Data-driven Predictive Control Research Articles

Implicit Predictors in Regularized Data-Driven Predictive Control

We introduce the notion of implicit predictors, which characterize the input-(state)-output prediction behavior underlying a predictive control scheme, even if it is not explicitly enforced as an equality constraint (as in traditional model or subspace predictive control). To demonstrate this concept, we derive and analyze implicit predictors for some basic data-driven predictive control (DPC) schemes, which offers a new perspective on this popular approach that may form the basis for modified DPC schemes and further theoretical insights.

Data-Driven Multiple Shooting for Stochastic Optimal Control

The implementation of data-driven predictive control schemes based on Willems’ fundamental lemma often relies on a single-shooting approach, i.e., it uses one large Hankel matrix to cover the entire optimization horizon. However, the numerical solution is fostered by the use of multiple segmented horizons which require less data in smaller Hankel matrices. This letter extends the segmentation idea towards multiple shooting for data-driven optimal control of stochastic LTI systems. Using a stochastic variant of the fundamental lemma and polynomial chaos expansions, we propose a multiple-shooting formulation which combines trajectory segmentation and moment matching. We show that, for LTI systems subject to Gaussian noise of finite variance, our formulation is without loss of optimality while it allows for a significant reduction of the problem dimension in Gaussian and non-Gaussian settings. We draw upon a numerical example to compare the proposed framework to the usual single-shooting approach.

Towards Data-Driven Predictive Control Using Wavelets*

Recently, data-driven predictive control schemes based on the fundamental lemma by Willems et al. (2005) have received widespread research attention. However, the large and dense Hankel matrices appearing in the equality constraints of the underlying optimal control problem can lead to numerical complications. This paper tailors the fundamental lemma to LTI dynamics resulting from the application of the wavelet transform to input-output trajectory data. Directly using wavelet coefficients to construct Hankel matrices and to formalize the online optimization problem, we propose a data-driven predictive control scheme. Due to the down-sampling nature of the wavelet transform, the scheme is built around Hankel matrices of reduced size, which is advantageous for computations. Furthermore, in the presence of substantial measurement noise the wavelet transform is beneficial for closed-loop performance. We draw upon simulation examples to illustrate the efficacy of the proposed methodology.

Maximum Likelihood Estimation in Data-Driven Modeling and Control

Recently, various algorithms for data-driven simulation and control have been proposed based on the Willems’ fundamental lemma. However, when collected data are noisy, these methods lead to ill-conditioned data-driven model structures. In this article, we present a maximum likelihood framework to obtain an optimal data-driven model, the signal matrix model, in the presence of output noise. Data compression and noise-level estimation schemes are also proposed to apply the algorithm efficiently to large datasets and unknown noise-level scenarios. Two approaches in system identification and receding horizon control are developed based on the derived optimal estimator. The first one identifies a finite impulse response model. This approach improves the least-squares estimator with less restrictive assumptions. The second one applies the signal matrix model as the predictor in predictive control. The control performance is shown to be better than existing data-driven predictive control algorithms, especially under high noise levels. Both approaches demonstrate that the derived estimator provides a promising framework to apply data-driven algorithms to noisy data.

Data-driven predictive control for floating offshore wind turbines based on deep learning and multi-objective optimization

In order to deal with the problems of complicated modeling and the conflicts of control objectives in the control of floating offshore wind turbines (FOWTs), a multi-objective predictive control strategy for FOWTs based on a deep learning model and multi-objective optimization is proposed. In this strategy, the dynamic prediction model of the FOWT based on a gated recurrent neural network is established. Based on the dynamic prediction model, a multi-objective predictive control algorithm for individual pitch control of FOWTs is developed. The multi-objective distribution estimation algorithm is used to optimize the pitch angle considering the constraints of the pitch angle setting. The proposed method is simulated in different wind conditions by FAST. The results show that, compared with the collective pitch control and the gain scheduling PI individual pitch control, the output power of the proposed method is closer to the rated power, and the proposed method significantly reduces the mechanical load of the blade root. Moreover, compared with the gain scheduling PI individual pitch control, the proposed method effectively restrains platform pitching motion.

