Data-driven Model Predictive Control Research Articles

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.

Dynamic Programming in Data Driven Model Predictive Control?

In this short note, one data driven model predictive control is studied to design the optimal control sequence. The idea of data driven means the actual output value in cost function for model predictive control is identi_ed through input-output observed data in case of unknown but bounded noise and martingale di_erence sequence. After substituting the identi_ed actual output in cost function, the total cost function in model predictive control is reformulated as the other standard form, so that dynamic programming can be applied directly. As dynamic programming is only used in optimization theory, so to extend its advantage in control theory, dynamic programming algorithm is proposed to construct the optimal control sequence. Furthermore, stability analysis for data drive model predictive control is also given based on dynamic programming strategy. Generally, the goal of this short note is to bridge the dynamic programming, system identi_cation and model predictive control. Finally, one simulation example is used to prove the e_ciency of our proposed theory

Distributed data driven control for multi-agent consensus with unknown system dynamics

This study investigates the consensus tracking problem for unknown multi-agent systems (MASs) with time-varying communication topology by using the methods of data-driven control and model predictive control. Under the proposed distributed iterative protocol, sufficient conditions for reducing tracking error are analyzed for both time invariable and time varying desired trajectories. The main feature of the proposed protocol is that the dynamics of the multi-agent systems are not required to be known and only local input-output data are utilized for each agent. Numerical simulations are presented to illustrate the effectiveness of the derived consensus conditions.

Image-based model predictive control via dynamic mode decomposition

We present a data-driven model predictive control (MPC) framework for systems with high state–space dimensionality. This work is motivated by the need to exploit sensor data that appears in the form of images (e.g., 2D or 3D spatial fields captured by thermal cameras). We propose to use dynamic mode decomposition (DMD) to directly build a low-dimensional model from image data and we use such model to obtain a tractable MPC controller. We demonstrate the scalability of this approach (which we call DMD-MPC) by using a 2D thermal diffusion system. Here, we assume that the evolution of the thermal field is captured by 50 x 50 pixel images, which results in a 2500-dimensional state–space. We show that the dynamics of this high-dimensional space can be accurately captured by using a 40-dimensional DMD model and we show that the field can be manipulated satisfactorily by using an MPC controller that embeds the low-dimensional DMD model. We also show that the DMD-MPC controller outperforms a standard MPC controller that uses data collected from a finite set of spatial locations (proxy locations) to manipulate the high-dimensional thermal field. This illustrates the value of information embedded in image data.

Data-driven model predictive control for power demand management and fast demand response of commercial buildings using support vector regression

Demand response (DR) of commercial buildings by directly shutting down part of operating chillers could provide an immediate power reduction for power grids. In this special fast DR event, effective control needs to guarantee expected power reduction and ensure an acceptable indoor environment. This study, therefore, developed a data-driven model predictive control (MPC) using support vector regression (SVR) for fast DR events. According to the characteristics of fast DR events, the optimized hyperparameters of SVR and shortened searching range of genetic algorithm are used to improve the control performance. Meanwhile, a comprehensive comparison with RC-based MPC is conducted based on three scenarios of power demand controls. Test results show that the proposed SVR-based MPC could fulfill the control objectives of power demand and indoor temperature simultaneously. Compared with RC-based MPC, the SVR-based MPC could alleviate the time/labor cost of model development without sacrificing the control performance of fast DR events.

Data-driven model predictive control: closed-loop guarantees and experimental results

Abstract We provide a comprehensive review and practical implementation of a recently developed model predictive control (MPC) framework for controlling unknown systems using only measured data and no explicit model knowledge. Our approach relies on an implicit system parametrization from behavioral systems theory based on one measured input-output trajectory. The presented MPC schemes guarantee closed-loop stability for unknown linear time-invariant (LTI) systems, even if the data are affected by noise. Further, we extend this MPC framework to control unknown nonlinear systems by continuously updating the data-driven system representation using new measurements. The simple and intuitive applicability of our approach is demonstrated with a nonlinear four-tank system in simulation and in an experiment.

Introducing Dynamic Programming and Persistently Exciting into Data-Driven Model Predictive Control

In this paper, one new data-driven model predictive control scheme is proposed to adjust the varying coupling conditions between different parts of the system; it means that each group of linked subsystems is grouped as data-driven scheme, and this group is independently controlled through a decentralized model predictive control scheme. After combing coalitional scheme and model predictive control, coalitional model predictive control is used to design each controller, respectively. As the dynamic programming is only used in optimization theory, to extend its advantage in control theory, the idea of dynamic programming is applied to analyze the minimum principle and stability for the data-driven model predictive control. Further, the goal of this short note is to bridge the dynamic programming with model predictive control. Through adding the inequality constraint to the constructed model predictive control, one persistently exciting data-driven model predictive control is obtained. The inequality constraint corresponds to the condition of persistent excitation, coming from the theory of system identification. According to the numerical optimization theory, the necessary optimality condition is applied to acquire the optimal control input. Finally, one simulation example is used to prove the efficiency of our proposed theory.

