Data-driven Control Research Articles

Distributed Koopman-Based Control of Improved Swing Equation

This paper presents a data-driven control for a set of synchronous generators based on the improved swing equation model by using the Koopman operator. First, the nonlinear dynamic of the generators is represented by a linear model in lifted space using extended dynamic mode decomposition (EDMD). Then, a linear predictor is built and used for the design of a model predictive control following three strategies: decentralized, non-cooperative, and cooperative. The Koopman representation of the generator is used to carry out an analysis, determining its eigenvalues. Several interconnected generators are controlled showing the performance of the interconnected system including voltage faults.

Informativity conditions for data-driven control based on input-state data and polyhedral cross-covariance noise bounds

Modeling and control of dynamical systems rely on measured data, which contains information about the system. Finite data measurements typically lead to a set of system models that are unfalsified, i.e., that explain the data. The problem of data-informativity for stabilization or control with quadratic performance is concerned with the existence of a controller that stabilizes all unfalsified systems or achieves a desired quadratic performance. Recent results in the literature provide informativity conditions for control based on input-state data and ellipsoidal noise bounds, such as energy or magnitude bounds. In this paper, we consider informativity of input-state data for control where noise bounds are defined through the cross-covariance of the noise with respect to an instrumental variable; bounds that were introduced originally as a noise characterization in parameter bounding identification. The considered cross-covariance bounds are defined by a finite number of hyperplanes, which induce a (possibly unbounded) polyhedral set of unfalsified systems. We provide informativity conditions for input-state data with polyhedral cross-covariance bounds for stabilization and H2/H∞ control through vertex/half-space representations of the polyhedral set of unfalsified systems.

Data-driven Control of Temporally and Spatially Redundant Systems

The present study proposes a data-driven design method for redundant systems where temporal and spatial redundancy are achieved by multi-rate design and multiple actuators, respectively. In the proposed method, the noniterative correlation-based tuning method for non-redundant systems is extended to temporally and spatially redundant systems. The effectiveness of the proposed method is demonstrated through experimental results.

Direct Data-Driven Design for a Sparse Feedback Controller Based on VRFT and LASSO regression

Direct data-driven controller design has attracted considerable attention because of simple design procedure. This paper presents a direct model-referenced data-driven design for obtaining sparse controller to prevent over learning from single-experiment data. In conventional methods, controller parameters are obtained for controller with order defined by user. In case where there is little plant information, it is difficult to define controller order to achieve model-matching. Also, if high order of the controller is simply set, over learning may occur. Thus, the sparse controller design method is proposed. The proposed method is based on VRFT (virtual reference feedback tuning) and LASSO (least absolute shrinkage and selection operator) regression. A simulation is performed to verify the proposed method. The results show that the sparse controller can be obtained for the controller with high order.

Data-Driven Aggregation Control for Thermoelectric Loads in Demand Response

Within the concept of a smart grid, aggregators have the task of coordinating the behavior of large sets of Distributed Energy Resources, each of them offering small power/energy capacities, which help to balance the power grid and can serve as providers of services. Adequate coordination strategies are required to optimally exploit these resources in the ancillary services market. However, deriving model-based control policies for them is complex due to the heterogeneity and uncertainty related to the large set of associated agents. Then, a data-driven model is an adequate solution for this sort of situation. This paper presents the application of the Youla–Kucera Data-Driven Control strategy for the development of an aggregator to regulate the power consumption of a set of thermoelectric refrigerators, avoiding the modeling process and directly designing a controller from data. A detailed simulation framework was executed to verify the validity of the proposed methodology. It is shown that the derived aggregator is able to offer frequency containment reserves service, achieving the required settling time of 30 seconds and with a tracking error below 4.7%.

Control-Oriented Modeling using Koopman Operator: An application to the Cahn-Hilliard Coarsening Problem

In this paper, we present results for the data-driven control oriented modeling of complex dynamics that arise in phase separation of multi-phase immiscible system. This phase separation phenomena is modeled using a complicated nonlinear partial differential equations which are not suitable for control. We use simulation data generated from a detailed physics-based model for the data-driven modeling. We employ Koopman-based lifting for the identification of linear models from the data both under controlled and uncontrolled setting. Spectral analysis of Koopman and its adjoint Perron-Frobenius operator helps us identify invariant structure and dominant modes for the reduced-order representation from the data. Simulation results are presented for the reconstruction and validation of the controlled dynamical model.

