Data-driven Model Predictive Control Research Articles

An Overview of Systems-Theoretic Guarantees in Data-Driven Model Predictive Control

The development of control methods based on data has seen a surge of interest in recent years. When applying data-driven controllers in real-world applications, providing theoretical guarantees for the closed-loop system is of crucial importance to ensure reliable operation. In this review, we provide an overview of data-driven model predictive control (MPC) methods for controlling unknown systems with guarantees on systems-theoretic properties such as stability, robustness, and constraint satisfaction. The considered approaches rely on the fundamental lemma from behavioral theory in order to predict input–output trajectories directly from data. We cover various setups, ranging from linear systems and noise-free data to more realistic formulations with noise and nonlinearities, and we provide an overview of different techniques to ensure guarantees for the closed-loop system. Moreover, we discuss avenues for future research that may further improve the theoretical understanding and practical applicability of data-driven MPC.

A robust data-driven model predictive thermal control for rack-based data center

Optimizing and controlling of air-cooled data centers cooling systems are essential for reducing energy consumption. However, traditional cooling system control strategies have been proven inadequate due to the thermodynamic processess complexity and the challenge for accuratly modeling the thermal behavior of data center (DC). Therefore, a data-driven control method whithout explicit modeling process is urgently needed. In this paper, a robust data-driven model predictive control (MPC) method for air-cooled rack-based DCs, based on Willems fundamental lemma, is proposed. The methodology is executed in three phases: Firstly, we show that the system is approximately linear time-invariant (LTI) by zonal model method and experiment. Secondly, we propose a data-driven MPC framework for air-cooled rack-based DC. Thirdly, considering the uncertainties caused by disturbances and the nonlinear dynamics, the data-driven MPC approach is tailored as a robust one. Finally, the proposed approach is verified by computational fluid dynamics simulation experiments. This approach ensures the rack-based DC cold aisle temperature to the reference temperature as well as within acceptable limits. The experiment shows that the steady-state error is guaranteed to be less than 2%, with a control accuracy increased by 2.4% compared with the regular MPC. Thus, this method provides an alternative solution for maintaining the reference temperature in air-cooled rack-based DCs by utilizing only input–output data.

Data-Driven Model Predictive Control for Redundant Manipulators With Unknown Model.

The tracking control of redundant manipulators plays a crucial role in robotics research and generally requires accurate knowledge of models of redundant manipulators. When the model information of a redundant manipulator is unknown, the trajectory-tracking control with model-based methods may fail to complete a given task. To this end, this article proposes a data-driven neural dynamics-based model predictive control (NDMPC) algorithm, which consists of a model predictive control (MPC) scheme, a neural dynamics (ND) solver, and a discrete-time Jacobian matrix (DTJM) updating law. With the help of the DTJM updating law, the future output of the model-unknown redundant manipulator is predicted, and the MPC scheme for trajectory tracking is constructed. The ND solver is designed to solve the MPC scheme to generate control input driving the redundant manipulator. The convergence of the proposed data-driven NDMPC algorithm is proven via theoretical analyses, and its feasibility and superiority are demonstrated via simulations and experiments on a redundant manipulator. Under the drive of the proposed algorithm, the redundant manipulator successfully carries out the trajectory-tracking task without the need for its kinematics model.

Data-driven system identification and model predictive control of pneumatic conveying using nonlinear dynamics analysis for optimised energy consumption

Pneumatic conveying systems provide secure transportation of particulate material and a dust-free environment. These systems face high energy consumption, material degradation, and pipeline blockages. This research presents an innovative solution by integrating nonlinear dynamics analysis of electrostatic sensor data, including chaos and recurrence quantification analysis, sparse identification of nonlinear dynamics with control (SINDYc) and model predictive control (MPC). The Lyapunov exponent, approximate entropy and recurrence rate of electrostatic sensor data reveal the chaotic nature of gas-solid flows. MPC framework was tailored for real-time optimisation of a pneumatic conveying system. SINDYc system models were developed using data collected from an open-loop control pneumatic conveying process to conduct MPC simulations and select an appropriate model for real-time control. This research illustrates the potential of integrating nonlinear dynamics analysis, SINDYc integrated and MPC for enhanced system performance, showcased a significant reduction in energy consumption without compromising the system's efficiency or reliability.

