Data-driven Model Predictive Control Research Articles

RHONN Modelling-Enabled Nonlinear Predictive Control for Lateral Dynamics Stabilization of an In-Wheel Motor Driven Vehicle

Featuring the fast response and flexibility in control allocation, an electric vehicle with in-wheel motors is a good platform for implementing advanced vehicle dynamics control. Among many active safety functions of an in-wheel motor driven vehicle (IMDV), lateral stability control is a key technology, which can be realized through torque vectoring. To further advance the lateral stabilization performance of the IMDV, in this article a novel data-driven nonlinear model predictive control (NMPC) is proposed based the recurrent high-order neural network (RHONN) modelling method. First, the new RHONN model is developed to represent vehicle’s nonlinear dynamic behaviors. Different from the conventional physics-based modelling method, the RHONN model forms high-order polynomials by neuron states to feature nonlinear dynamics. Based on the RHONN model, the steady-state responses of vehicle’s yaw rate and sideslip angle are iteratively optimized and set as the control objectives for low-level controller, aiming to improve the system robustness. Besides, a nonlinear model predictive controller is designed based on the RHONN, which is expected to improve the prediction accuracy during the receding horizon control. Further, a constrained optimization problem is formulated to derive the required yaw moment for vehicle lateral dynamics stabilization. Finally, the performance of the developed RHONN-based nonlinear MPC is validated on an IMDV in the CarSim/Simulink simulation environment. The validation results show that the developed approach outperforms the conventional method, and further improves the stable margin of the system. It is able to enhance the lateral stabilization performance of the IMDV under various driving scenarios, demonstrating the feasibility and effectiveness of the proposed approach.

Experimental data-driven model predictive control of a hospital HVAC system during regular use

Herein we report a multi-zone, heating, ventilation and air-conditioning (HVAC) control case study of an industrial plant responsible for cooling a hospital surgery center. The adopted approach to guaranteeing thermal comfort and reducing electrical energy consumption is based on a statistical non-parametric, non-linear regression technique named Gaussian processes. Our study aimed at assessing the suitability of the aforementioned technique to learning the building dynamics and yielding models for our model predictive control (MPC) scheme. Experimental results gathered while the building was under regular use showcase the final controller performance while subject to a number of measured and unmeasured disturbances. Finally, we provide readers with practical details and recommendations on how to manage the computational complexity of the on-line optimization problem and obtain high-quality solutions from solvers.

An improved data-driven based model predictive control for zero-sequence circulating current suppression in paralleled converters

To address the requirement of improved power capacity, reliability and operation, parallel converters have been widely applied in micro-grid. However, the connections between DC and AC sides of different parallel converters may lead to the surge of zero-sequence circulating current (ZSCC), which would result in the deterioration of system functionality. Regarding the stated problem above, this paper proposes an improved data-driven based model predictive control for parallel converters. Specifically, a model-free adaptive control (MFAC), which is based on the measured input/output data, is incorporated into the finite control-set model predictive control (FCS-MPC) framework with multi-objective constraints, thus allowing for the suppression of ZSCC and the improvement of robustness performance. Furthermore, to avoid the tuning of weighting factors, a novel cost function is constructed based on the multi-objective decision making method. The main contribution of the proposed methodology relies on the fact that no knowledge of any model parameters and weighting factors in whole control process are required, which leads to a significant enhancement in the robustness and reliability of the control system in the presence of parametric uncertainties. Furthermore, by this proposal, the accurate current tracking and ZSCC suppression can be achieved. Finally, the validity of the proposed FCS-MPC scheme is verified by comprehensive case studies.

Data-Driven Model Predictive Control for Wave Energy Converters Using Gaussian Process

The energy harvested by an ocean wave energy converter (WEC) can be enhanced by a well-designed wave-by-wave control strategy. One of such superior control methods is model predictive control (MPC), which is a nonlinear constrained optimization control strategy. A limitation of the classical MPC algorithm is its requirement of an accurate WEC dynamic model for real-time implementation. This article overcomes this challenge by proposing a data-driven MPC scheme for wave energy converters. The data-based WEC model is developed by a Gaussian process (encompassing mean predictions and symmetric uncertainties) for a more accurate description of nonlinear and unmodeled system dynamics. A cross-entropy solver for data-driven MPC is employed for rapid, high-performance results, which samples trajectories from Gaussian distributions based on the concept of the symmetry principle. The proposed strategy is verified numerically by simulations which demonstrate its superior performance over a classical complex-conjugate controller.

