Stochastic model predictive control — how does it work?

Heirung, Tor Aksel N.; Paulson, Joel A.; O'Leary, Jared; Mesbah, Ali

doi:10.1016/j.compchemeng.2017.10.026

Cited by 132 publications

(77 citation statements)

References 40 publications

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“…18 Stochastic programming (SP), as another popular mathematical optimization approach, optimizes the expected value of the cost function, 19,20 based on the exact distribution of the disturbance and thus does not incorporate distribution ambiguity into the calculation. 10,21 However, the actual distribution of the random variables is typically unknown, 22 and hence some Monte Carlo sampling approaches have to be adopted for approximation. 23 For example, sample average approximation (SAA) method is widely utilized to estimate the expectation of the measure through empirical mean of historical data.…”

Section: Introductionmentioning

confidence: 99%

Soft‐constrained model predictive control based on data‐driven distributionally robust optimization

Lee

You

2020

AIChE Journal

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This article proposes a novel distributionally robust optimization (DRO)‐based soft‐constrained model predictive control (MPC) framework to explicitly hedge against unknown external input terms in a linear state‐space system. Without a priori knowledge of the exact uncertainty distribution, this framework works with a lifted ambiguity set constructed using machine learning to incorporate the first‐order moment information. By adopting a linear performance measure and considering input and state constraints robustly with respect to a lifted support set, the DRO‐based MPC is reformulated as a robust optimization problem. The constraints are softened to ensure recursive feasibility. Theoretical results on optimality, feasibility, and stability are further discussed. Performance and computational efficiency of the proposed method are illustrated through motion control and building energy control systems, showing 18.3% less cost and 78.8% less constraint violations, respectively, while requiring one third of the CPU time compared to multi‐stage scenario based stochastic MPC.

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Section: Introductionmentioning

confidence: 99%

Soft‐constrained model predictive control based on data‐driven distributionally robust optimization

Lee

You

2020

AIChE Journal

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“…Because of this issues, performance and stability deteriorate during real‐time implementation since all the practical processes are more or less affected by the stochastic factors. In this context, the notion of stochastic model predictive control (SMPC) has drawn significant interest . In an SMPC scheme, KF/EKF/DEKF/UKF–based estimation techniques are exploited to estimate the model states taking into account the effects of stochastic uncertainties and therefore offers better closed‐loop performance despite the presence of noises and random exogenous disturbances .…”

Section: Introductionmentioning

confidence: 99%

“…39 In an SMPC scheme, KF/EKF/DEKF/UKF-based estimation techniques 40 are exploited to estimate the model states taking into account the effects of stochastic uncertainties and therefore offers better closed-loop performance despite the presence of noises and random exogenous disturbances. 39 Apart from state estimation, often parameter estimation also becomes necessary especially when the parameters are uncertain or keep on varying. For example, in the work of Walker, 41 KF has been used for parameter estimation involving state constraints.…”

Section: Introductionmentioning

confidence: 99%

Design and application of nonlinear model‐based tracking control schemes employing DEKF estimation

Bhadra

Panda

Bhowmick

et al. 2019

Optim Control Appl Methods

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Summary This paper deals with the design and application of nonlinear model‐based control schemes for stable and nonlinear benchmark industrial processes. The primary control objective is to facilitate set‐point (constant/time‐varying) tracking in the presence of external disturbances, process noise, measurement noise, parametric uncertainty, and model mismatch. We first propose a “noninferential‐type” model‐based control scheme which involves a finite‐dimensional, nonlinear, and deterministic process model to generate the model states. Secondly, an “inferential‐type” model‐based control scheme has been introduced particularly to take into account the stochastic uncertainties such as process noise and measurement noise. The second scheme exploits the dual extended Kalman filter for estimating the immeasurable states and the process parameters through which disturbance is injected. Unlike fixed‐parameter controllers, the proposed schemes update the controller gains at each step depending on the real‐time process gains. In order to demonstrate the usefulness of the proposed closed‐loop tracking control schemes, two exhaustive case studies have been carried out on the CSTR and Van de Vusse reactor processes, which are considered to be benchmark industrial processes due to highly nonlinear and unpredictable behaviour and due to nonminimum phase property. Finally, the performance of the proposed schemes are compared with an EKF‐based adaptive PI control framework and the simulation results reveal that the transient performance of the proposed schemes are better than that of the aforementioned PI technique especially in perturbed condition (ie, in presence of model mismatch and measurement noise).

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“…Model uncertainty can lead to constraint violations and worse performance. To mitigate the effect of uncertainty on MPC, robust MPC [30] and stochastic MPC [31,32] methods have been developed.…”

Section: Introductionmentioning

confidence: 99%

Stochastic Nonlinear Model Predictive Control Using Gaussian Processes

Bradford¹,

Imsland²

2018

2018 European Control Conference (ECC)

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Nonlinear model predictive control (NMPC) is one of the few control methods that can handle multivariable nonlinear control systems with constraints. Gaussian processes (GPs) present a powerful tool to identify the required plant model and quantify the residual uncertainty of the plant-model mismatch given its probabilistic nature . It is crucial to account for this uncertainty, since it may lead to worse control performance and constraint violations. In this paper we propose a new method to design a GP-based NMPC algorithm for finite horizon control problems. The method generates Monte Carlo samples of the GP offline for constraint tightening using back-offs. The tightened constraints then guarantee the satisfaction of joint chance constraints online. Advantages of our proposed approach over existing methods include fast online evaluation time, consideration of closed-loop behaviour, and the possibility to alleviate conservativeness by accounting for both online learning and state dependency of the uncertainty. The algorithm is verified on a challenging semi-batch bioprocess case study, with its high performance thoroughly demonstrated.

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Stochastic model predictive control — how does it work?

Cited by 132 publications

References 40 publications

Soft‐constrained model predictive control based on data‐driven distributionally robust optimization

Soft‐constrained model predictive control based on data‐driven distributionally robust optimization

Design and application of nonlinear model‐based tracking control schemes employing DEKF estimation

Stochastic Nonlinear Model Predictive Control Using Gaussian Processes

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