Data-Driven Model Predictive Control for Hybrid Charging Stations Using Ensemble Learning

Data-Driven Model Predictive Control for Hybrid Charging Stations Using Ensemble Learning

A Data-Driven Predictive Control Method for Modeling Doubly-Fed Variable-Speed Pumped Storage Units

In this study, a data-driven model predictive control (MPC) method is proposed for the optimal control of a doubly-fed variable-speed pumped storage unit. This method combines modern control theory with the dynamic characteristics of the pumped storage unit to establish an accurate dynamic model based on actual operating data. In each control cycle, the MPC uses the system model to predict future system behavior and determines the optimal control input sequence by solving the constrained optimization problem, thereby effectively dealing with the nonlinearity, time-varying characteristics, and multivariable coupling problems of the system. When compared with a traditional PID control, this method significantly improves control accuracy, response speed, and system stability. The simulation results show that the proposed MPC method exhibits better steady-state error, overshoot, adjustment time, and control energy under various operating conditions, demonstrating its advantages in complex multivariable systems. This study provides an innovative solution for the efficient control of doubly-fed variable-speed pumped storage units and lays a solid foundation for the efficient utilization of new energy sources.

Data-Driven Nonlinear Model Predictive Control for Power Sharing of Inverter-Based Resources

Data-Driven Nonlinear Model Predictive Control for Power Sharing of Inverter-Based Resources

Frequency regulation feasible region assessment and optimization of wind farm based on data-driven model predictive control

With the integration of large-scale wind turbines (WTs) into grids via electronic interfaces, power system operators have necessitated frequency support from wind farms. Due to the large number of WTs and their complex dynamic characteristics, it is necessary to assess the primary frequency regulation (PFR) capability and construct feasible region of wind farms. In order to cope with the problems of incomplete parameters, analytical solving complexity and the coupling influence of power system regulation characteristics, this paper develops a data-driven state space mapping linear model predictive control (MPC) to assess the maximum PFR capability of wind farms and reasonably distribute coefficients to WTs. Besides, a coordinated iteration framework between dispatching center and wind farms is proposed to further optimize the wind farm regulation feasible region. The simulation results verify that the proposed method has the advantages of independence from physical parameters, fast analytical solution, and lower requirements of training samples on limited scenarios.

SINDy-Based Feature Extraction for Data Driven Model Predictive Control of a Buck Boost Switch Mode Power Supply

Abstract This paper presents two methods of creating model predictive control strategies for efficient real-time control algorithms for power electronics. Two novel methods of performing nonlinear modeling are presented in this research, the first being novel Takagi-Sugeno model, which combines two linear state space models using a membership function to model the nonlinear transitions between operating points. The second method involves using sparse identification of nonlinear dynamics, a nonlinear modeling technique that uses L1 regularization of least squares on for time series data to define a parsimonious polynomial function set. This set is used to define the input feature space to extended dynamic mode decomposition with control. These models are then used for data-driven model predictive control of a buck switch mode power supply to find the optimal duty cycle that regulates the output voltage over a finite receding horizon and validated using an LTSPICE simulation to assess their effectiveness in comparison to a tuned proportional integral derivative controller. Numerical accuracy challenges are discussed, and strategies are offered for their mitigation.

A Data-Driven Approach to Set-Theoretic Model Predictive Control for Nonlinear Systems

In this paper, we present a data-driven model predictive control (DDMPC) framework specifically designed for constrained single-input single-output (SISO) nonlinear systems. Our approach involves customizing a set-theoretic receding horizon controller within a data-driven context. To achieve this, we translate model-based conditions into data series of available input and output signals. This translation process leverages recent advances in data-driven control theory, enabling the controller to operate effectively without relying on explicit system models. The proposed framework incorporates a robust methodology for managing system constraints, ensuring that the control actions remain within predefined bounds. By means of time sequences, the controller learns the underlying system dynamics and adapts to changes in real time, providing enhanced performance and reliability. The integration of set-theoretic methods allows for the systematic handling of uncertainties and disturbances, which are common when the trajectory of a nonlinear system is embedded inside a linear trajectory state tube. To validate the effectiveness of our DDMPC framework, we conduct extensive simulations on a nonlinear DC motor system. The results demonstrate significant improvements in control performance, highlighting the robustness and adaptability of our approach compared to traditional model-based MPC techniques.

