Data-driven Predictive Control Research Articles

Robust data-driven predictive control for unknown linear time-invariant systems

This paper presents a new robust data-driven predictive control scheme for unknown linear time-invariant systems by using input-state-output or input–output data based on whether the state is measurable. To remove the need for the persistently exciting (PE) condition of a sufficiently high order on pre-collected data, a set containing all systems capable of generating such data is constructed. Then, at each time step, an upper bound on a given objective function is derived for all systems in the set, and a feedback controller is designed to minimize this bound. The optimal control gain at each time step is determined by solving a set of linear matrix inequalities. We prove that if the synthesis problem is feasible at the initial time step, it remains feasible for all future time steps. Unlike current data-driven predictive control schemes based on behavioral system theory, our approach requires less stringent conditions for the pre-collected data, facilitating easier implementation. The effectiveness of our proposed methods is demonstrated through application to an unknown and unstable batch reactor.

Data-Driven Distributed Predictive Control for Voltage Regulation and Current Sharing in DC Microgrids With Communication Constraints.

The use of nonideal communication networks makes communication constraints become a topical issue in the research of dc microgrids. How to design a distributed secondary control scheme for voltage recovery and accurate current sharing in islanded dc microgrids subject to communication constraints is of interest in this article. In order to restore the bus voltage to the rated value, a nonlinear element is first introduced into the primary control layer. Then, the closed-loop system of primary control is modeled as a data-driven time-varying linear system. Based on the established model, considering communication constraints, a distributed secondary predictive control strategy is developed to achieve accurate current sharing. While actively compensating for network delays and packet losses, the proposed method renders mathematical physical models unnecessary for the traditional predictive control, and simultaneously completes the multitask in dc microgrids. Finally, several case studies are conducted on a hardware microgrid experimental platform, which not only verifies the effectiveness of the designed data-driven predictive control strategy but also tests microgrid properties such as the plug-and-play ability.

Decentralized optimal voltage control for wind farm with deep learning-based data-driven modeling

The random fluctuations of wind energy and external grid voltage disturbances can both lead to serious voltage fluctuations and voltage deviations in the wind farm (WF). Voltage/reactive power control is an effective way to improve the voltage stability of WF. The existing research is based on complex physical models with prior parameter information, and the accuracy and calculation speed of the WF model are difficult to guarantee. To address this issue, this paper explores a decentralized optimal voltage control method for WF with deep learning-based (DL) data-driven modeling (DL-DOVC). A hybrid convolutional neural network (CNN)-Transformer architecture is proposed to establish the data-driven model of WF, leveraging its enhanced capabilities for extracting time series correlation, to learn complex patterns and dynamics from time series data. Then, we develop a fully decentralized voltage control method for WF to regulate the terminal bus voltage of wind turbines (WTs) within a feasible range. A DL-based data-driven predictive controller is specially designed to solve the established data-driven voltage optimization problem, it eliminates the necessity for frequent manual model maintenance and is suitable for real-time application. Additionally, the difficulty of WF decentralized optimal voltage control arises from the inability of local controllers to fully consider the impact of all non-local WTs on the local WT states. By designing the DL-based auxiliary state-feedback controller, the effects of non-local WTs are implicitly considered in the auxiliary feedback control law. A WF with 32*6.25 MW WTs is used to test the proposed DL-DOVC method. Simulation results show that the proposed DL-based model can efficiently learn and predict the WF dynamics under different operating scenarios. The near-global optimal voltage control performance is achieved only with local measurements by employing the DL-DOVC method.

An improved data-driven predictive optimal control approach for designing hybrid electric vehicle energy management strategies

This paper proposes an improved “prediction + optimal control” method for energy management in hybrid electric vehicles equipped with planetary gears. A differentiable predictor and a differentiable optimal controller are developed using supervised learning and reinforcement learning approaches, respectively. Three training steps are performed for the initial predictor, the optimal controller, and the final predictor. This method improves the traditional energy management predictive optimal control approach by incorporating an additional step of retraining the differentiable predictor. This adjustment ensures that the predictor does not blindly improve its performance based on evaluation criterion irrelevant to energy management, which was commonly used in previous studies. Instead, it focuses on enhancing the overall performance of energy management under the “prediction + optimal control” framework. The approach introduced in this paper is compared with the globally optimal dynamic programming results and traditional predictive optimal control methods on the Next Generation Simulation (NGSIM) data. Our method outperforms traditional approaches in energy management on both the training dataset and the test dataset. This further illustrates that the conventional practice of presumptuously optimizing predictors in “prediction + optimal control” methods can be improved using the proposed method.

