Robust optimal control with adjustable uncertainty sets

Zhang, Xiaojing; Kamgarpour, Maryam; Georghiou, Angelos; Goulart, Paul J.; Lygeros, John

doi:10.1016/j.automatica.2016.09.016

Cited by 107 publications

(96 citation statements)

References 31 publications

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“…which is termed as generalized affine decision rule (GADF) based on lifted uncertainties [37], [38]. The GADF also allows for a compact expression:…”

Section: A Generalized Affine Disturbance Feedbackmentioning

confidence: 99%

Robust Model Predictive Control of Irrigation Systems With Active Uncertainty Learning and Data Analytics

Chen

Stroock

et al. 2020

IEEE Trans. Contr. Syst. Technol.

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We develop a novel data-driven robust model predictive control (DDRMPC) approach for automatic control of irrigation systems. The fundamental idea is to integrate both mechanistic models, which describe dynamics in soil moisture variations, and data-driven models, which characterize uncertainty in forecast errors of evapotranspiration and precipitation, into a holistic systems control framework. To better capture the support of uncertainty distribution, we take a new learningbased approach by constructing uncertainty sets from historical data. For evapotranspiration forecast error, the support vector clustering-based uncertainty set is adopted, which can be conveniently built from historical data. As for precipitation forecast errors, we analyze the dependence of their distribution on forecast values, and further design a tailored uncertainty set based on the properties of this type of uncertainty. In this way, the overall uncertainty distribution can be elaborately described, which finally contributes to rational and efficient control decisions. To assure the quality of data-driven uncertainty sets, a training-calibration scheme is used to provide theoretical performance guarantees. A generalized affine decision rule is adopted to obtain tractable approximations of optimal control problems, thereby ensuring the practicability of DDRMPC. Case studies using real data show that, DDRMPC can reliably maintain soil moisture above the safety level and avoid crop devastation. The proposed DDRMPC approach leads to a 40% reduction of total water consumption compared to the fine-tuned open-loop control strategy. In comparison with the carefully tuned rulebased control and certainty equivalent model predictive control, the proposed DDRMPC approach can significantly reduce the total water consumption and improve the control performance.

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“…which is termed as generalized affine decision rule (GADF) based on lifted uncertainties [37], [38]. The GADF also allows for a compact expression:…”

Section: A Generalized Affine Disturbance Feedbackmentioning

confidence: 99%

Robust Model Predictive Control of Irrigation Systems With Active Uncertainty Learning and Data Analytics

Chen

Stroock

et al. 2020

IEEE Trans. Contr. Syst. Technol.

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“…In this section we first review the finite-horizon robust optimal control problem with adjustable uncertainty sets from [7], before we introduce the concept of Robust Model Predictive Control with adjustable uncertainty sets. Also, A ⇒ B means that A implies B, i.e., if A is true then B must be true.…”

Section: Problem Formulationmentioning

confidence: 99%

“…Specifically, we extend the work of [7] to the infinite horizon case by employing ideas from standard Robust MPC. The resulting algorithm, called Robust MPC with Adjustable Uncertainty Sets (RMPC-AU), ensures satisfaction of state and input constraints for all future time steps, a notion known as persistent feasibility in the literature [11].…”

Section: Introductionmentioning

confidence: 99%

Robust Model Predictive Control with Adjustable Uncertainty Sets

Kim

Zhang

Guanetti

et al. 2018

2018 IEEE Conference on Decision and Control (CDC)

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In this paper, we present Robust Model Predictive Control (MPC) problems with adjustable uncertainty sets. In contrast to standard Robust MPC problems with known uncertainty sets, we treat the uncertainty sets in our problems as additional decision variables. In particular, given a metric for adjusting the uncertainty sets, we address the question of determining the optimal size and shape of those uncertainty sets, while ensuring robust constraint satisfaction. The focus of this paper is on ensuring constraint satisfaction over an infinite horizon, also known as persistent feasibility. We show that, similar as in standard Robust MPC, persistent feasibility can be guaranteed if the terminal set is an invariant set with respect to both the state of the system and the adjustable uncertainty set. We also present an algorithm for computing such invariant sets, and illustrate the effectiveness of our approach in a cooperative adaptive cruise control application.

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“…Several theoretical works have then proposed frameworks for computing the tracking capabil-ity of such systems. Several model-based methods using robust programming concepts have been proposed including [14], [15], [16], [17]. Other works have proposed analytical methods to analyze the aggregate flexibility of populations of loads in order to characterize it as an equivalent 'virtual battery' [4], [18], [19], [20].…”

Section: Introductionmentioning

confidence: 99%

Experimental demonstration of buildings providing frequency regulation services in the Swiss market

Gorecki

Fabietti

Jones

2017

Energy and Buildings

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This paper investigates the potential of commercial buildings to offer ancillary services to the grid. We consider a tracking procurement inspired by secondary frequency control, where the resource needs to commit to a nominal consumption profile ahead of time and then receives a power consumption deviation around this profile. We propose a model-based predictive scheme which formally assesses the amount of power flexibility that can be offered by the resource and of attaining the best trade-off between comfort and financial gain during real-time operation by adjusting the nominal power consumption with a delay, in accordance to the regulations of the Swiss energy market. Extensive simulation results highlight how the possibility to perform adjustments on the scheduled energy profile is of paramount importance for both maintaining comfortable operational conditions and offering larger tracking flexibility. Finally, the effectiveness and robustness of the proposed methodology are demonstrated by means of full-day experiments in an occupied office space.

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Robust optimal control with adjustable uncertainty sets

Cited by 107 publications

References 31 publications

Robust Model Predictive Control of Irrigation Systems With Active Uncertainty Learning and Data Analytics

Robust Model Predictive Control of Irrigation Systems With Active Uncertainty Learning and Data Analytics

Robust Model Predictive Control with Adjustable Uncertainty Sets

Experimental demonstration of buildings providing frequency regulation services in the Swiss market

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