Minimizing total annualized cost per tonne of feed processed of a semicontinuous distillation process utilizing data-driven model predictive control

Semicontinuous distillation is a separation technique used to purify multicomponent mixtures with low to medium throughput. This research addresses the problem of designing a Data-driven Model Predictive Control (MPC) approach that enables minimizing the Total Annualized Cost (TAC) of the semicontinuous process per tonne of feed processed while maintaining the required product purity. In lieu of typically unavailable first principles models, the manuscript demonstrates the implementation of data-driven technique using data collected from an Aspen Plus Dynamics simulation as a test bed. A subspace model identification technique is adapted to develop a multi-model framework to capture the dynamic behavior of the process and then utilized within a Shrinking Horizon MPC (SHMPC) scheme, to achieve the required objective. The simulation results demonstrate a lowering of the TAC/tonne of feed by 11.4% compared to the traditional PI setup used in the previous studies.

Data-driven Koopman model predictive control for hybrid energy storage system of electric vehicles under vehicle-following scenarios

In the current studies on energy management strategy (EMS) for vehicle-following scenarios, the accuracy of vehicle state predictions based on mechanistic models is influenced by the time-varying conditions, affecting the optimization control performance. To address this issue, a data-driven Koopman model predictive control for hybrid energy storage system (HESS) of electric vehicles (EVs) in vehicle-following scenarios is proposed, combining the safety speed planning and energy management strategy. Firstly, a data-driven Koopman vehicle state prediction model is constructed in the upper layer for estimating parameters, such as road surface smoothness and slope. This model is then integrated into Model Predictive Control (MPC) to optimize the speed of the following vehicle. Subsequently, in the lower layer, utilizing the output from the upper layer and predicting load power, the load power is further allocated within the HESS. Simulation results demonstrate that in scenarios considering factors like slope, the hierarchical MPC with the Koopman model reduces energy consumption by 5.55% compared to the hierarchical MPC with mechanistic model.

Energy flexibility quantification of a tropical net-zero office building using physically consistent neural network-based model predictive control

Building energy flexibility plays a critical role in demand-side management for reducing utility costs for building owners and sustainable, reliable, and smart grids. Realizing building energy flexibility in tropical regions requires solar photovoltaics and energy storage systems. However, quantifying the energy flexibility of buildings utilizing such technologies in tropical regions has yet to be explored, and a robust control sequence is needed for this scenario. Hence, this work presents a case study to evaluate the building energy flexibility controls and operations of a net-zero energy office building in Singapore. The case study utilizes a data-driven energy flexibility quantification workflow and employs a novel data-driven model predictive control (MPC) framework based on the physically consistent neural network (PCNN) model to optimize the building energy flexibility. To the best of our knowledge, this is the first instance that PCNN is applied to a mathematical MPC setting, and the stability of the system is formally proved. Three scenarios are evaluated and compared: the default regulated flat tariff, a real-time pricing mechanism, and an on-site battery energy storage system (BESS). Our findings indicate that incorporating real-time pricing into the MPC framework could be more beneficial to leverage building energy flexibility for control decisions than the flat-rate approach. Moreover, adding BESS to the on-site PV generation improved the building self-sufficiency and the PV self-consumption by 17% and 20%, respectively. This integration also addresses model mismatch issues within the MPC framework, thus ensuring a more reliable local energy supply. Future research can leverage the proposed PCNN-MPC framework for different data-driven energy flexibility quantification types.

Real-life data-driven model predictive control for building energy systems comparing different machine learning models

By considering forecasts and exploiting storage effects, model predictive control can achieve significant energy and cost savings in the building sector. However, due to the high individual modeling effort, model predictive control lacks practical applicability. For that reason, data-driven process models, approximating the system behavior based on measurements, have become increasingly popular in recent years. Still, scientific literature lacks consent about the most promising model types and efficient workflows to integrate different machine learning models into a model predictive controller. With this work, we present a workflow to provide efficient model predictive controllers based on measurement data automatically. The main idea is to translate different machine learning models into optimization syntax to enable efficient optimization with full access to gradients. We currently consider artificial neural networks, gaussian process regression, and simple linear regression process models. We use a generic model ontology to automatize the controller generation further and test the methodology on two real-life use cases. The first use case is the application of five office rooms with smart thermostat valves. The second use case is a test hall with an air handling unit and a concrete core activation. Using only two days of initial training data, we deploy controllers based on the different model types for six weeks in the offices and apply online learning to improve the models continuously. We observe only minor differences in controller performance despite the artificial neural networks showing the highest prediction accuracy. The second use case shows that the simple linear models require less controller tuning effort. Thus, for practical applications, we recommend linear regression models.

