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A big data-driven predictive control approach for nonlinear processes using behaviour clusters 使用行为集群的非线性过程大数据驱动预测控制方法
IF 4.2 2区 计算机科学 Q1 Mathematics Pub Date : 2024-06-07 DOI: 10.1016/j.jprocont.2024.103252
Shuangyu Han , Yitao Yan , Jie Bao , Biao Huang

A novel big data-driven predictive control (BDPC) approach for nonlinear processes is proposed. To deal with nonlinear process behaviours, the process behaviour space, represented by a set of input–output variable trajectories, is partitioned into linear sub-behaviour spaces (clusters), based on linear inclusion of nonlinear behaviours. A behaviour space (represented using Hankel matrices) partitioning approach is developed based on subspace angles. During online control, the BDPC controller locates the most relevant linear sub-behaviour based on the current online trajectory, which is then used to determine predictive control actions using receding horizon optimisation. The incremental stability and dissipativity conditions are developed to attenuate the effect of the error of approximating linear sub-behaviours on the output and guarantee closed-loop stability. These conditions are implemented as additional constraints during online data-driven predictive control. An example of controlling the Hall–Héroult process is used to illustrate the proposed approach.

针对非线性过程提出了一种新颖的大数据驱动预测控制(BDPC)方法。为了处理非线性过程行为,根据非线性行为的线性包含关系,将输入输出变量轨迹集所代表的过程行为空间划分为线性子行为空间(群组)。基于子空间角度,开发了一种行为空间(使用汉克尔矩阵表示)划分方法。在在线控制过程中,BDPC 控制器会根据当前的在线轨迹找到最相关的线性子行为,然后利用后退视界优化来确定预测控制行动。开发增量稳定性和耗散性条件是为了减弱近似线性子行为的误差对输出的影响,并保证闭环稳定性。这些条件在在线数据驱动预测控制中作为附加约束条件实施。以控制霍尔-赫鲁特过程为例,说明了所提出的方法。
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引用次数: 0
Predicting goal attainment in process-oriented behavioral interventions using a data-driven system identification approach 使用数据驱动的系统识别方法预测过程导向行为干预的目标实现情况
IF 4.2 2区 计算机科学 Q1 Mathematics Pub Date : 2024-05-27 DOI: 10.1016/j.jprocont.2024.103242
Sarasij Banerjee , Rachael T. Kha , Daniel E. Rivera , Eric Hekler

Behavioral interventions (such as those developed to increase physical activity, achieve smoking cessation, or weight loss) can be represented as dynamic process systems incorporating a multitude of factors, ranging from cognitive (internal) to environmental (external) influences. This facilitates the application of system identification and control engineering methods to address questions such as: what drives individuals to improve health behaviors (such as engaging in physical activity)? In this paper, the goal is to efficiently estimate personalized, dynamic models which in turn will lead to control systems that can optimize this behavior. This problem is examined in system identification applied to the Just Walk study that aimed to increase walking behavior in sedentary adults. The paper presents a Discrete Simultaneous Perturbation Stochastic Approximation (DSPSA)-based modeling of the Goal Attainment construct estimated using AutoRegressive with eXogenous inputs (ARX) models. Feature selection of participants and ARX order selection is achieved through the DSPSA algorithm, which efficiently handles computationally expensive calculations. DSPSA can search over large sets of features as well as regressor structures in an informed, principled manner to model behavioral data within reasonable computational time. DSPSA estimation highlights the large individual variability in motivating factors among participants in Just Walk, thus emphasizing the importance of a personalized approach for optimized behavioral interventions.

行为干预措施(如为增加体育锻炼、戒烟或减肥而开发的干预措施)可以表示为包含多种因素的动态过程系统,这些因素包括认知(内部)影响因素和环境(外部)影响因素。这有助于应用系统识别和控制工程方法来解决以下问题:是什么促使个人改善健康行为(如参加体育锻炼)?本文的目标是有效估算个性化动态模型,进而建立能够优化这种行为的控制系统。本文通过系统识别对这一问题进行了研究,并将其应用于旨在增加久坐不动的成年人步行行为的研究中。本文介绍了一种基于离散同步扰动随机逼近(DSPSA)的建模方法,该方法使用具有外生输入的自回归(ARX)模型对结构进行估计。参与者的特征选择和 ARX 序列选择是通过 DSPSA 算法实现的,该算法可有效处理计算成本高昂的计算。DSPSA 可以在合理的计算时间内,以知情、有原则的方式搜索大量特征集和回归器结构,从而为行为数据建模。DSPSA 估算突出了《侏罗纪世界》中参与者在动机因素方面的巨大个体差异,从而强调了个性化方法对于优化行为干预的重要性。
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引用次数: 0
Data-driven identification and comparison of full multivariable models for propofol–remifentanil induced general anesthesia 数据驱动的异丙酚-瑞芬太尼诱导全身麻醉全多变量模型的识别与比较
IF 4.2 2区 计算机科学 Q1 Mathematics Pub Date : 2024-05-27 DOI: 10.1016/j.jprocont.2024.103243
Erhan Yumuk , Dana Copot , Clara M. Ionescu , Martine Neckebroek