Data-Driven Predictive Control of Exoskeleton for Hand Rehabilitation with Subspace Identification.

This study proposed a control method, a data-driven predictive control (DDPC), for the hand exoskeleton used for active, passive, and resistive rehabilitation. DDPC is a model-free approach based on past system data. One of the strengths of DDPC is that constraints of states can be added to the controller while performing the controller design. These features of the control algorithm eliminate an essential problem for rehabilitation robots in terms of easy customization and safe repetitive rehabilitation tasks that can be planned within certain constraints. Experiments were carried out with a designed hand rehabilitation system under repetitive and various therapy tasks. Real-time experiment results demonstrate the feasibility and efficiency of the proposed control approach to rehabilitation systems.

Distributed Data-Driven Predictive Control for Hybrid Connected Vehicle Platoons With Guaranteed Robustness and String Stability

As a critical component of the Internet of Things, connected automated vehicles (CAVs) are progressively gaining attention for their benefits in terms of increased safety and reduced traffic congestion. In this article, a novel distributed data-driven model-predictive control (DDMPC) approach including feedforward for disturbance is proposed for cruise control of a hybrid platoon with a combination of human-operated and autonomous vehicles. By employing a predictor constructed from input/output data, predictive controllers are obtained without depending on the characteristic information of the system. A robustness analysis is performed with a combination of the input-to-state stability (ISS) theory with the sampled-data systems theory, and the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mathcal {L}_{2}$ </tex-math></inline-formula> -norm string stability is ensured by strict mathematical proof. In addition, we also discuss the asymptotic stability when the controller switches. CarSim simulation and bench experiment results verify that the DDMPC for connected vehicles can be robust to velocity disturbances and achieve satisfactory performance in ensuring string stability.

Toward data-driven predictive control of multi-energy distribution systems

The necessity to obtain, to parametrize, and to maintain models of the underlying dynamics impedes predictive control of energy systems in many real-world applications. To alleviate the need for explicit model knowledge this paper proposes a framework for the operation of distributed multi-energy systems via data-driven predictive control with stochastic uncertainties. Instead of modeling the dynamics of the individual distributed energy resources, our approach relies on measured input–output data of the distributed resources only. Moreover, we combine data-driven predictive control with forecasts of exogenous signals (renewable generations and demands) by Gaussian processes. A simulation study based on realistic data illustrates the efficacy of the proposed scheme to handle mild non-linearities and measurement noise.

A learning-based approach towards the data-driven predictive control of combined wastewater networks – An experimental study

Smart control in water systems aims to reduce the cost of infrastructure expansion by better utilizing the available capacity through real-time control. The recent availability of sensors and advanced data processing is expected to transform the view of water system operators, increasing the need for deploying a new generation of data-driven control solutions. To that end, this paper proposes a data-driven control framework for combined wastewater and stormwater networks. We propose to learn the effect of wet- and dry-weather flows through the variation of water levels by deploying a number of level sensors in the network. To tackle the challenges associated with combining hydraulic and hydrologic modelling, we adopt a Gaussian process-based predictive control tool to capture the dynamic effect of rain and wastewater inflows, while applying domain knowledge to preserve the balance of water volumes. To show the practical feasibility of the approach, we test the control performance on a laboratory setup, inspired by the topology of a real-world wastewater network. We compare our method to a rule-based controller currently used by the water utility operating the proposed network. Overall, the controller learns the wastewater load and the temporal dynamics of the network, and therefore significantly outperforms the baseline controller, especially during high-intensity rain periods. Finally, we discuss the benefits and drawbacks of the approach for practical real-time control implementations.