Stability Margin of Data-Driven LQR and Its Application to Consensus Problem

In contrast with traditional control input design techniques based on mathematical models of the system, in data-driven control approaches, which have recently gained substantial attention, the controller is derived directly from the data that are collected from experiments or observations of the target system. In particular, several data-driven optimal control and model predictive control (MPC) techniques have been proposed. In this paper, it is shown that the recently proposed data-driven LQR (Linear Quadratic Regulator) has a stability margin that is the set of the uncertainties in the control input channels maintaining the closed-loop stability. As an application of the proposed stability margin of the data-driven LQR, the consensus problem is considered. Since the control design for the consensus of multi-agent systems can be reformulated into the robust stabilization of a linear system with uncertainty in the input channel, it is demonstrated that the derived stability margin can be used to design a controller for the consensus of multi-agent systems.

Identification for control approach to data-driven model predictive control

Identification for control approach to data-driven model predictive control

Identification for Control Approach to Data-Driven Model Predictive Control

Identification for Control Approach to Data-Driven Model Predictive Control

Data-Driven Model Predictive Control for Uncalibrated Visual Servoing

This paper addresses the image-based visual servoing (IBVS) control problem with an uncalibrated camera, unknown dynamics, and constraints. A novel data-driven uncalibrated IBVS (UIBVS) strategy is proposed, incorporated with the Koopman-based model predictive control (KMPC) algorithm and the adaptive robust Kalman filter (ARKF). First, to alleviate the need for calibration of the camera’s intrinsic and extrinsic parameters, the ARKF with an adaptive factor is utilized to estimate the image Jacobian matrix online, thereby eliminating the laborious camera calibration procedures and improving robustness against camera disturbances. Then, a data-driven MPC strategy is proposed, wherein the unknown nonlinear dynamic model is learned using the Koopman operator theory, resulting in a linear Koopman prediction model. Only input–output data are used to construct the prediction model, and hence, the proposed approach is robust against model uncertainties. Furthermore, with a symmetric quadratic cost function, the proposed approach solves the quadratic programming problem online, and visibility constraints as well as joint torque constraints are taken into account. As a result, the proposed KMPC scheme can be implemented in real time, and the UIBVS performance degradation which arises from the control torque constraints can be avoided. Simulations and comparisons for a 2-DOF robotic manipulator demonstrate the feasibility of the proposed approach. Simulation results further validate that the computation time of the proposed approach is comparable to the one of kinematic-based methods.

Quantitative comparison of reinforcement learning and data-driven model predictive control for chemical and biological processes

As manufacturing processes transition towards digitalization, data-driven process control is emerging as a key area of interest in future artificial intelligence technology. A crucial aspect in implementing data-driven process control is “What should we learn from the data?”. In general, the data-driven control method can be categorized into two main approaches: Learning the model and learning the value. To assist in selecting the more suitable approach, this paper applies six different control methods, with three falling under each approach, to three distinct manufacturing process systems. The simulation results indicate that the model-learning approaches display higher data efficiency and exhibit lower variance in total cost. These methods prove to be particularly advantageous for addressing the regulation problems. Conversely, value-learning approaches show competitive potential in closed-loop identification and in managing economic cost problems. The remaining challenges associated with each technique are discussed, along with practical considerations for their implementation.

Data-Driven Self-Triggered Control via Trajectory Prediction

Self-triggered control, a well-documented technique for reducing the communication overhead while ensuring desired system performance, is gaining increasing popularity. However, a majority of existing self-triggered control methods require explicit system models. An end-to-end control paradigm known as data-driven control designs control laws directly from data and offers a competing alternative to the routine system identification-then-control strategy. In this context, the present paper puts forth data-driven self-triggered control schemes for unknown linear systems using input-output data collected offline. Specifically, a data-driven model predictive control (MPC) scheme is proposed, which computes a sequence of control inputs while generating a predicted system trajectory. In addition, a data-driven self-triggering mechanism is designed, which determines the next triggering time using the solution of the data-driven MPC and the newly collected measurements. Finally, both feasibility and stability are established for the proposed self-triggered controller, which are validated using a numerical example.