Data-Driven Predictive Control Strategy to Improve Robust Performance for Three-Level Inverters With Reduced Common-Mode Voltage

Data-Driven Predictive Control Strategy to Improve Robust Performance for Three-Level Inverters With Reduced Common-Mode Voltage

Long-term experimental evaluation and comparison of advanced controls for HVAC systems

The tremendous energy usage from buildings leads to research studies on their improvement, among which advanced building control plays an important role. In advanced building controls, data-driven predictive control (DDPC), differentiable predictive control (DPC), and reinforcement learning (RL) have shown advantages, but their comparison often lacks in existing studies. The simulation-based prior comparison studies have inconsistent results due to different assumptions and simplifications. Therefore, to comprehensively compare the three advanced strategies for real-time building HVAC controls, we implemented DDPC, specifically, hierarchical DDPC (HDDPC), DPC, and RL in a real building testbed for more than 5 months. The results show that all three advanced controls maintained the indoor environmental quality (IEQ) cost-effectively. Overall, HDDPC outperformed the baseline control with more than 50% energy savings, followed by RL with 48%, and DPC with 30.6%. Most control failures were related to API communication issues. Besides, the information gaps between room and system level controllers and non-optimal control decisions will degrade HDDPC's performance. Such degradation did not happen in DPC and RL, which led to better performance of agent-based control over HDDPC. Moreover, HDDPC needs minutes to make control decisions whereas DPC and RL need milliseconds, indicating higher online computing resources required by HDDPC. For agent training, DPC is faster than RL, as DPC training needs minutes and RL needs hours, but its performance is not as good as RL. This study provides a comprehensive understanding and assessment of the pros and cons of advanced building controls and sheds light on future research on building controls.

Impact of practical challenges on the implementation of data-driven services for building operation: Insights from a real-life case study

Data-driven applications in buildings using AI and machine learning have generated a lot of interest, but scaling these applications is challenging due to the uniqueness of each building. During the process of implementing a data-driven predictive heating control in a full-scale real-life office building in Norway, 24 practical challenges were encountered. In this work, those practical challenges are presented, discussed and attributed to four main categories: i) physical limitations, ii) data acquisition and communication, iii) data and model definition and iv) building occupants. Detailed examples for the challenges are provided and more than 15 lessons-learned with regards to developing and implementing data-driven services for building operation are presented. Furthermore, this work discusses how the practical challenges impact the choice of a data-driven approach to control the operation of an office building heating system in a predictive manner and how the practical challenges influence the creation of variation in the measurement data needed to identify a model during normal building operation. Finally, it is shown that a substantial number of practical challenges that were encountered during the operational phase are rooted in the design and construction phase of a building project or from rehabilitation during the operational phase. This highlights the fact that the possible use of data-driven services for building operation should be considered during the tendering and design phase to minimize the number of challenges regarding the widespread implementation of data-driven services for building operation, especially regarding predictive control.

Distributed Data-Driven Predictive Control via Dissipative Behavior Synthesis

Distributed Data-Driven Predictive Control via Dissipative Behavior Synthesis

Efficient data-driven event-triggered predictive control for cyber-physical systems

As a multi-dimensional complex system that integrates computing, network, and physical environments, cyber-physical system (CPS) involves a large amount of system data in its real-time control process. The efficiency of data processing and transmission in CPS plays an important role in its control performance, however, few results have addressed such problems. This paper proposes a novel data-driven event-trigger mechanism to alleviate the data processing and transmission load for the data-driven predictive control method in CPS. The design of the event-triggered law can be transformed into solving a linear matrix inequality (LMI) based on the measured system data, while ensuring the stability of the integrated system. The improved performances are illustrated by the explicit simulation results, which indicates its potential application in CPS.