Input‐mapping based data‐driven model predictive control for unknown linear systems via online learning

Data-driven model predictive control (MPC) is an effective control method in controlling unknown constrained systems. The existing data-driven MPC methods either estimate the system online (adaptive) with extra computation efforts, or use the initially measured trajectory from offline trials to design controller. The offline trials are economically expensive for many practical systems. To overcome these limitations, we propose a multistep input-mapping data-driven scheme. It maps the current and future inputs to the past online measured input-state trajectories and expresses the future state as a linear combination of the past states. A moving data window is used to update the data online. Based on this scheme, two computationally efficient multistep input-mapping data-driven robust model predictive controllers with guarantee of feasibility and stability are proposed. The simulation results verify the improved performance and better computation efficiency of the resulting methods.

Learning-based model predictive current control for synchronous machines: An LSTM approach

In this work, a data-driven model predictive control (MPC) approach for the current control of synchronous machines is presented. The model of the motor is represented via a long-short term memory (LSTM) neural network (NN). The model is obtained purely from collected data and doesn’t include any physical knowledge. As an online optimization using the obtained data-driven model is not easily implementable in the available sampling time, the neural model is used to solve an MPC problem offline. Finally, the control policy is learned via another computationally implementable NN that runs in real-time as a current controller. The proposed data-driven MPC controller is tested experimentally, and is bench-marked against MPC schemes that incorporate the well-known physically-based first-principles linear and nonlinear model11The term first-principles model is used throughout the paper to call the machine model derived from the physical laws governing the functionality of the synchronous motor, whether it is the mostly used LTI model or the nonlinear model with the inductance/flux current-dependant maps.of the machine.

Data-Driven Model Predictive Control Method for Wind Farms to Provide Frequency Support

As the wind power penetration increases, wind farms are required by the grid codes to provide frequency regulation services. This article develops a fully data-driven model predictive control (DMPC) scheme for the wind farm to provide temporal frequency support. The main technical challenge is the complexity and the nonlinearity of wind turbine dynamics that make the DMPC intractable. Based on Koopman operator (KO) theory, a specialized dynamic mode decomposition (SDMD) algorithm is proposed, which fits a global linear dynamic model of the wind turbines. The performance of learning dynamics is powered through integrating the physical knowledge of the wind turbine into the specialized observables of KO. To stabilize the rotor speeds in frequency regulation, the active power contribution is optimally dispatched in a moving horizon fashion. Simulation results show that the DMPC can efficiently learn and predict the wind turbine dynamics. During the frequency response process, the proposed method can effectively track the frequency support order specified by the utility grid operator while significantly stabilizing the rotor speeds.

Semiclosed Greenhouse Climate Control Under Uncertainty via Machine Learning and Data-Driven Robust Model Predictive Control

This work proposes a novel data-driven robust model predictive control (DDRMPC) framework for automatic control of greenhouse in-door climate. The framework integrates dynamic control models of greenhouse temperature, humidity, and CO₂ concentration level with data-driven robust optimization models that accurately and rigorously capture uncertainty in weather forecast error. Data-driven uncertainty sets for ambient temperature, solar radiation, and humidity are constructed from historical data by leveraging a machine learning approach, namely, support vector clustering with weighted generalized intersection kernel. A training-calibration procedure that tunes the size of uncertainty sets is implemented to ensure that data-driven uncertainty sets attain an appropriate performance guarantee. In order to solve the optimization problem in DDRMPC, an affine disturbance feedback policy is utilized to obtain tractable approximations of optimal control. A case study of controlling temperature, humidity, and CO₂ concentration of a semiclosed greenhouse in New York City is presented. The results show that the DDRMPC approach ends up with 14% and 4% lower total cost than rule-based control and robust model predictive control with L₁-norm-based uncertainty set, respectively. The constraint violation probability, which is the percentage of time that the greenhouse system states violate the constraint throughout the whole growing period, for DDRMPC is only 0.39%. Hence, the proposed DDRMPC framework can prevent the greenhouse climate from becoming harmful to plants and fruits. In conclusion, the proposed DDRMPC approach can improve the greenhouse climate control performance and reduce cost compared with other control strategies.