In this paper, we present results with clinical data to enable a 2x2 input–output multivariable patient model for hypnosis and analgesia. Nonlinear multi-drug interaction models are identified from data recorded from 70 patients undergoing surgery during total intravenous anesthesia (TIVA) with several medical monitors for variables such as Bispectral Index, Nociception level (Medasense), skin conductance (Medstorm) and advanced spectral analysis conductance (AnspecPro). Bispectral index measures the depth of hypnosis (lack of consciousness), while nociception related indices from Medasense, Medstorm, and AnspecPro devices measure levels related to analgesia (lack of reaction to noxious stimuli). A comparison is given among three response surface model (RSM) structures – Minto, Greco, and Reduced Greco – for hypnotic and analgesic states during Propofol–Remifentanil interaction. The identified models capture the pharmacodynamic properties of dose–effect concentrations of Propofol/Remifentanil while the pharmacokinetic part of the patient model is calculated from patient’s biometric values using Schnider/Minto (SM), and Eleveld/Eleveld (EE) models. In presence of strict clinical protocols delivering data under poor identifiability conditions, we propose two methods of identification: (i) based on steady-state gains, and (ii) using all available data which includes part of the dynamic transient. The model parameters are optimized with Genetic Algorithm based on a goodness of fit performance measure complemented with root mean square error. The results suggest that the EE model combination is advantageous for Bispectral index pharmacokinetic modeling at the cost of numerical complexity, therefore reducing the uncertainty left to be identified in the pharmacodynamic part of the patient model. By contrast, the SM model combination is less computationally demanding and provides some improvement in the RSM accuracy for nociception level indicators. The comparison of three devices for nociception levels evaluation suggests that clinical data captured with the Medasense monitor provides best fitted RSMs with the Reduced Greco RSM structure, despite having fewer parameters.

在本文中,我们介绍了利用临床数据建立 2x2 输入输出多变量患者催眠和镇痛模型的结果。非线性多药相互作用模型是从 70 名接受全静脉麻醉(TIVA)手术的患者记录的数据中确定的,这些数据包括双光谱指数、痛觉水平(Medasense)、皮肤电导率(Medstorm)和高级频谱分析电导率(AnspecPro)等变量的多个医疗监控器。双谱指数测量的是催眠深度(缺乏意识),而 Medasense、Medstorm 和 AnspecPro 设备中与痛觉相关的指数测量的是与镇痛相关的水平(对有害刺激缺乏反应)。针对丙泊酚-瑞芬太尼相互作用过程中的催眠和镇痛状态,比较了三种反应曲面模型(RSM)结构--明托、格雷科和还原格雷科。已确定的模型捕捉到了丙泊酚/瑞芬太尼剂量效应浓度的药效学特性,而患者模型的药代动力学部分则是通过施奈德/明托(SM)和埃勒维尔德/埃勒维尔德(EE)模型,根据患者的生物特征值计算得出的。在严格的临床协议下,数据的可识别性较差,因此我们提出了两种识别方法:(i) 基于稳态增益;(ii) 使用所有可用数据,包括部分动态瞬态数据。模型参数采用遗传算法进行优化,该算法基于拟合优度和均方根误差。结果表明,EE 模型组合在双谱指数药代动力学建模方面具有优势,但代价是数值复杂性,因此减少了患者模型药效学部分有待确定的不确定性。相比之下,SM 模型组合对计算的要求较低,并在一定程度上提高了痛觉水平指标的 RSM 精确度。对用于评估痛觉水平的三种设备进行的比较表明,尽管参数较少,但通过 Medasense 监护仪采集的临床数据提供了与 Reduced Greco RSM 结构最匹配的 RSM。
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引用次数: 0
Applications of Lagrangian relaxation-based algorithms to industrial scheduling problems, especially in production workshop scenarios: A review 基于拉格朗日松弛的算法在工业调度问题中的应用,尤其是在生产车间场景中的应用:综述
IF 4.2 2区 计算机科学 Q1 Mathematics Pub Date : 2024-05-27 DOI: 10.1016/j.jprocont.2024.103233
Liangliang Sun , Ruimin Yang , Jing Feng, Ge Guo