Dynamic-Linearization-Based Predictive Control of a Voltage-Source Inverter

In pursuit of accurate and fast trajectory tracking of power converters, an explicit model is commonly used in the finite control-set model predictive control (FCS-MPC) framework to predict precise behaviors of controlled variables. In reality, however, the model mismatch is inevitable, which causes the inherent challenges of parameter sensitivity and model uncertainties of the FCS-MPC method. This article proposes a dynamic-linearization-based predictive control architecture to circumvent such model dependence while keeping the attractive features of the conventional FCS-MPC method. By integrating the data-driven feature of the dynamic-linearization approach, the detailed model used in the FCS-MPC controller is replaced by a virtual equivalent data model, creating a data-driven predictive control architecture. The suggested method selects optimal control action solely based on the input-output data, exhibiting strong rejection against parameter variations whilst inheriting the distinctive property of the conventional FCS-MPC method. Finally, the proposed design is validated through comparative simulation and experimental results on a three-level neutral-point-clamped inverter.

Implementation and Experimental Validation of Data-Driven Predictive Control for Dissipating Stop-and-Go Waves in Mixed Traffic

Implementation and Experimental Validation of Data-Driven Predictive Control for Dissipating Stop-and-Go Waves in Mixed Traffic

Workflow-Based Fast Data-Driven Predictive Control With Disturbance Observer in Cloud-Edge Collaborative Architecture

Data-driven predictive control (DPC) has been studied and applied in various scenarios. However, the challenge of computational efficiency remains. With the development of cloud computing, it provides potential solutions to the computational problem. Hence, this paper proposes a workflow-based fast DPC method in cloud-edge collaborative architecture. First, a workflow construction method of DPC is designed to make full use of the distributed computing ability of cloud computing. Next, to tackle the uncertainty in the cloud workflow processing, we design a cloud-edge collaborative scheme. In this scheme, a edge data-driven disturbance observer is proposed to estimate and compensate the uncertain event with guaranteed UUB stability. Then, An autonomous cloud control experimental system based on container technology is designed and implemented to execute the workflow-based DPC controller. Evaluations demonstrate that computation times are reduced by 45.19 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\%$</tex-math> </inline-formula> and 74.35 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\%$</tex-math> </inline-formula> for two real-time control examples, and by a maximum of 85.10 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\%$</tex-math> </inline-formula> for a high-dimensional control example. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —This work is motivated by the challenge of the further combination of cloud computing and control system such as DPC. In the existing cloud-based control system, the computation mission of native control algorithm is deployed in a single cloud server directly. However, the structure of cloud environment is distributed, and the existing computation mode could not make full use of the parallel computing of cloud computing. Thus, the computation time could not be reduced significantly, and would still have serious effects on the control quality. In this work, a novel workflow-based DPC system in cloud-edge collaborative architecture is proposed, which decompose the native control mission into distributed cloud workflow with multiple smaller computation tasks. Then, an edge disturbance observer is designed to compensate the uncertainty occurring in the cloud workflow processing. As the evaluations show, the proposed workflow-based control system in cloud-edge collaborative architecture could be applied in the control mission with real-time requirement and the high-dimension control mission with intensive data.

Frequency-Domain Data-Driven Predictive Control

In this paper, we propose a data-driven predictive control scheme based on measured frequency-domain data of the plant. This novel scheme complements the well-known data-driven predictive control (DeePC) approach based on time series data. To develop this new frequency-domain data-driven predictive control (FreePC) scheme, we introduce a novel version of Willems’ fundamental lemma based on frequency-domain data. By exploiting frequency-domain data, we allow recent direct data-driven (predictive) control methodologies to benefit from the available expertise and techniques for non-parametric frequency-domain identification in academia and industry. We prove that, under appropriate conditions, the new FreePC scheme is equivalent to the corresponding DeePC scheme. The strengths of FreePC are demonstrated in a numerical case study.

Data-Driven Predictive Control and MPC: Do we achieve optimality?

