actuator networks with the observer-based ***,a centralized observer which makes use of the measurement information provided by the fixed sensors is designed to estimate the distributedparameter *** mobile agents,each of which is affixed with a controller and an actuator,can provide the observer-based control for the target *** using Lyapunov stability arguments,the stability for the estimation error system and distributedparameter control system is proved,meanwhile a guidance scheme for each mobile actuator is provided to improve the control performance.A numerical example is finally used to demonstrate the effectiveness and the advantages of the proposed approaches.
We focus on the output tracking problem of distributed parameter systems (DPSs) which can be described by a set of nonlinear dissipative partial differential equations (PDEs). The infinite-dimensional modal representa...
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We focus on the output tracking problem of distributed parameter systems (DPSs) which can be described by a set of nonlinear dissipative partial differential equations (PDEs). The infinite-dimensional modal representation of such systems in appropriate subspaces can be decomposed to finite-dimensional slow and probably unstable, and infinite-dimensional fast and stable subsystems. Taking advantage of this decomposition, adaptive model reduction techniques and specifically adaptive proper orthogonal decomposition (APOD) can be used for the recursive construction of locally accurate low dimensional reduced order models (ROMs). The proposed geometric APOD-based control structure is the combination of a nonlinear Luenberger-like geometric dynamic observer and a globally linearizing controller (GLC) designed for tracking the desired output. The proposed geometric control approach is successfully illustrated on the output tracking of target thermal dynamics for a catalytic reactor. Specifically, the geometric output tracking strategy is used to reduce the hot spot temperature and manage the thermal energy distribution through reactor length during process evolution with limited number of actuators and sensors. (C) 2014 Elsevier Ltd. All rights reserved.
We focus on the Lyapunov-based output feedback control problem for a class of distributed parameter systems with spatiotemporal dynamics described by input-affine linear and semilinear dissipative partial differential...
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We focus on the Lyapunov-based output feedback control problem for a class of distributed parameter systems with spatiotemporal dynamics described by input-affine linear and semilinear dissipative partial differential equations (DPDEs). The control problem is addressed via model order reduction. Galerkin projection is applied to discretize the DPDE and derive low-dimensional reduced order models (ROMs). The empirical basis functions needed for this discretization are recursively computed using adaptive proper orthogonal decomposition (APOD). To update the basis functions during process operation, APOD needs measurements of the system state's complete profile (called snapshots) at revision times. This paper's main objective is to minimize the demand for snapshots from the spatially distributed sensors by the control structure while maintaining closed-loop stability and performance. A control Lyapunov function is defined, and its value is monitored as the system evolves. Only when the value violates a closed-loop stability threshold, snapshots are requested for a brief period by APOD after which the ROM is updated, and the controller is reconfigured. The proposed approach is applied to stabilize the Kuramoto-Sivashinsky equation. (C) 2021 Elsevier Ltd. All rights reserved.
This paper introduces it new simple quantitative robust control technique designing applicable to one-point feedback controllers for distributed parameter systems (DPSs) with uncertainty. The paper considers the spati...
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This paper introduces it new simple quantitative robust control technique designing applicable to one-point feedback controllers for distributed parameter systems (DPSs) with uncertainty. The paper considers the spatial distribution of the relevant points where the inputs and the outputs of the control system are applied (actuators, sensors, disturbances and control objectives) and introduces a new set of transfer functions (TFs) that describe the relationships between the distributed inputs and Outputs of the system. Based on these TFs, the paper extends the classical robust stability and performance specifications to the DPS case and presents a new set of quadratic inequalities to define the quantitative feedback theory bounds. The method can also deal with uncertainty in both the model and the spatial distribution of the inputs and the outputs. Some examples illustrate the use and simplicity of the proposed methodology. Copyright (c) 2006 John Wiley & Sons, Ltd.
A geometric homogeneity is introduced for evolution equations in a Banach space. Scalability property of solutions of homogeneous evolution equations is proven. Some qualitative characteristics of stability of trivial...
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A geometric homogeneity is introduced for evolution equations in a Banach space. Scalability property of solutions of homogeneous evolution equations is proven. Some qualitative characteristics of stability of trivial solution are also provided. In particular, finite-time stability of homogeneous evolution equations is studied. Theoretical results are illustrated on important classes of partial differential equations.