Data-driven robust model predictive control framework for stem water potential regulation and irrigation in water management

In this work, we propose a data-driven robust model predictive control (DDRMPC) framework that utilizes stem water potential (SWP) as a basis for effective irrigation control of high value-added crops. By linearizing and discretizing a nonlinear dynamic model of water dynamics, we develop a state-space model that predicts the dynamic state of SWP. In the model, soil, root, and stem are the three compartments to describe current water status of the system. In addition, evapotranspiration and precipitation are the driving force and the water inlet, respectively. A robust optimal control problem is formulated to maintain SWP above a safe level to avoid detrimental effects on crops. To describe the uncertainty within prediction errors of evapotranspiration and precipitation, a data-driven approach is adopted, which achieves a desirable tradeoff between constraint satisfaction and water saving. Meanwhile, it is shown that the proposed DDRMPC ensures both feasibility and stability. A case study based on almond tree is carried out to showcase the effectiveness of the DDRMPC strategy relative to on–off control, certainty equivalent MPC and robust MPC. In particular, the control of tree stem water potential through DDRMPC can reduce the water consumption by 7.9% compared with on–off control while maintaining zero probability of constraint violation.

Fast Data-Driven Model Predictive Control Strategy for Connected and Automated Vehicles

Abstract We present a fast data-driven model predictive control (MPC) strategy for connected and automated vehicles, which can ensure collision avoidance in the presence of uncertainty in shared/predicted trajectory of preceding vehicles. The proposed control strategy focuses on improvement in fuel economy and computational efficiency. We exploit a data-driven modeling approach to identify a linear predictor for the nonlinear system and evaluate a deterministic equivalent of the probabilistic collision avoidance constraint to formulate the equivalent convex optimal control problem. We then develop a hierarchical control framework with sampling-based high-level control and fast MPC-based low-level control. Simulation results show the efficacy of the proposed approach both in terms of computation time and fuel efficiency.

Online predictive connected and automated eco-driving on signalized arterials considering traffic control devices and road geometry constraints under uncertain traffic conditions

For energy-efficient Connected and Automated Vehicle (CAV) Eco-driving control on signalized arterials under uncertain traffic conditions, this paper explicitly considers traffic control devices (e.g., road markings, traffic signs, and traffic signals) and road geometry (e.g., road shapes, road boundaries, and road grades) constraints in a data-driven optimization-based Model Predictive Control (MPC) modeling framework. This modeling framework uses real-time vehicle driving and traffic signal data via Vehicle-to-Infrastructure (V2I) and Vehicle-to-Vehicle (V2V) communications. In the MPC-based control model, this paper mathematically formulates location-based traffic control devices and road geometry constraints using the geographic information from High-Definition (HD) maps. The location-based traffic control devices and road geometry constraints have the potential to improve the safety, energy, efficiency, driving comfort, and robustness of connected and automated driving on real roads by considering interrupted flow facility locations and road geometry in the formulation. We predict a set of uncertain driving states for the preceding vehicles through an online learning-based driving dynamics prediction model. We then solve a constrained finite-horizon optimal control problem with the predicted driving states to obtain a set of Eco-driving references for the controlled vehicle. To obtain the optimal acceleration or deceleration commands for the controlled vehicle with the set of Eco-driving references, we formulate a Distributionally Robust Stochastic Optimization (DRSO) model (i.e., a special case of data-driven optimization models under moment bounds) with Distributionally Robust Chance Constraints (DRCC) with location-based traffic control devices and road geometry constraints. We design experiments to demonstrate the proposed model under different traffic conditions using real-world connected vehicle trajectory data and Signal Phasing and Timing (SPaT) data on a coordinated arterial with six actuated intersections on Fuller Road in Ann Arbor, Michigan from the Safety Pilot Model Deployment (SPMD) project.

Data-driven LPV model predictive control of a cold atmospheric plasma jet for biomaterials processing

Cold atmospheric plasmas (CAPs) are increasingly used for treatment of complex surfaces in biomedical and biomaterials processing applications. However, the multivariable, distributed-parameter, and nonlinear nature of CAP dynamics and plasma–surface interactions, coupled with the sensitivity of plasmas to exogenous disturbances, make their safe, reproducible and effective operation challenging. This paper adopts a data-driven linear parameter-varying (LPV) modeling framework to learn a control-oriented model for predictive control of a kHz-excited atmospheric pressure plasma jet in Helium. A hierarchical model-based control strategy is proposed based on a supervisory LPV-based model predictive controller (LPV–MPC) to regulate the nonlinear thermal effects of plasma on a surface. Real-time control experiments demonstrate the effectiveness of the proposed LPV–MPC strategy for the multivariable control of surface temperature and plasma optical intensity, as well as for controlling the spatial delivery of the cumulative thermal effects of the plasma jet on a surface.

