Data-enabled predictive control (DeePC) is a recently proposed approach that combines system identification, estimation and control in a single optimization problem, for which only recorded input/output data of the examined system is required. The same premise holds for the subspace predictive control (SPC) method in which a multi-step prediction model is identified from the same data as required for DeePC. This model is then used to formulate a similar optimal control problem. In this work we investigate the relationship between DeePC and SPC. Our primary contribution is to show that SPC is equivalent to DeePC in the deterministic case. We also show the equivalence of both methods in a special case for the non-deterministic formulation. We investigate the advantages and shortcomings of DeePC as opposed to SPC with and without measurement noise and illustrate them with a simulation example.
Direct data-driven control has attracted substantial interest since it enables optimization-based control without the need for a parametric model. This paper presents a new Instrumental Variable~(IV) approach to Data-enabled Predictive Control (DeePC) that results in favorable noise mitigation properties, and demonstrates the direct equivalence between DeePC and Subspace Predictive Control (SPC). The methodology relies on the derivation of the characteristic equation in DeePC along the lines of subspace identification algorithms. A particular choice of IVs is presented that is uncorrelated wit…
Willems' fundamental lemma and system level synthesis both characterize a linear dynamic system by its input/output sequences. In this work, we extend the application of the fundamental lemma from deterministic to uncertain LTI systems and then further prove this extension to be equivalent to system level synthesis. Based on this uncertain extension, a robust closed-loop data-enabled predictive control scheme is proposed, where a causal feedback control law is further derived. Two numerical experiments, including the temperature control of a single-zone building, are carried out to validate th…
This paper presents a robust and kernelized data-enabled predictive control (RoKDeePC) algorithm to perform model-free optimal control for nonlinear systems using only input and output data. The algorithm combines robust predictive control and a non-parametric representation of nonlinear systems enabled by regularized kernel methods. The latter is based on implicitly learning the nonlinear behavior of the system via the representer theorem. Instead of seeking a model and then performing control design, our method goes directly from data to control. This allows us to robustify the control input…
Data-driven control that circumvents the process of system identification by providing optimal control inputs directly from system data has attracted renewed attention in recent years. In this paper, we focus on understanding the effects of the regularization on the data-enabled predictive control (DeePC) algorithm. We provide theoretical motivation and interpretation for including a quadratic regularization term. Our analysis shows that the quadratic regularization term leads to robust and optimal solutions with regards to disturbances affecting the data. Moreover, when the input/output const…
Network-Realised Model Predictive Control Part I: NRF-Enabled Closed-loop Decomposition
Department of Automatic Control；Systems Engineering, ``Politehnica'' University of Bucharest, Bucharest, Romania -2.5mm；Laboratoire des Signaux et Syst\`emes, CentraleSup\'elec, Paris-Saclay University, Gif-sur-Yvette, France -10mm
Individual Pitch Control (IPC) is an effective and widely-used strategy to mitigate blade loads in wind turbines. However, conventional IPC fails to cope with blade and actuator faults, and this situation may lead to an emergency shutdown and increased maintenance costs. In this paper, a Fault-Tolerant Individual Pitch Control (FTIPC) scheme is developed to accommodate these faults in Floating Offshore Wind Turbines (FOWTs), based on a Subspace Predictive Repetitive Control (SPRC) approach. To fulfill this goal, an online subspace identification paradigm is implemented to derive a linear appro…
Modern wind turbine control algorithms typically utilize rotor effective wind speed measured from an anemometer on the turbine's nacelle. Unfortunately, the measured wind speed from such a single measurement point does not give a good representation of the effective wind speed over the blades, as it does not take the varying wind condition within the entire rotor area into account. As such, Blade Effective Wind Speed (BEWS) estimation can be seen as a more accurate alternative. This paper introduces a novel Subspace Predictive Repetitive Estimator (SPRE) approach to estimate the BEWS using bla…