KNODE-MPC: A Knowledge-Based Data-Driven Predictive Control Framework for Aerial Robots

In this letter, we consider the problem of deriving and incorporating accurate dynamic models for model predictive control (MPC) with an application to quadrotor control. MPC relies on precise dynamic models to achieve the desired closed-loop performance. However, the presence of uncertainties in complex systems and the environments they operate in poses a challenge in obtaining sufficiently accurate representations of the system dynamics. In this letter, we make use of a deep learning tool, knowledge-based neural ordinary differential equations (KNODE), to augment a model obtained from first principles. The resulting hybrid model encompasses both a nominal first-principle model and a neural network learnt from simulated or real-world experimental data. Using a quadrotor, we benchmark our hybrid model against a state-of-the-art Gaussian Process (GP) model and show that the hybrid model provides more accurate predictions of the quadrotor dynamics and is able to generalize beyond the training data. To improve closed-loop performance, the hybrid model is integrated into a novel MPC framework, known as KNODE-MPC. Results show that the integrated framework achieves 60.2&#x0025; improvement in simulations and more than 21&#x0025; in physical experiments, in terms of trajectory tracking performance.

Pseudo-spectral optimization and data-driven control of vehicle start process with dual-clutch transmission

In this study, a dual-clutch transmission start control strategy based on pseudo-spectral optimization and data-driven control is proposed to respond to the time-varying start intentions, to reduce friction and jerk, and to improve the start quality. First, taking the jerk, start time, and friction work as the optimization indexes, the adaptive pseudo-spectral method is used to accurately determine the optimal clutch engagement target trajectory. Then, a real-time planning method for the target clutch engagement trajectory is proposed based on a dual deep gated recurrent unit network. Second, through partial least squares identification, a data-driven predictive control (DDPC) method based on the autoregressive with exogenous model is proposed. The model parameters are updated online by a multi-model filtering algorithm based on input and output data, allowing real-time adaptation to the system uncertainty and nonlinear characteristics. Simulations and experiments show that the proposed target clutch trajectory planning method can effectively respond to time-varying start intentions in real-time. In addition, the DDPC controller can adapt to the uncertainty and nonlinear characteristics of the system and, hence, improve the control accuracy.

Data-Driven Predictive Control With Switched Subspace Matrices for an SCR System

Selective catalytic reduction (SCR) systems are distributed systems with strong time-varying parameter characteristics such that an accurate model for it is difficult to establish. Its control task simultaneously achieving high NO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><i>x</i></sub> conversion efficiency and low NH <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sub> slip is a typical multi-objective and multi-constraint problem, which is suitable to be solved in the framework of the model predictive control (MPC). However, how to find a data-driven identification method based on the dynamic characteristics of an SCR system and a corresponding MPC method for satisfying its emission requirements remain a formidable challenge. The sufficient identification for the traditional identification method with fixed subspace model requires an excessively high order subspace matrix, such that a degradation in real-time performance is caused and the generality of the method under non-identification conditions is limited. In this paper, utilizing the transient data of the SCR system under the WHTC cycle, a novel identification method for some lower order subspace matrices excited by the segmented data referring to the dynamic of the ammonia coverage ratio is established. A corresponding predictive controller with the switched subspace matrices according to working conditions is designed in order to further improve its real-time performance, generality and robustness. The simulation results show that under the identification condition the proposed predictive controller compared to the traditional method can improve the emissions of NO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><i>x</i></sub> and NH <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sub> , that under the non-identification condition the proposed predictive controller can also improve the emissions and its optimization effects have better robustness to uncertainties of the transient cycle, and that the proposed predictive controller saves an significant computation time.

Data-driven MPC of descriptor systems: A case study for power networks

Recently, data-driven predictive control of linear systems has received wide-spread research attention. It hinges on the fundamental lemma by Willems et al. In a previous paper, we have shown how this framework can be applied to predictive control of linear time-invariant descriptor systems. In the present paper, we present a case study wherein we apply data-driven predictive control to a discrete-time descriptor model obtained by discretization of the power-swing equations for a nine-bus system. Our results show the efficacy of the proposed control scheme and they underpin the prospect of the data-driven framework for control of descriptor systems.