Simplified data-driven models for model predictive control of residential buildings

Owing to recent advancements in Internet of Things technologies, data-driven model predictive control (MPC) has received significant research interest as a promising strategy to optimize building operation. As the MPC performance relies on the model prediction accuracy, complex building prediction models have been used in MPC applications, despite their high computational cost for optimization. This study examines whether linear-form prediction models are reliable to support the MPC of residential buildings equipped with single types of heating systems. This study developed linear-form models, namely an autoregressive with exogenous inputs (ARX) for predicting the indoor temperature and threshold-piecewise models for the return and supply water temperatures. The MPC performance on the basis of the linear models was evaluated under varying prediction horizons and weights associated with objective attributes. A case study of a residential unit through the simulated virtual building showed that the proposed models achieved the high goodness-of fit values greater than 0.9. The resulting MPC framework achieved heating energy savings up to approximately 12% relative to a simple on/off thermostat or reduction of comfort violation magnitude less than 0.5 °C. The influences of weight and prediction horizon on MPC performance were also investigated.

Rolling-optimized model predictive vibration controller for offshore platforms subjected to random waves and winds under uncertain sensing delay

In this paper, we investigate the vibration control problem in an offshore platform control structure. A model predictive controller is designed under internal model principle (IMP) and model predictive control (MPC) on the basis of linear quadratic optimal theory, where a rolling-optimized observer is taken to observe and estimate mixed external disturbance. Firstly, a steel jacket offshore platform is modelled as a single-degree-of-freedom (SDOF) vibration system subjected to varying waves and winds containing sensing delay. And the process of finding a vibration suppression controller is summarized as a global optimization problem. Secondly, an optimal quadratic regulator is proposed to attenuate the structure vibration, which naturally adopts IMP considering the varying dynamics of marine disturbance. Data-driven MPC method is then adopted to deal with leading disturbance items. Thirdly, a rolling-horizon optimal algorithm is applied to the proposed disturbance observer so that desired predictive states in deriving the optimal control law are obtained regardless of disturbance sensing delay. Lyapunov stability of the proposed control strategy is proved and comparable simulation experiments are conducted with other controllers.

Data-driven model predictive control design for offset-free tracking of nonlinear systems

We propose a design of data-driven Model Predictive Control (MPC) using a suboptimal trajectory and the linear time-varying (LTV) models from data-driven trajectory optimisation that achieves offset-free tracking. Data-driven constrained differential dynamic programming (CDDP) is exploited to improve the trajectory iteratively without the knowledge of the nonlinear model. A trajectory is divided to the transient and steady state regions, controlled by the Linear time-varying MPC (LTVMPC) and the offset-free linear MPC (LMPC), respectively. We prove the feasibility of the proposed LTVMPC in the transient region, and the offset-free tracking property of LMPC. The proposed scheme is validated to a continuous stirred tank reactor (CSTR) process. Simulation studies show that the suboptimal trajectory and LTV models are generated by CDDP, and the proposed MPC achieves offset-free tracking and disturbance rejection for a set of initial conditions and set points in the operating region.

Synthesis analysis for data driven model predictive control*

This paper shows our new contributions on data driven model predictive control, such as persistent excitation, optimal state feedback controller, output predictor and stability. After reviewing the definition of persistent excitation and its important property, the idea of data driven is introduced in model predictive control to construct our considered data driven model predictive control, whose state information and output variable are generated by measured data online. Variation tool is applied to obtain the optimal controller or predictive controller through our own derivation. Furthermore, for the cost function in data driven model predictive control, its preliminary stability is analysed by using the linear matrix inequality and one single optimal state feedback controller is given. To bridge the gap between our derived results and other control strategies, output predictor is constructed from the point of data driven idea, i.e. using some collected input–output data from one experiment to establish the output predictor at any later time instant. Finally, one simulation example is given to prove the efficiency of our derived results.