Industrial scheduling problems (ISPs), especially industrial production workshop scheduling problems (IPWSPs) in various sectors like manufacturing, and power require allocating resources to tasks within multiple constraints. Addressing these complex challenges involves computationally solving problems with numerous variables and constraints. Lagrangian relaxation-based algorithms (LRAs) effectively tackle ISPs (particularly IPWSPs) by relaxing constraints through multipliers. While LRAs may violate original constraints, heuristic algorithms rectify this by crafting feasible solutions. LRAs offer efficient problem-solving and yield high-quality results with manageable computational effort. This review presents the cutting-edge LRAs for ISPs, based on 200 papers from the fields of supply chain, manufacture, power, etc. It exemplifies LRAs’ principles through practical cases, and provides a classification of problems in detail, along with LRA’s problem-solving process. We discuss strengths, weaknesses, and future research prospects, offering comprehensive guidance. Summarizing these findings, the review enhances understanding of LRAs’ application potential in solving ISPs for practitioners and researchers.

工业调度问题(ISPs),尤其是制造和电力等各行业的工业生产车间调度问题(IPWSPs),需要在多重约束条件下为任务分配资源。要应对这些复杂的挑战,就必须通过计算解决存在大量变量和约束条件的问题。基于拉格朗日松弛的算法(LRA)通过乘法放宽约束条件,可有效解决 ISP(尤其是 IPWSP)问题。虽然拉格朗日松弛算法可能会违反原始约束条件,但启发式算法可以通过制定可行的解决方案来纠正这种情况。LRA 可以高效解决问题,并以可控的计算量获得高质量的结果。本综述以供应链、制造、电力等领域的 200 篇论文为基础,介绍了用于 ISP 的前沿 LRA。它通过实际案例阐释了 LRA 的原理,并提供了详细的问题分类以及 LRA 的问题解决流程。我们讨论了 LRA 的优势、劣势和未来研究前景,提供了全面的指导。通过总结这些发现,本综述加深了从业人员和研究人员对 LRA 在解决 ISP 方面的应用潜力的理解。
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引用次数: 0
Data/mechanism hybrid-driven modeling of blast furnace smelting system and global sequential optimization 高炉冶炼系统的数据/机制混合驱动建模和全局顺序优化
IF 4.2 2区 计算机科学 Q1 Mathematics Pub Date : 2024-05-21 DOI: 10.1016/j.jprocont.2024.103235
Siwei Lou , Chunjie Yang , Xujie Zhang , Hanwen Zhang , Ping Wu

Within the crucial domain of blast furnace ironmaking and sintering, the quality of sinter ore and molten iron holds supreme importance, with direct implications for downstream processes. However, the complexities of utilizing operational experience, understanding mechanisms, leveraging extensive data for precise modeling, and optimizing multiple objectives have persistently posed challenges for engineers. In this research, we propose an novel data/mechanism hybrid-driven modeling and global sequential optimization framework, with three core contributions: (1) Synthesizing field operation insights and mechanistic principles to construct models for molten iron production and energy consumption in ironmaking. (2) Crafting the broad learning approximate-aided subspace identification method (BLASIM), encapsulating the system’s dynamic and nonlinear characteristics. This method pioneers a parametric modeling strategy predicated on correlation error for dynamic nonlinear system identification, with its feasibility robustly underpinned by theoretical verification. (3) Streamlining the optimization process by applying expert knowledge to deconstruct a complex multi-objective optimization problem into manageable single-objective tasks. These tasks are addressed sequentially, reflecting operational chronology, and are adeptly resolved using gray wolf optimization algorithm with a sequence relaxant factor. To conclude, the proposed methods are thoroughly validated using real-world blast furnace smelting data, affirming the feasibility and efficiency of modeling accuracy and optimization performance.