In this paper we consider an optimal control problem described by a system of nonlinear first order hyperbolic partial differential equations with deviating argument, including integral inequality constraints. The con...
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In this paper we consider an optimal control problem described by a system of nonlinear first order hyperbolic partial differential equations with deviating argument, including integral inequality constraints. The control variables are assumed to be measurable, with the corresponding state variables in Lp. We introduce the adjoint equations, derive an integral representation of the increments of the functionals involved, and use separation theorems of functional analysis to obtain new necessary optimality conditions in the form of the Pontryagin maximum principle. (C) 1996 Academic Press, Inc.
The paper deals with the optimal sensor location problem associated with minimax filtering for linear distributed parameter systems under the moving sensors. The problem of optimal choice of a measurement trajectory i...
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The paper deals with the optimal sensor location problem associated with minimax filtering for linear distributed parameter systems under the moving sensors. The problem of optimal choice of a measurement trajectory is treated here as an H(infinity)-optimal control one under phase constraints with the objective to minimize a given 'weak' performance index under 'worst' possible disturbances. Existence of a solution to such a problem is established for the case of quadratic constraints on the disturbances and necessary conditions for optimality are derived on the basis of constructing a sequence of suboptimal solutions associated, in turn, with a sequence of finite-dimensional maximum principles.
Benefitting from the technology of integral reinforcement learning, the nonzero sum (NZS) game for distributed parameter systems is effectively solved in this paper when the information of system dynamics are unavaila...
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Benefitting from the technology of integral reinforcement learning, the nonzero sum (NZS) game for distributed parameter systems is effectively solved in this paper when the information of system dynamics are unavailable. The Karhunen-Loeve decomposition (KLD) is employed to convert the partial differential equation (PDE) systems into high-order ordinary differential equation (ODE) systems. Moreover, the off-policy IRL technology is introduced to design the optimal strategies for the NZS game. To confirm that the presented algorithm will converge to the optimal value functions, the traditional adaptive dynamic programming (ADP) method is first discussed. Then, the equivalence between the traditional ADP method and the presented off-policy method is proved. For implementing the presented off-policy IRL method, actor and critic neural networks are utilized to approach the value functions and control strategies in the iteration process, individually. Finally, a numerical simulation is shown to illustrate the effectiveness of the proposal off-policy algorithm.
It is well known that optimal control trajectories can be highly sensitive to perturbations in the model parameters. Computationally efficient numerical algorithms are presented for the worst-case analysis of the effe...
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It is well known that optimal control trajectories can be highly sensitive to perturbations in the model parameters. Computationally efficient numerical algorithms are presented for the worst-case analysis of the effects of parametric uncertainties on boundary control problems for finite-time distributed parameter systems. The approach is based on replacing the full-order model of the system with a power series expansion that is analyzed by linear matrix inequalities or power iteration, which are polynomial-time algorithms. Theory and algorithms are provided for computing the most positive and most negative worst-case deviation in a state or output, in contrast to the 'two-sided' deviations normally computed in worst-case analyses. Application to the Dirichlet boundary control of the reaction diffusion equation to track a desired two-dimensional concentration field illustrates the promise of the approach. Copyright (C) 2010 John Wiley & Sons, Ltd.
In this work we suggest hierarchical sliding mode observers for complex systems which include distributed parameter systems and combinations of distributedparameter and lumped parametersystems, modeling, for example...
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In this work we suggest hierarchical sliding mode observers for complex systems which include distributed parameter systems and combinations of distributedparameter and lumped parametersystems, modeling, for example, an actuator dynamics. The main idea is based on the observer suggested previously for general nonlinear lumped parametersystems that is using the equivalent values of the discontinuous function to obtain additional information about the system state. Such observers can be written directly into system's original variables without requiring the state transformation. In this paper, using a modal representation of the distributed system and the hierarchy of sliding modes, we develop a structure of such an observer for a wide class of systems described by partial differential equations or combinations of ordinary and partial differential equations. An example is presented which illustrates the proposed method.
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