A novel data-driven controller for plug-in hybrid electric vehicles with improved adaptabilities to driving environment

Instantaneous application optimality is one of the indispensable indicators to assess energy management performance of plug-in hybrid electric vehicles (PHEVs). The momentary optimality, nevertheless, cannot be flexibly reachable under various driving environments due to the partial unobservabilities in control algorithms. To cope with it, a novel data-driven controller for PHEVs is proposed in this paper to achieve the instantaneous optimality of energy management. The well-designed machine learning based controller translates the knowledge of global optimization to real-time controlling scheme with the consideration of adaptabilities to disperse driving conditions. To start with, the universal global optimal control policies for varying driving environment are generated offline based on the chaotic quantum particle swarm optimization with sequential quadratic programming (CQPSO-SQP). Then, the offline optimized global control policies are assembled to construct the dataset for training the least square support vector machine (LSSVM) based controller, which features the superior capability in instantly optimal policy making under different driving conditions. At last, the detailed assessment is performed in simulation test and hardware-in-loop (HIL) test to validate the promising role of CQPSO-PSO and LSSVM in designing the novel energy management controller, and the corresponding results highlight the preferable controlling performance of the proposed novel controller in practical applications.

Improved model-free adaptive predictive control method for direct data-driven control of a wastewater treatment process with high performance

In this paper, an improved model-free adaptive predictive control (IMFAPC) method with controller parameters sensitivity discrimination and optimization is proposed, to solve the problem that using conventional methods is difficult to effectively control the nitrate concentration and dissolved oxygen concentration of wastewater treatment process (WWTP). First, aiming at the nonstationary dynamic characteristics of WWTP and the limitation of control accuracy of conventional MFAPC method in the nonlinear dynamic system control, a novel improved MFAPC method is proposed considering the effect of the WWTP output tracking error variation on the control of nitrate concentration and dissolved oxygen concentration. Meanwhile, in order to obtain the optimum control performance, the sensitivity discrimination and optimization for the multi-parameter set of the proposed IMFAPC method are performed by combining the Monte Carlo experiment based multi-parameter sensitivity analysis and the hybrid intelligent optimization. Then, the stability of the proposed IMFAPC scheme is analyzed and proved by the BIBO method. Finally, various data experiments are carried out to verify the proposed method. The experimental results demonstrate that the proposed method can control the nitrate nitrogen and dissolved oxygen concentration rapidly and accurately under different operating conditions.

Model-free LQR design by Q-function learning

Reinforcement learning methods such as Q-learning have shown promising results in the model-free design of linear quadratic regulator (LQR) controllers for linear time-invariant (LTI) systems. However, challenges such as sample-efficiency, sensitivity to hyper-parameters, and compatibility with classical control paradigms limit the integration of such algorithms in critical control applications. This paper aims to take some steps towards bridging the well-known classical control requirements and learning algorithms by using optimization frameworks and properties of conic constraints. Accordingly, a new off-policy model-free approach is proposed for learning the Q-function and designing the discrete-time LQR controller. The design procedure is based on non-iterative semi-definite programs (SDP) with linear matrix inequality (LMI) constraints. It is sample-efficient, inherently robust to model uncertainties, and does not require an initial stabilizing controller. The proposed model-free approach is extended to distributed control of interconnected systems, as well. The performance of the presented design is evaluated on several stable and unstable synthetic systems. The data-driven control scheme is also implemented on the IEEE 39-bus New England power grid. The results confirm optimality, sample-efficiency, and satisfactory performance of the proposed approach in centralized and distributed design.

Event-triggered data-driven control of discrete-time nonlinear systems with unknown disturbance

This paper is dedicated to event-triggered data-driven control of nonlinear systems with unknown disturbance via model free iterative learning approach. An extended state observer is employed to reconstruct the disturbance in system output. An event-triggered model free iterative learning control strategy is constructed by system input, system output and the reconstructed disturbance. Sufficient conditions are proposed to make the resultant tracking error system be uniform ultimate bounded. Simulation examples are provided to validate the effectiveness of the proposed scheme.

BALLU2: A Safe and Affordable Buoyancy Assisted Biped.