We introduce a general framework for robust data-enabled predictive control (DeePC) for linear time-invariant (LTI) systems. The proposed framework enables us to obtain model-free optimal control for LTI systems based on noisy input/output data. More specifically, robust DeePC solves a min-max optimization problem to compute the optimal control sequence that is resilient to all possible realizations of the uncertainties in the input/output data within a prescribed uncertainty set. We present computationally tractable reformulations of the min-max problem with various uncertainty sets. Furtherm…
Individual Pitch Control (IPC) is an effective control strategy to mitigate the blade loads on large-scale wind turbines. Since IPC usually requires high pitch actuation, the safety constraints of the pitch actuator should be taken into account when designing the controller. This paper introduces a constrained Subspace Predictive Repetitive Control (SPRC) approach, which considers the limitation of blade pitch angle and pitch rate. To fulfill this goal, a model predictive control scheme is implemented in the fully data-driven SPRC approach to incorporate the physical limitations of the pitch a…
We employ a novel data-enabled predictive control (DeePC) algorithm in voltage source converter (VSC) based high-voltage DC (HVDC) stations to perform safe and optimal wide-area control for power system oscillation damping. Conventional optimal wide-area control is model-based. However, in practice detailed and accurate parametric power system models are rarely available. In contrast, the DeePC algorithm uses only input/output data measured from the unknown system to predict the future trajectories and calculate the optimal control policy. We showcase that the DeePC algorithm can effectively a…
As Floating Offshore Wind Turbines (FOWTs) operate in deep waters and are subjected to stressful wind and wave induced loads, they are more prone than onshore counterparts to experience faults and failure. In particular, the pitch system may experience Pitch Actuator Stuck (PAS) type of faults, which will result in a complete loss of control authority. In this paper, a novel fast and adaptive solution is developed by integrating a model-based Fault Diagnosis (FD) scheme and the Subspace Predictive Repetitive Control (SPRC). The FD role is to quickly detect and isolate the failed pitch actuator…
Velocity-Form Data-Enabled Predictive Control of Soft Robots under Unknown External Payloads
Department of Mechanical Engineering, Michigan State University（机械工程系，密歇根州立大学）；Department of Mechanical Engineering, University of California Riverside（机械工程系，加州大学河滨分校）；Department of Electrical and Computer Engineering, Michigan State University（电气与计算机工程系，密歇根州立大学）；Department of Electrical and Computer Engineering, University of Michigan（电气与计算机工程系，密歇根大学）
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 paper a novel data-driven nonlinear model predictive control (NMPC) is proposed based the recurrent high-order neural network (RHONN) modelling method. First, the new RH…
National University of Sciences and Technology（国立科技大学）
We analyze damage propagation modeling of turbo-engines in a data-driven approach. We investigate subspace tracking assuming a low dimensional manifold structure and a static behavior during the healthy state of the machines. Our damage propagation model is based on the deviation of the data from the static behavior and uses the notion of health index as a measure of the condition. Hence, we incorporate condition-based maintenance and estimate the remaining useful life based on the current and previous health indexes. This paper proposes an algorithm that adapts well to the dynamics of the dat…
Model-Free Control for Residential Heating: Deployment and Simulation of Nonlinear Data-Enabled Predictive Control
University of Oslo（奥斯陆大学）；Swiss Federal Laboratories for Materials Science and Technology (Empa)（瑞士联邦材料科技与工程研究院）；University of Pennsylvania（宾夕法尼亚大学）；Eindhoven University of Technology（埃因霍温理工大学）；University of Groningen（格罗宁根大学）
Willems' fundamental lemma asserts that all trajectories of a linear time-invariant system can be obtained from a finite number of measured ones, assuming that controllability and a persistency of excitation condition hold. We show that these two conditions can be relaxed. First, we prove that the controllability condition can be replaced by a condition on the controllable subspace, unobservable subspace, and a certain subspace associated with the measured trajectories. Second, we prove that the persistency of excitation requirement can be relaxed if the degree of a certain minimal polynomial …
