An input/output approach to the optimal transition control of a class of distributed chemical reactors

Li, Mingheng; Christofides, Panagiotis D.

doi:10.1016/j.ces.2007.02.046

Cited by 21 publications

(23 citation statements)

References 35 publications

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“…However, it is not easy due to spatio-temporal coupled, nonlinear and infinite-dimensional dynamics. Due to different an input-output model [11]. A time-invariant Green's function model can be estimated using singular value decomposition (SVD) method [12].…”

Section: Introductionmentioning

confidence: 99%

A fuzzy-based spatio-temporal multi-modeling for nonlinear distributed parameter processes

et al. 2014

Applied Soft Computing

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Section: Introductionmentioning

confidence: 99%

A fuzzy-based spatio-temporal multi-modeling for nonlinear distributed parameter processes

et al. 2014

Applied Soft Computing

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“…Due to the underlying physical spatial-temporal phenomena, such as diffusion, convection, phase-dispersion, vibration, flow, etc., spatially distributed processes (SDPs) are essentially a nonlinear partial differential equation (PDE) system. Until now, many optimal control approaches − have been reported for PDE systems, which could be generally divided into two classes. The first class is the design-then-reduce ,,− methods, where an infinite-dimensional controller is synthesized based on the original PDE systems and then lumped for realization.…”

Section: Introductionmentioning

confidence: 99%

“…One popular approach for model reduction is Galerkin’s method based on empirical eigenfunctions (EEFs) or analytical basis functions. Recently, some optimal control approaches together with model reduction have been developed, such as nonlinear programming, dual heuristic programming, model predictive control, ,, the offline model-based iterative method, and the input/output approach using residence time distributions . However, most of these existing approaches require the full PDE system model, which is often unavailable for many practical industrial SDPs, such as chemical processes, thermal process, traffic flows, fluid dynamics, aeronautics, and astronautics.…”

Section: Introductionmentioning

confidence: 99%

Data-based Suboptimal Neuro-control Design with Reinforcement Learning for Dissipative Spatially Distributed Processes

Luo

2014

Ind. Eng. Chem. Res.

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For many real complicated industrial processes, the accurate system model is often unavailable. In this paper, we consider the partially unknown spatially distributed processes (SDPs) which are described by general highly dissipative nonlinear partial differential equations (PDEs) and develop a data-based adaptive suboptimal neuro-control method by introducing the thought of reinforcement learning (RL). First, based on the empirical eigenfunctions computed with Karhunen−Loeve decomposition, singular perturbation theory is used to derive a reduced-order model of an ordinary differential equation that represents the dominant dynamics of the SDP. Second, the Hamilton−Jacobi−Bellman (HJB) approach is used for the suboptimal control design, and the thought of policy iteration (PI) is introduced for online learning of the solution of the HJB equation, and its convergence is established. Third, a neural network (NN) is employed to approximate the cost function in the PI procedure, and a NN weight tuning algorithm based on the gradient descent method is proposed. We prove that the developed online adaptive suboptimal neuro-controller can ensure that the original closed-loop PDE system is semiglobally uniformly ultimately bounded. Finally, the developed data-based control method is applied to a nonlinear diffusion-reaction process, and the achieved results demonstrate its effectiveness.

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“…In some cases, the transfer function or Green’s function can be derived from first-principles knowledge. , If the analytical transfer function or Green’s function is not available, it can be estimated from the input–output data. For example, using the concept of residence time distribution, an input–output model is constructed for optimal control that is actually a linear kernel model . On the basis of a singular function expansion, a time-invariant Green’s function model can be estimated using a singular value decomposition (SVD) method .…”

Section: Introductionmentioning

confidence: 99%

Kernel-Based Spatiotemporal Multimodeling for Nonlinear Distributed Parameter Industrial Processes

et al. 2012

Ind. Eng. Chem. Res.

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Many industrial processes are nonlinear distributed parameter systems (DPS) that have significant spatiotemporal dynamics. Due to different production and working conditions, they often need to work at a large operating range with multiple working points. However, direct global modeling and persistently exciting experiment in a large working region are very costly in many cases. The complex spatiotemporal coupling and infinite-dimensional nature make the problem more difficult. In this study, a kernel-based spatiotemporal multimodeling approach is proposed for the nonlinear DPS with multiple working points. To obtain a reasonable operating space division, an iterative approach is proposed where the operating space division and local modeling are performed iteratively. The working range of the current local model will help to determine the next operating point required for modeling. Utilizing the potential of each local model, the number of regions can be reduced. In the local modeling, the Karhunen−Loeve method is used for the space/time separation and dimension reduction, and after that unknown parameters of kernels are estimated. Due to consideration of time-scale properties in the dimension reduction, the modeling approach is particularly suitable for dissipative PDEs, particularly of parabolic type. The multimodeling and space/time separation techniques can largely reduce the complexity of global nonlinear spatiotemporal modeling. Finally, to guarantee a smooth transition between local spatiotemporal models, a scheduling integration method is used to provide a global spatiotemporal model. To design scheduling functions, a two-stage training method is proposed to reduce the design complexity. Compared with direct global modeling, the exciting experiment and modeling for each local region become easier. Compared with one local modeling, the multimodel integration will improve modeling accuracy. The effectiveness of the proposed modeling approach is verified by simulations.

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An input/output approach to the optimal transition control of a class of distributed chemical reactors

Cited by 21 publications

References 35 publications

A fuzzy-based spatio-temporal multi-modeling for nonlinear distributed parameter processes

A fuzzy-based spatio-temporal multi-modeling for nonlinear distributed parameter processes

Data-based Suboptimal Neuro-control Design with Reinforcement Learning for Dissipative Spatially Distributed Processes

Kernel-Based Spatiotemporal Multimodeling for Nonlinear Distributed Parameter Industrial Processes

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