Building Energy Management With Reinforcement Learning and Model Predictive Control: A Survey

Building energy management has been recognized as of significant importance on improving the overall system efficiency and reducing the greenhouse gas emission. However, the building energy management system is now facing more challenges and uncertainties with the increasing penetration of renewable energy and increasing adoption of different types of electrical appliances and equipment. Classical model predictive control (MPC) has shown effective in building energy management, although it suffers from labour-intensive modelling and complex online control optimization. Recently, with the growing accessibility to building control and automation data, data-driven solutions such as data-driven MPC and reinforcement learning (RL)-based methods have attracted more research interest. However, the potential of integrating these two types of methods and how to choose suitable control algorithms have not been well discussed. In this work, we first present a compact review of the recent advances in data-driven MPC and RL-based control methods for building energy management. Furthermore, the main challenges in these approaches and general discussions on the selection of control methods are discussed.

Data-driven model identification and predictive control for path-following of underactuated ships with unknown dynamics

With the trends towards autonomous shipping, advanced ship motion control methods have received increased attention in recent years. The validity of ship models is crucial in designing motion controllers and directly affects their performances. However, accurate models that could reflect true ship dynamics are highly nonlinear, complex and complicated to identify, especially in situations when the experimental conditions are limited. This paper proposes a data-driven predictive control method for path-following of under-actuated cargo ships with unknown dynamics, which makes use of data gathered during operation to improve the model and the path-following performance. Based on the ship navigation data set, the relations between the heading angle and the rudder angle of the ship are fitted with seven typical regression algorithms, which acts as the prediction model in the path-following controller. Simulation study is carried out to choose the most suitable regression algorithm, among which elastic net regression is selected. The Antenna Mutation Beetle Swarm Predictive (AMBS-P) algorithm is introduced to find the optimal weights in the model identification process. A Line-of-Sight (LOS) algorithm is used as the guidance law to transform reference way-points into reference heading angles, and the path-following controller is designed also based on and the AMBS-P algorithm. Simulation results show that the proposed data-driven control method performs well in the path-following task without having prior knowledge regarding the hydrodynamic coefficients and ship parameters. • The proposed data-driven control strategy allows the users to exploit the advantage of the predictive control scheme, as well as exploiting the approximate model knowledge captured from data without having prior knowledge regarding the hydrodynamic coefficients and ship parameters. • A quantitative analysis of the model identification performances of seven typical regression algorithms is carried out. • The Antenna Mutation Beetle Swarm Predictive (AMBS-P) algorithm is proposed and applied in finding the optimal weights in the model identification process and in designing the path-following controller with a LOS guidance principle. This could save the efforts spend in weight selection and controller parameter adjustments. It is also fast and easy to implement, which could facilitate its use in practice.

Data-Driven Robust Model Predictive Control with Personalized Driving Style for Mixed Vehicle Platoon

Data-Driven Robust Model Predictive Control with Personalized Driving Style for Mixed Vehicle Platoon

Data-driven distributed MPC of dynamically coupled linear systems

In this paper, we present a data-driven distributed model predictive control (MPC) scheme to stabilise the origin of dynamically coupled discrete-time linear systems subject to decoupled input constraints. The local optimisation problems solved by the subsystems rely on a distributed adaptation of the Fundamental Lemma by Willems et al., allowing to parametrise system trajectories using only measured input-output data without explicit model knowledge. For the local predictions, the subsystems rely on communicated assumed trajectories of neighbours. Each subsystem guarantees a small deviation from these trajectories via a consistency constraint. We provide a theoretical analysis of the resulting non-iterative distributed MPC scheme, including proofs of recursive feasibility and (practical) stability. Finally, the approach is successfully applied to a numerical example.

Hybrid Physics-based and Data-driven Model Predictive Control for Multi-Zone Building's Thermal Comfort Under Disjunctive Uncertainty

This paper develops a hybrid approach that utilizes the distributional information of the disjunctive uncertainty sets and incorporates them into the model predictive control (MPC). This approach aims at the multi-zone building control to the thermal comfort, and it's robust to the uncertain weather forecast errors. The control objective is to maintain each zone's temperature and relative humidity within the specified ranges using the minimum cost of energy of the underlying heating system. The hybrid model is constructed using a physics-based and regression method for the temperature and relative humidity of each zone in the building. The uncertainty space is based on historical weather forecast error data, which are captured by a group of disjunctive uncertainty sets using k-means clustering algorithm. Machine learning approaches based on principal component analysis and kernel density estimation are used to construct each basic uncertainty set and reduce the conservatism of resulting robust control action under disturbances. A robust MPC framework is developed based on the proposed hybrid model and data-driven disjunctive uncertainty set. An affine disturbance feedback rule is employed to obtain a tractable approximation of the robust MPC problem. A case study of controlling temperature and relative humidity of a multi-zone building in Ithaca, New York, USA, is presented. The results demonstrate that the proposed hybrid approach can reduce 9.8% to 17.9% of total energy consumption compared to conventional robust MPC approaches. Moreover, the proposed hybrid approach can essentially satisfy the thermal constraints that certainty equivalent MPC and robust MPC largely violate.

