Statistical <scp>machine‐learning–</scp>based predictive control of uncertain nonlinear processes

Wu, Zhe; Alnajdi, Aisha; Gu, Quanquan; Christofides, Panagiotis D.

doi:10.1002/aic.17642

Cited by 29 publications

(17 citation statements)

References 22 publications

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“…Equation 19 is capable of keeping the Lyapunov function decreasing in a range. The existence of constant ε/Δ means that there certainly exists a minimum level set Ω ρs (x td k ) around the origin; satisfying that ∀x td k ∈ Ω ρ /Ω ρs makes the problem (22) feasible. The details are presented in the Stability Analysis subsection.…”

Section: = [mentioning

confidence: 99%

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Implementable Stability Guaranteed Lyapunov-Based Data-Driven Model Predictive Control with Evolving Gaussian Process

Zhang

Zheng

2022

Ind. Eng. Chem. Res.

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In this paper, we integrate the blueonline-updating Gaussian Process (GP) models into the Model Predictive Control (MPC) design of nonlinear systems with time-varying dynamics to obtain a more accurate data-based prediction of state, and more relaxed constraints. Specifically, considering that the GP inferred from the Bayesian framework provides both the predictive value and the estimation of uncertainties, a mechanism of updating the predictive model and the stability constraint based on the Lyapunov techniques is designed according to the online estimation of the mismatch between the prediction by GP and that of the real system. It keeps the feasibility of the designed MPC system. Besides, the stability of the closed-loop system is proven to be guaranteed under a certain probability. Applying the designed method to a chemical process shows the efficiency of the proposed data-driven MPC.

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Section: = [mentioning

confidence: 99%

“…Here, the level set Ω ρs is used in (22g) as a condition to relax the problem (22). The Ω ρs can be obtained by solving following problem.…”

Section: = [mentioning

confidence: 99%

Implementable Stability Guaranteed Lyapunov-Based Data-Driven Model Predictive Control with Evolving Gaussian Process

Zhang

Zheng

2022

Ind. Eng. Chem. Res.

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“…where Φ(x, u) ∈ F n k (nu+1)×1 is the lifting vector function which contains the primer modes of system (10) are selected, the ω m is the mismatch caused by the ignored modes. When the lifting function ϕ is an infinite dimension radius function or it makes the lifting space close ω m = 0.…”

Section: Koopman Approximationmentioning

confidence: 99%

“…Remark 4.1. It can be seen from (10) which is a linear model, x is one of the elements of the state vector Φ(x). Φ(x(t)) can be calculated as the form of Φ(x(t)) = M Φ(x(t 0 )) + t t 0 N u(τ )dτ , where M and N are matrixes and only related to time t. Considering the input u is piece-wise, Φ(x(t)) can be written as the linear combination of u(t k ), u(t k+1 ), .…”

Section: Almpc Designmentioning

confidence: 99%

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Koopman Approximator based Adaptive Model Predictive Control of Continuous Nonlinear Systems

Zheng¹,

Zhang

Li³

et al. 2022

Preprint

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This paper considers the real-time control of a class of complex continuous nonlinear systems with an increasing requirement on control accuracy and unknown dynamics at the start time due to their complex dynamics and uncertainties. A Koopman approximate model-based adaptive MPC design using the Lyapunov technique is explored. Specifically, the nonlinear system is modeled/transformed into a linear model in a lifting space with the Koopman operator. A recursive update of the approximator is provided by which the parameters set of the approximator is in a nested form and a shrinking of the boundary of the approximator’s mismatch from the real system is obtained. Also, based on the Koopman model and its mismatch boundary, a sufficient condition that ensures the states of the nonlinear system eventually converge to a small neighborhood of the origin is deduced. An FCCU example is employed to show the effectiveness of the proposed control law.

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Modeling and predictive control of nonlinear processes using transfer learning method

Xiao

2023

AIChE Journal

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This work develops a transfer learning (TL) framework for modeling and predictive control of nonlinear systems using recurrent neural networks (RNNs) with the knowledge obtained in modeling one process transferred to another. Specifically, transfer learning uses a pretrained model developed based on a source domain as the starting point, and adapts the model to a target process with similar configurations. The generalization error for TL‐based RNN (TL‐RNN) is first derived to demonstrate the generalization capability on the target process. The theoretical error bound that depends on model capacity and the discrepancy between source and target domains is then utilized to guide the development of pretrained models for improved model transferability. Subsequently, the TL‐RNN model is utilized as the prediction model in model predictive controller (MPC) for the target process. Finally, the simulation study of chemical reactors via Aspen Plus Dynamics is used to demonstrate the benefits of transfer learning.

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Statistical machine‐learning–based predictive control of uncertain nonlinear processes

Cited by 29 publications

References 22 publications

Implementable Stability Guaranteed Lyapunov-Based Data-Driven Model Predictive Control with Evolving Gaussian Process

Implementable Stability Guaranteed Lyapunov-Based Data-Driven Model Predictive Control with Evolving Gaussian Process

Koopman Approximator based Adaptive Model Predictive Control of Continuous Nonlinear Systems

Modeling and predictive control of nonlinear processes using transfer learning method

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