This work presents the first full disclosure of BALLU, Buoyancy Assisted Lightweight Legged Unit, and describes the advantages and challenges of its concept, the hardware design of a new implementation (BALLU2), a motion analysis, and a data-driven walking controller. BALLU is a robot that never falls down due to the buoyancy provided by a set of helium balloons attached to the lightweight body, which solves many issues that hinder current robots from operating close to humans. The advantages gained also lead to the platform’s distinct difficulties caused by severe nonlinearities and external forces such as buoyancy and drag. The paper describes the nonconventional characteristics of BALLU as a legged robot and then gives an analysis of its unique behavior. Based on the analysis, a data-driven approach is proposed to achieve non-teleoperated walking: a statistical process using Spearman Correlation Coefficient is proposed to form low-dimensional state vectors from the simulation data, and an artificial neural network-based controller is trained on the same data. The controller is tested both on simulation and on real-world hardware. Its performance is assessed by observing the robot’s limit cycles and trajectories in the Cartesian coordinate. The controller generates periodic walking sequences in simulation as well as on the real-world robot even without additional transfer learning. It is also shown that the controller can deal with unseen conditions during the training phase. The resulting behavior not only shows the robustness of the controller but also implies that the proposed statistical process effectively extracts a state vector that is low-dimensional yet contains the essential information of the high-dimensional dynamics of BALLU’s walking.

Derivative-Based Koopman Operators for Real-Time Control of Robotic Systems

This article presents a generalizable methodology for data-driven identification of nonlinear dynamics that bounds the model error in terms of the prediction horizon and the magnitude of the derivatives of the system states. Using higher order derivatives of general nonlinear dynamics that need not be known, we construct a Koopman-operator-based linear representation and utilize Taylor series accuracy analysis to derive an error bound. The resulting error formula is used to choose the order of derivatives in the basis functions and obtain a data-driven Koopman model using a closed-form expression that can be computed in real time. Using the inverted pendulum system, we illustrate the robustness of the error bounds given noisy measurements of unknown dynamics, where the derivatives are estimated numerically. When combined with control, the Koopman representation of the nonlinear system has marginally better performance than competing nonlinear modeling methods, such as SINDy and NARX. In addition, as a linear model, the Koopman approach lends itself readily to efficient control design tools, such as linear–quadratic regulator, whereas the other modeling approaches require nonlinear control methods. The efficacy of the approach is further demonstrated with simulation and experimental results on the control of a tail-actuated robotic fish. Experimental results show that the proposed data-driven control approach outperforms a tuned proportional–integral–derivative controller and that updating the data-driven model online significantly improves performance in the presence of unmodeled fluid disturbance. This article is complemented with a video available at <uri xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">https://youtu.be/9_wx0tdDta0</uri> .

Broad Learning Aided Model Predictive Control With Application to Continuous Stirred Tank Heater

This paper presents a data-driven predictive controller based on the broad learning algorithm without any prior knowledge of the system model. The predictive controller is realized by regressing the predictive model using online process data and the incremental broad learning algorithm. The proposed model predictive control (MPC) approach requires less online computational load compared to other neural network based MPC approaches. More importantly, the precision of the predictive model is enhanced with reduced computational load by operating an appropriate approximation of the predictive model. The approximation is proved to have no influence on the convergence of the predictive control algorithm. Compared with the partial form dynamic linearization aided model free control (PFDL-MFC), the control performance of the proposed predictive controller is illustrated through the continuous stirred tank heater (CSTH) benchmark.

Estimated Response Iterative Tuning with signal projection

This paper discusses about a data-driven control method which is called Estimated Response Iterative Tuning (ERIT). ERIT focuses on a two-degree of freedom control system, and updates the feedforward controller from one-shot experiment. The main contribution of this paper is to propose a pre-processing for ERIT to improve robustness against noise. In particular, this paper proposes to project the measured output onto a subspace, and regard the projected signal as a noise-free output. How to design this subspace is also proposed in this paper. A practical experiment with flexible link system is shown to demonstrate the effectiveness of the proposed method.

A New Data-Driven Control System for MEMSs Gyroscopes: Dynamics Estimation by Type-3 Fuzzy Systems.

In this study, a novel data-driven control scheme is presented for MEMS gyroscopes (MEMS-Gs). The uncertainties are tackled by suggested type-3 fuzzy system with non-singleton fuzzification (NT3FS). Besides the dynamics uncertainties, the suggested NT3FS can also handle the input measurement errors. The rules of NT3FS are online tuned to better compensate the disturbances. By the input-output data set a data-driven scheme is designed, and a new LMI set is presented to ensure the stability. By several simulations and comparisons the superiority of the introduced control scheme is demonstrated.