在高炉炼铁和烧结这一关键领域,烧结矿和铁水的质量至关重要,对下游工艺有着直接影响。然而,利用操作经验、了解机理、利用大量数据进行精确建模以及优化多个目标的复杂性一直是工程师面临的挑战。在这项研究中,我们提出了一种新颖的数据/机制混合驱动建模和全局顺序优化框架,其核心贡献有三:(1) 综合现场操作见解和机制原理,构建炼铁过程中的铁水生产和能耗模型。(2) 创造了广义学习近似辅助子空间识别方法(BLASIM),囊括了系统的动态和非线性特征。该方法开创了以相关误差为前提的参数建模策略,用于动态非线性系统识别,其可行性得到了理论验证的有力支持。(3) 运用专家知识将复杂的多目标优化问题分解为易于管理的单目标任务,从而简化优化过程。这些任务按顺序处理,反映了操作时序,并使用带有顺序松弛因子的灰狼优化算法巧妙地加以解决。最后,利用实际高炉冶炼数据对提出的方法进行了全面验证,肯定了建模精度和优化性能的可行性和效率。
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引用次数: 0
A nonlinear disturbance observer for sliding mode control of surge in centrifugal compressors via TCV actuator 通过 TCV 执行器实现离心压缩机浪涌滑模控制的非线性扰动观测器
IF 4.2 2区 计算机科学 Q1 Mathematics Pub Date : 2024-05-21 DOI: 10.1016/j.jprocont.2024.103227
Nima Rabiee Roudsari , Mohammad Ataei , Hamid Reza Koofigar , Allahyar Montazeri

Surge is a form of dynamic instability created as an unstable pattern in the flow of fluid and can severely affect centrifugal compressor performance by causing fluctuations in flow and pressure parameters. Due to the heavy and costly damage that the surge may cause in various industrial processes such as petrochemical plants, it is necessary to design an appropriate control system to reduce the effect of this phenomenon. The problem of active surge control of a centrifugal compressor using the throttle control valve (TCV) in the presence of compressor parametric uncertainties as well as large demands on upstream and downstream loads is investigated in this work. The control objective was to design a robust control system that can stabilize the compressor over a wide operating range without knowing the upper bound for the uncertainties and load demand. The controller should also react quickly by generating a smooth control signal without saturating the control input. These objectives are achieved by designing a sliding mode controller along with a nonlinear disturbance observer. The performance of the proposed disturbance observer-based controller is evaluated under various operational and load conditions and the results are compared against fuzzy type 1, conventional sliding mode, and wavelet-based neural network robust adaptive controllers. The results show that the proposed method can tolerate large disturbances without any knowledge on the upper bound of the incident disturbance, both on the downstream pressure and upstream mass flow which is highly desirable in practice. The comparative study proves the efficacy of the proposed method using various performance measures. The study also confirms the superior robust performance and stability of the proposed method in front of matched and mismatched disturbances as well as model uncertainties especially close to the instability boundary. Although choosing a TCV actuator has made the control system design easier, the sensitivity of the control valve to flow coefficient and zero calibration under different operating ranges of the compression system is studied carefully and some recommendations for the users are provided.

浪涌是一种动态不稳定现象,是流体流动中的一种不稳定形态,会导致流量和压力参数的波动,从而严重影响离心压缩机的性能。由于浪涌可能会对石化厂等各种工业流程造成严重和代价高昂的损害,因此有必要设计一种适当的控制系统来减少这种现象的影响。本研究探讨了在压缩机参数不确定以及上下游负载需求较大的情况下,利用节流控制阀(TCV)对离心式压缩机进行主动浪涌控制的问题。控制目标是设计一种稳健的控制系统,能够在不知道不确定性和负载需求上限的情况下,在较宽的运行范围内稳定压缩机。控制器还应在控制输入不饱和的情况下产生平滑的控制信号,从而做出快速反应。这些目标可通过设计滑模控制器和非线性干扰观测器来实现。在各种运行和负载条件下,对所提出的基于扰动观测器的控制器的性能进行了评估,并将结果与模糊 1 型、传统滑动模式和基于小波的神经网络鲁棒自适应控制器进行了比较。结果表明,所提出的方法可以在不知道入射扰动上限值的情况下,对下游压力和上游质量流量都能承受较大的扰动,这在实际应用中是非常理想的。比较研究利用各种性能指标证明了所提方法的有效性。研究还证实,在匹配和不匹配干扰以及模型不确定性面前,特别是在接近不稳定边界时,所提出的方法具有卓越的鲁棒性能和稳定性。虽然选择 TCV 执行器简化了控制系统的设计,但还是仔细研究了压缩系统不同工作范围下控制阀对流量系数和零点校准的敏感性,并为用户提供了一些建议。
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引用次数: 0
Mathematical modeling and system analysis for preventing unsteady bulging in continuous slab casting machines 防止板坯连铸机不稳定鼓包的数学建模和系统分析
IF 4.2 2区 计算机科学 Q1 Mathematics Pub Date : 2024-05-18 DOI: 10.1016/j.jprocont.2024.103232
J. Landauer , L. Marko , A. Kugi , A. Steinboeck