A Data-Driven Model Predictive Control for Alleviating Thermal Overloads in the Presence of Possible False Data

Effective mitigation of thermal overloads is crucial in preventing power grid outages. With large-scale adoption of phasor measurement units, new and more effective mitigation opportunities have emerged. However, the possibility of false data attacks on the measured data, or the relay status information, threatens the promise of utilizing measurements for timely mitigation of thermal overloads. False data can lead to wrong estimation of the system states and the power flow model, which may eventually lead to wrong mitigations. To address these newly introduced challenges, in this article, a data-driven model-predictive control method is introduced for mitigation of the thermal overloads, which is resilient to false data injection attacks. This is achieved by constructing a data-driven power flow model from the trustworthy system measurements, which is independent from system topology and model parameters. Hence, the power flow model becomes immune to wrong system model information. To eliminate the adverse impacts of false data on the measurements, the actual system states are recovered from the historical trustworthy data if an attack is detected. Case studies demonstrate that the developed model predictive control methodology effectively identifies the optimal mitigations in a finite prediction horizon.

Robust analysis for data-driven model predictive control

Here the idea of data driven is introduced in model predictive control to establish our proposed data-driven model predictive control. Considering one first-order discrete time nonlinear dynamical system, the main essence of data driven means the actual output value in cost function for model predictive control is identified through input–output observed data in case of unknown but bounded noise and martingale difference sequence. After substituting the identified actual output in cost function, the total cost function in model predictive control is reformulated as its standard form, i.e. one quadratic program problem with input and output constraints. Then semidefinite relaxation scheme is used to derive a lower bound for its optimal value, and the robust counterpart of an uncertain quadratic program is reduced to one conic quadratic problem. The above semidefinite relaxation scheme and conic quadratic problem correspond to the similar robust analysis based on convex optimization theory. Finally, one simulation example is used to prove the efficiency of our proposed theory.

Data-Driven Model Predictive Control of DC-to-DC Buck-Boost Converter

The data-driven model predictive control (DDMPC) scheme is proposed to obtain fast convergence to a desired reference and to be utilised to mitigate the destabilising effects that a DC-to-DC buck-boost converter (BBC) with an active load experiences. The DDMPC strategy uses the observed state to derive an optimal control policy using a reinforcement learning (RL) algorithm. The employed Proximal Policy Optimisation (PPO) algorithm's performance is benchmarked against the PI controller. From the simulated results obtained using the MATLAB Simulink solver, the most robust methods for short settling time and stability were the hybrid methods. These methods take advantage of the short settling time provided by the PPO algorithm and the stability provided by the PI controller or the filtering mechanism over the transient time. The source code for this study is available on GitHub to support reproducible research in industrial electronics society.

Teaching MPC: Which Way to the Promised Land?

Abstract Since the earliest conceptualizations by Lee and Markus, and Propoi in the 1960s, Model Predictive Control (MPC) has become a major success story of systems and control with respect to industrial impact and with respect to continued and wide-spread research interest. The field has evolved from conceptually simple linear-quadratic (convex) settings in discrete and continuous time to nonlinear and distributed settings including hybrid, stochastic, and infinite-dimensional systems. Put differently, essentially the entire spectrum of dynamic systems can be considered in the MPC framework with respect to both—system theoretic analysis and tailored numerics. Moreover, recent developments in machine learning also leverage MPC concepts and learning-based and data-driven MPC have become highly active research areas. However, this evident and continued success renders it increasingly complex to live up to industrial expectations while enabling graduate students for state-of-the-art research in teaching MPC. Hence, this position paper attempts to trigger a discussion on teaching MPC. To lay the basis for a fruitful debate, we subsequently investigate the prospect of covering MPC in undergraduate courses; we comment on teaching textbooks; and we discuss the increasing complexity of research-oriented graduate teaching of MPC.

On the design of terminal ingredients for data-driven MPC

We present a model predictive control (MPC) scheme to control linear time-invariant systems using only measured input-output data and no model knowledge. The scheme includes a terminal cost and a terminal set constraint on an extended state containing past input-output values. We provide an explicit design procedure for the corresponding terminal ingredients that only uses measured input-output data. Further, we prove that the MPC scheme based on these terminal ingredients exponentially stabilizes the desired setpoint in closed loop. Finally, we illustrate the advantages over existing data-driven MPC approaches with a numerical example.