Smart greenhouse control under harsh climate conditions based on data-driven robust model predictive control with principal component analysis and kernel density estimation

Efficient greenhouse climate control under harsh climate conditions at locations such as Qatar is a challenge because of the high temperature and high relative humidity. This work presents an application of a data-driven robust model predictive control for intelligent control of greenhouse indoor climate in Qatar. The framework integrates dynamic control models of temperature, CO2 concentration level, and humidity of a greenhouse with a data-driven robust optimization framework that accurately and rigorously captures uncertainty in weather forecast error. A machine learning approach combining principal component analysis (PCA) with kernel density estimation (KDE) is adopted to construct data-driven uncertainty sets for temperature, solar radiation, and humidity from historical data. The optimal control inputs that minimize control costs and state violations are obtained by solving a data-driven robust optimization problem at each time step. The application of controlling a greenhouse growing tomatoes located in Doha, Qatar is presented. The results suggest that the proposed PCA and KDE-based data-driven robust model predictive control approach needs lower total control cost than rule-based control and other model predictive control to maintain the greenhouse climate for supporting crop production under harsh climate conditions.

Data-driven offset-free multilinear model predictive control using constrained differential dynamic programming

Multilinear model predictive control (MLMPC) can regulate a nonlinear process with wide operating regions based on a set of linear models. Although online computational cost is reduced compare to nonlinear MPC (NMPC), it is difficult to obtain a reliable full nonlinear model or set of linear models in practice. In this paper, we propose a combination of MLMPC with differential dynamic programming (DDP), so that the system can be controlled offset-free in the absence of a full nonlinear model. DDP is a ‘trajectory-centric’ optimization technique that solves nonlinear optimal control problems. The trajectory can be optimized even if the full model for the system is unknown, because DDP uses only the gradients around the visited trajectory, which is easily obtained by input excitations. Moreover, the gradient information can provide linear models in the subsequent MLMPC step. In the proposed scheme, a novel model selection based on gap metric and weighting method are employed for MLMPC. We prove the offset tracking property of DDP assisted MLMPC. A continuous stirred tank reactor (CSTR) process is studied to demonstrate the effectiveness of the proposed algorithms. Simulation studies show that CDDP designed by the proposed algorithm improves the trajectory over iterations, and the resulting MLMPC achieves offset-free tracking property regardless of an initial point and a set-point in the operating region.

Energy utilization assessment of a semi-closed greenhouse using data-driven model predictive control

With the global increase in food demand, closed and controlled greenhouses are an essential source for year-round crop production. Maintaining the optimum conditions inside the greenhouse throughout the year is critical to improving crop quality and yield. However, greenhouses consume more resources than other commercial buildings due to their inefficient operation and structure. Therefore, a data-driven model predictive control approach for a semi-closed greenhouse is proposed for temperature control and reducing energy consumption in this study. The proposed method consists of a multilayer perceptron model representing the greenhouse system integrated with an objective function and an optimization algorithm. The multilayer perceptron model is trained using historical data from the greenhouse with solar radiation, outside temperature, humidity difference, fan speed, HVAC control as the input parameters to predict the temperature. The greenhouse model's performance is evaluated under varying scenarios, such as increasing the prediction time step and changing the number of samples in the training data set. Results illustrated that the MPC approach had a better temperature control than the greenhouse adaptive control system for winter and summer with an RMSE value of 0.33 °C and 0.36 °C, respectively. Similarly, model predictive control resulted in an energy reduction of 7.70% for winter and 16.57% for the summer season. The proposed model predictive control framework is flexible and can be applied to other greenhouse systems by tuning the model on the new data set.