In this paper, we explore the interplay between Predictive Control and closed-loop optimality, spanning from Model Predictive Control to Data-Driven Predictive Control. Predictive Control in general relies on some form of prediction scheme on the real system trajectories. However, these predictions may not accurately capture the real system dynamics, for e.g., due to stochasticity, resulting in sub-optimal control policies. This lack of optimality is a critical issue in case of problems with economic objectives. We address this by providing sufficient conditions on the underlying prediction scheme such that a Predictive Controller can achieve closed-loop optimality. However, these conditions do not readily extend to Data-Driven Predictive Control. In this context of closed-loop optimality, we conclude that the factor distinguishing the approaches within Data-Driven Predictive Control is if they can be cast as a sequential decision-making process or not, rather than the dichotomy of model-based vs. model-free. Furthermore, we show that the conventional approach of improving the prediction accuracy from data may not guarantee optimality.

Stochastic Data-Driven Predictive Control: Regularization, Estimation, and Constraint Tightening

Data-driven predictive control methods based on the Willems’ fundamental lemma have shown great success in recent years. These approaches use receding horizon predictive control with nonparametric data-driven predictors instead of model-based predictors. This study addresses three problems of applying such algorithms under unbounded stochastic uncertainties: 1) tuning-free regularizer design, 2) initial condition estimation, and 3) reliable constraint satisfaction, by using stochastic prediction error quantification. The regularizer is designed by leveraging the expected output cost. An initial condition estimator is proposed by filtering the measurements with the one-step-ahead stochastic data-driven prediction. A novel constraint-tightening method, using second-order cone constraints, is presented to ensure high-probability chance constraint satisfaction. Numerical results demonstrate that the proposed methods lead to satisfactory control performance in terms of both control cost and constraint satisfaction, with significantly improved initial condition estimation.

Data-driven Predictive Control for a Class of Nonlinear Systems with Polynomial Terms

This article proposes a non-parametric representation for a class of high-order unknown nonlinear systems comprising polynomial functions. A data-driven approach is introduced that uses pure data for future simulation based on any given input set. We also consider a comprehensive class of nonlinear autoregressive exogenous (NARX) models which covers other existing representations as special cases. Then, a non-parametric representation of this class of NARX models are investigated by leveraging the idea of re-expressing the system in the context of a non-minimal state-space reformulation. A data-driven predictive control (DDPC) approach is as a result introduced that uses the fundamental lemma for future prediction during the open-loop optimization. The recursive feasibility analysis and the proof of stability are also given. Finally, the simulation results quantify the effectiveness of the proposed approach in different scenarios.

Computationally Tractable Gaussian Process-based Stochastic Predictive Control Using Backoffs

Current stochastic nonlinear model predictive control (SNMPC) hinges on the lack of high-fidelity models that describe the system behavior and the lack of tractable solution methods that handle chance constraints. Motivated by this, a model-and data-driven predictive control approach using Gaussian processes (GP-MDPC) is synthesized in this paper. It exploits GPs to learn the unknown dynamics and apply Taylor expansion for uncertainty propagation through probabilistic modeling. A backoff approximation method is explored to reformulate the chance constraints into tractable expressions. Finally, a finite-horizon stochastic optimal control problem (FH-SOCP) is formulated.

On the Equivalence of Direct and Indirect Data-Driven Predictive Control Approaches

On the Equivalence of Direct and Indirect Data-Driven Predictive Control Approaches

A Time-Delay Modeling Approach for Data-Driven Predictive Control of Continuous-Time Systems

A Time-Delay Modeling Approach for Data-Driven Predictive Control of Continuous-Time Systems

Fast and memory-efficient optimization for large-scale data-driven predictive control

Recently, data-enabled predictive control (DeePC) schemes based on Willems’ fundamental lemma have attracted considerable attention. At the core are computations using Hankel-like matrices and their connection to the concept of persistency of excitation. We propose an iterative solver for the underlying data-driven optimal control problems resulting from linear discrete-time systems. To this end, we apply factorizations based on the discrete Fourier transform of the Hankel-like matrices, which enable fast and memory-efficient computations. To take advantage of this factorization in an optimal control solver and to reduce the effect of inherent bad conditioning of the Hankel-like matrices, we propose an augmented Lagrangian BFGS-method. We illustrate the performance of our method by means of a numerical study.