In the continuous casting of steel slabs, the ferrostatic pressure in the liquid core of the strand leads to bending, i.e., bulging, of the strand shell between the guiding rolls. Unsteady bulging means that this bending process is time-varying. During the continuous casting process, the emergence of unsteady bulging can be observed, leading to unwanted mold level fluctuations and lowering the quality of the cast strand. This work presents a detailed nonlinear beam model, an approximated nonlinear beam model, and a control-oriented linear model to gain new insights into the mechanism of unsteady bulging. Simulation results show that the linear model allows real-time computation, making it feasible to design advanced model-based control and state estimation strategies. The developed models are validated using measurements from the literature and an industrial continuous casting plant. More specifically, these models permit, for the first time, a detailed stability analysis of the overall mold level control loop, which gives a system-theoretic explanation for the root cause of unsteady bulging and why it is tied to particular frequencies of mold level fluctuations. This analysis shows that the emergence of unsteady bulging is related to an unstable closed-loop system and opens up different strategies to eliminate the observed instability.

在钢坯连铸过程中,钢绞线液芯中的铁静压会导致钢绞线外壳在导向辊之间发生弯曲,即鼓包。不稳定的鼓包意味着这种弯曲过程是随时间变化的。在连铸过程中,可以观察到不稳定鼓包的出现,从而导致不必要的模具水平波动,降低铸件的质量。本研究提出了一个详细的非线性梁模型、一个近似的非线性梁模型和一个以控制为导向的线性模型,以获得对不稳定鼓包机理的新见解。仿真结果表明,线性模型可以进行实时计算,使设计基于模型的高级控制和状态估计策略变得可行。利用文献和工业连铸机的测量结果对所开发的模型进行了验证。更具体地说,这些模型首次对整个模位控制环路进行了详细的稳定性分析,从系统理论上解释了不稳定鼓包的根本原因,以及为什么不稳定鼓包与特定频率的模位波动有关。该分析表明,不稳定鼓包的出现与不稳定的闭环系统有关,并提出了消除所观察到的不稳定性的不同策略。
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引用次数: 0
Economic Performance of Model Predictive Control at Back-off Operating Point 模型预测控制在后备运行点的经济性能
IF 4.2 2区 计算机科学 Q1 Mathematics Pub Date : 2024-05-16 DOI: 10.1016/j.jprocont.2024.103231
Nabil Magbool Jan , Sridharakumar Narasimhan

In this paper, we address the economic performance of Model Predictive Control (MPC) while operating at a backed-off operating point. Operating the plant at a constrained optimal point will often cause constraint violations due to uncertainties such as disturbances and measurement errors, etc. To ensure dynamic feasibility, the concept of economic back-off is used. In this work, we select the set point as the economic back-off point such that the dynamic operating region should have the least variability in the active constrained variables while ensuring the feasibility of other variables. In other words, the dynamic operating region is oriented by the proper design of a controller such that variability in active constrained variables is as low as possible. This controller design can be transformed into equivalent objective function weights of the MPC controller. In this study, we demonstrate that the determined back-off point is optimal for both linear controller and MPC controller when there are no unconstrained degrees of freedom. For the case with unconstrained degrees of freedom, the back-off point determined using the presented approach is optimal only for a linear controller but suboptimal for an MPC controller. Demonstrative case studies are presented to illustrate the economic performance of the MPC controller at the determined economic back-off point.