Data-driven control of room temperature and bidirectional EV charging using deep reinforcement learning: Simulations and experiments

The control of modern buildings is a complex multi-loop problem due to the integration of renewable energy generation, storage devices, and electric vehicles (EVs). Additionally, it is a complex multi-criteria problem due to the need to optimize overall energy use while satisfying users’ comfort. Both conventional rule-based (RB) controllers, which are difficult to apply in multi-loop settings, and advanced model-based controllers, which require an accurate building model, cannot fulfil the requirements of the building automation industry to solve this problem optimally at low development and commissioning costs. This work presents a fully data-driven pipeline to obtain an optimal control policy from historical building and weather data, thus avoiding the need for complex physics-based modelling. We demonstrate the potential of this method by jointly controlling a room temperature and an EV to minimize the cost of electricity while retaining the comfort of the occupants. We model the room temperature with a recurrent neural network and use it as a simulation environment to learn a deep reinforcement learning (DRL) control policy. It achieves on average 17% energy savings and 19% better comfort satisfaction than a standard RB room temperature controller. When a bidirectional EV is connected additionally and a two-tariff electricity pricing is applied, it successfully leverages the battery and decreases the overall cost of electricity. Finally, we deployed it on a real building, where it achieved up to 30% energy savings while maintaining similar comfort levels compared to a conventional RB room temperature controller.

Hybrid model-driven and data-driven control method based on machine learning algorithm in energy hub and application

Energy forms the foundation for humans, but with the wastage of energy and energy consumption being at critical levels, energy saving has become an urgent priority. As a general term for various complex energy systems, energy hub and its control have become key research objects with regard to energy saving. In terms of control of an energy hub, the traditional model-driven approach and the currently rapidly developing data-driven approach have their own characteristics. In this paper, we propose a hybrid model-driven method and a data-driven control method using machine learning algorithms to combine the characteristics of the two driven approaches to realize the extraction of the data hiding mode. The Koopman operation is used to increase the dimension of the data to be linearized. Subsequently, the singular value decomposition method decomposes the data in polar coordinates, reducing dimensionality while ensuring linearization. The polynomial model obtained through machine learning training is simple and flexible. The online data of the energy hub can be used for fast coefficient fitting, and the speed and accuracy of the model can be guaranteed when external conditions change. Case studies on a circulating cooling water system show that this method could complete the process of data collection, learning, modeling, and control automatically when external changes occurred, and the time required for the entire process could meet the needs of a control response. It could rapidly and accurately complete the control process as well as effectively reduce the energy consumption, and it did not generate excessive control costs in the process.

Anaerobic Digestion Process Control Using a Data-Driven Internal Model Control Method

Anaerobic digestion processes offer the possibility for wastewater treatment while obtaining a benefit through the obtained biogas. This paper aims to continue the effort to adopt data-driven control methods in the case of anaerobic digestion processes. The paper proposes a data-based Internal Model Control approach applied to an anaerobic digestion process. The paper deals extensively with the issue of choosing the reference model and proposing an engineering approach to this issue. The paper also addresses the issue of verifying robust stability, a very important aspect considering the uncertainties that characterize bioprocesses in general. The approach proposed in the paper is validated through a numerical simulation using the Anaerobic Digestion Model No. 1. During the validation of the proposed control solution, the main operating conditions were analyzed, such as the setpoint tracking performance, the rejection of disturbance generated by variations in the influent concentration, and the effect of the measurement noise on the controlled variable.

Nonlinear Term Compensation with Data-Driven Control and its Application for Shaking-Table

Nonlinear Term Compensation with Data-Driven Control and its Application for Shaking-Table

Design of a Data-Driven Control System based on Reference Model using Predicted Input/Output Responses

In recent years, data-driven control schemes that do not require system modeling have been actively studied. These schemes use only a set of experimental data to design a controller that realizes the desired reference output offline. However, it is necessary to consider the output response and the input response since there is a limit of the actuator performance in actual machines. This paper proposes a new data-driven control scheme that can predict the input/output responses of an unknown system in offline using a set of operating data. The effectiveness of the proposed scheme is numerically verified by a simulation example.