Safety-Aware and Data-Driven Predictive Control for Connected Automated Vehicles at a Mixed Traffic Signalized Intersection⋆

A typical urban signalized intersection poses significant modeling and control challenges in a mixed traffic environment consisting of connected automated vehicles (CAVs) and human-driven vehicles (HDVs). In this paper, we address the problem of deriving safe trajectories for CAVs in a mixed traffic environment that prioritizes rear-end collision avoidance when the preceding HDVs approach the yellow and red signal phases of the intersection. We present a predictive control framework that employs a recursive least squares algorithm to approximate in real time the driving behavior of the preceding HDVs and then uses this approximation to derive safety-aware trajectory in a finite horizon. We validate the effectiveness of our proposed framework through numerical simulation and analyze the robustness of the control framework.

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.

Improving Automatic Control of Upper-Limb Prosthesis Wrists Using Gaze-Centered Eye Tracking and Deep Learning.

Many upper-limb prostheses lack proper wrist rotation functionality, leading to users performing poor compensatory strategies, leading to overuse or abandonment. In this study, we investigate the validity of creating and implementing a data-driven predictive control strategy in object grasping tasks performed in virtual reality. We propose the idea of using gaze-centered vision to predict the wrist rotations of a user and implement a user study to investigate the impact of using this predictive control. We demonstrate that using this vision-based predictive system leads to a decrease in compensatory movement in the shoulder, as well as task completion time. We discuss the cases in which the virtual prosthesis with the predictive model implemented did and did not make a physical improvement in various arm movements. We also discuss the cognitive value in implementing such predictive control strategies into prosthetic controllers. We find that gaze-centered vision provides information about the intent of the user when performing object reaching and that the performance of prosthetic hands improves greatly when wrist prediction is implemented. Lastly, we address the limitations of this study in the context of both the study itself as well as any future physical implementations.

Willems’ Fundamental Lemma for Linear Descriptor Systems and Its Use for Data-Driven Output-Feedback MPC

In this letter we investigate data-driven predictive control of discrete-time linear descriptor systems. Specifically, we give a tailored variant of Willems’ fundamental lemma, which shows that for descriptor systems the non-parametric modeling via a Hankel matrix requires less data compared to linear time-invariant systems without algebraic constraints. Moreover, we use this description to propose a data-driven framework for optimal control and predictive control of discrete-time linear descriptor systems. For the latter, we provide a sufficient stability condition for receding-horizon control before we illustrate our findings with an example.

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.

Data-driven predictive control for the swing process of a cutter suction dredger

The working process of cutter suction dredger is complex, so it is difficult to establish accurate model by traditional physical modeling method. The final yield of cutter suction dredger is directly related to the density of the slurry in the pipeline, while the density is controlled by the swing process. Therefore, by analyzing the measured data of the dredger, it establishes the swing process mathematical model based on subspace theory. The algorithm is based on input–output data, simulation results show the algorithm is effective for the control application.

Exploring New Building Energy Saving Control Strategy Application under the Energy Internet of Things

This paper makes innovative research on developing a data-driven control strategy under the Energy Internet of Things architecture. On the one hand, the platform aims to provide data representation and interpretable analysis for different stakeholders (end users, construction operators or managers) to realize the flexibility and scalability of the platform; on the other hand, it can improve the thermal comfort and also reduce the power consumption of buildings. However, to process vast amounts of data, it is critical to select appropriate control methods and design optimization issues. Data-driven predictive control (DPC) is a control technology that replaces model-based predictive control (MPC). When applied to complex building operations, MPC is implemented by using the control-oriented data-driven model. The key to DPC technology is the use of CatBoost algorithm, which is highly interpretable and easy to be operated by stakeholders. This paper chooses TDNN, LightGBM, and CatBoost to compare and analyze building energy consumption. Numerical simulation results show that the CatBoost algorithm’s performance is better than other algorithms, and the complexity and implementation cost is significantly reduced.