本文探讨了模型预测控制(MPC)在背离运行点运行时的经济性能。由于干扰和测量误差等不确定因素,在受约束的最佳点运行工厂往往会导致违反约束。为了确保动态可行性,我们采用了经济退让的概念。在这项工作中,我们选择设定点作为经济退让点,使动态运行区域在确保其他变量可行性的同时,主动受限变量的变异性最小。换句话说,动态运行区域是通过适当设计控制器来确定的,从而使有源约束变量的变化尽可能小。这种控制器设计可以转化为 MPC 控制器的等效目标函数权重。在本研究中,我们证明了当不存在无约束自由度时,线性控制器和 MPC 控制器所确定的后关点都是最佳的。而在自由度不受约束的情况下,使用本文提出的方法确定的后关点仅对线性控制器而言是最优的,但对 MPC 控制器而言则是次优的。演示案例研究说明了 MPC 控制器在确定的经济后关点上的经济性能。
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引用次数: 0
Time delay and model parameter estimation for nonlinear system with simultaneous approach 用同步方法估计非线性系统的时延和模型参数
IF 4.2 2区 计算机科学 Q1 Mathematics Pub Date : 2024-05-15 DOI: 10.1016/j.jprocont.2024.103234
Benyi Liu, Weifeng Chen

Time delay is a ubiquitous phenomenon in chemical engineering. In the development of a practical rigorous model for process system, the influence of time delay cannot be ignored. A simultaneous approach for estimating time delays and model parameters is proposed in this work. The critical issue is how to address the approximation for state variable with time delay, which depends on the quotient and remainder obtained by dividing time delay by length of finite element. The strategies for handling the unknown quotient and remainder are designed. Finally, two case studies are considered. The effectiveness of the proposed approach is verified. Moreover, the proposed approach exhibits better performance compared with the gradient-based sequential approach.

时间延迟是化学工程中无处不在的现象。在为工艺系统开发实用的严格模型时,时间延迟的影响不容忽视。本研究提出了一种同时估算时间延迟和模型参数的方法。关键问题是如何处理带有时间延迟的状态变量的近似值,该近似值取决于时间延迟除以有限元长度得到的商和余数。本文设计了处理未知商和余数的策略。最后,考虑了两个案例研究。验证了所提方法的有效性。此外,与基于梯度的顺序方法相比,建议的方法表现出更好的性能。
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引用次数: 0
Data-driven economic MPC with asymptotic stability and strong duality verification using Hankel matrix 利用 Hankel 矩阵实现具有渐近稳定性和强对偶性验证的数据驱动型经济 MPC
IF 4.2 2区 计算机科学 Q1 Mathematics Pub Date : 2024-05-11 DOI: 10.1016/j.jprocont.2024.103230
Fatemeh Ostovar , Leonhard Urbas , Ali Akbar Safavi

We consider the problem of dynamic regulation with an economic cost function to control unknown linear systems, in which improving the economic performance and guaranteeing the stability of economical optimal equilibrium point are control objectives. A data-driven economic MPC scheme is presented using measured input-output trajectories without a prior system identification step. Our method uses Hankel matrices which include one input-output data trajectory for prediction in economic MPC, while persistently exciting of the input generating the data is needed. One of the novelties of the presented framework is directly verifying the strong duality property from input-output trajectory with the general cost function, considered as the supply rate. This is used to find a Lyapunov function for data-driven economic MPC. Under the strong duality assumption, asymptotic stability of the economical optimal equilibrium point for the closed-loop system with terminal equality constraint is guaranteed. The proposed data-driven economic MPC approach needs only persistently exciting data trajectory along with an upper bound on the system order and need no model description and no online parameter estimation. The proposed scheme applicability compared to the existing model-based economic MPC and data-driven MPC is illustrated for continuous stirred tank reactor (CSTR) and a numerical example and the robustness of the proposed scheme is evaluated in the case of measurement noise, as well as nonlinear model for CSTR system.

我们考虑了用经济成本函数控制未知线性系统的动态调节问题,其中提高经济性能和保证经济最优平衡点的稳定性是控制目标。我们提出了一种数据驱动的经济 MPC 方案,该方案使用测量的输入输出轨迹,无需事先进行系统识别步骤。我们的方法使用 Hankel 矩阵,其中包括一个用于经济 MPC 预测的输入输出数据轨迹,同时需要持续激发产生数据的输入。本框架的新颖之处在于直接验证了输入-输出轨迹与一般成本函数(被视为供应率)之间的强对偶性。这可用于找到数据驱动经济 MPC 的 Lyapunov 函数。在强对偶性假设下,保证了具有终端相等约束的闭环系统经济最优平衡点的渐近稳定性。所提出的数据驱动经济 MPC 方法只需要持续激励的数据轨迹和系统阶次上限,无需模型描述和在线参数估计。以连续搅拌罐反应器(CSTR)为例,说明了与现有的基于模型的经济 MPC 和数据驱动 MPC 相比,所提方案的适用性,并以 CSTR 系统的非线性模型和测量噪声为例,评估了所提方案的鲁棒性。
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引用次数: 0
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