arXiv subjects

Tim Martin

Publications and source records attributed to Tim Martin.

12 recordsLinked to original sources

arXiv2025

Control-Oriented System Identification: Classical, Learning, and Physics-Informed Approaches

We survey classical, machine learning, and data-driven system identification approaches to learn control-relevant and physics-informed models of dynamical systems. Recently, machine learning approaches have enabled system identification from noisy, high-dimensional, and complex data. However, their utility is limited by their ability to provide provable guarantees on control-relevant properties. Meanwhile, control theory has identified several properties that are useful in analysis and control synthesis, such as dissipativity, monotonicity, energy conservation, and symmetry-preserving structures. We posit that merging system identification with such control-relevant or physics-informed properties can provide useful inductive bias, enhance explainability, enable control synthesis with provable guarantees, and improve sample complexity. We formulate system identification as an optimization problem where control-relevant properties can be enforced through direct parameterization (constraining the model structure to satisfy a desired property by construction), soft constraints (encouraging control-relevant properties through regularization or penalty terms), and hard constraints (imposing control-relevant properties as constraints in the optimization problem). Through this lens, we survey methods to learn physics-informed and control-relevant models spanning classical linear and nonlinear system identification, machine learning approaches, and direct identification through data-driven and behavioral representations. We also provide several expository examples that are accompanied by code and brief tutorials on a public Github repository. We also describe challenging directions for future research, including identification in networked, switched, and time-varying systems, experiment design, and bridging the gaps between data-driven, learning-based, and control-oriented approaches.

eess.SY↗

arXiv2024

On autoregressive deep learning models for day-ahead wind power forecasting with irregular shutdowns due to redispatching

Renewable energies and their operation are becoming increasingly vital for the stability of electrical power grids since conventional power plants are progressively being displaced, and their contribution to redispatch interventions is thereby diminishing. In order to consider renewable energies like Wind Power (WP) for such interventions as a substitute, day-ahead forecasts are necessary to communicate their availability for redispatch planning. In this context, automated and scalable forecasting models are required for the deployment to thousands of locally-distributed onshore WP turbines. Furthermore, the irregular interventions into the WP generation capabilities due to redispatch shutdowns pose challenges in the design and operation of WP forecasting models. Since state-of-the-art forecasting methods consider past WP generation values alongside day-ahead weather forecasts, redispatch shutdowns may impact the forecast. Therefore, the present paper highlights these challenges and analyzes state-of-the-art forecasting methods on data sets with both regular and irregular shutdowns. Specifically, we compare the forecasting accuracy of three autoregressive Deep Learning (DL) methods to methods based on WP curve modeling. Interestingly, the latter achieve lower forecasting errors, have fewer requirements for data cleaning during modeling and operation while being computationally more efficient, suggesting their advantages in practical applications.

cs.LG↗

arXiv2023

Guarantees for data-driven control of nonlinear systems using semidefinite programming: A survey

This survey presents recent research on determining control-theoretic properties and designing controllers with rigorous guarantees using semidefinite programming and for nonlinear systems for which no mathematical models but measured trajectories are available. Data-driven control techniques have been developed to circumvent a time-consuming modelling by first principles and because of the increasing availability of data. Recently, this research field has gained increased attention by the application of Willems' fundamental lemma, which provides a fertile ground for the development of data-driven control schemes with guarantees for linear time-invariant systems. While the fundamental lemma can be generalized to further system classes, there does not exist a comparable data-based system representation for nonlinear systems. At the same time, nonlinear systems constitute the majority of practical systems. Moreover, they include additional challenges such as data-based surrogate models that prevent system analysis and controller design by convex optimization. Therefore, a variety of data-driven control approaches has been developed with different required prior insights into the system to ensure a guaranteed inference. In this survey, we will discuss developments in the context of data-driven control for nonlinear systems. In particular, we will focus on methods based on system representations providing guarantees from finite data, while the analysis and the controller design boil down to convex optimization problems given as SDP. Thus, these approaches achieve reasonable advances compared to the state-of-the-art system analysis and controller design by models from system identification. Specifically, the paper covers system representations based on extensions of Willems' fundamental lemma, set membership, kernel techniques, the Koopman operator, and feedback linearization.

math.OC↗

arXiv2022

AutoPV: Automated photovoltaic forecasts with limited information using an ensemble of pre-trained models

Accurate PhotoVoltaic (PV) power generation forecasting is vital for the efficient operation of Smart Grids. The automated design of such accurate forecasting models for individual PV plants includes two challenges: First, information about the PV mounting configuration (i.e. inclination and azimuth angles) is often missing. Second, for new PV plants, the amount of historical data available to train a forecasting model is limited (cold-start problem). We address these two challenges by proposing a new method for day-ahead PV power generation forecasts called AutoPV. AutoPV is a weighted ensemble of forecasting models that represent different PV mounting configurations. This representation is achieved by pre-training each forecasting model on a separate PV plant and by scaling the model's output with the peak power rating of the corresponding PV plant. To tackle the cold-start problem, we initially weight each forecasting model in the ensemble equally. To tackle the problem of missing information about the PV mounting configuration, we use new data that become available during operation to adapt the ensemble weights to minimize the forecasting error. AutoPV is advantageous as the unknown PV mounting configuration is implicitly reflected in the ensemble weights, and only the PV plant's peak power rating is required to re-scale the ensemble's output. AutoPV also allows to represent PV plants with panels distributed on different roofs with varying alignments, as these mounting configurations can be reflected proportionally in the weighting. Additionally, the required computing memory is decoupled when scaling AutoPV to hundreds of PV plants, which is beneficial in Smart Grids with limited computing capabilities. For a real-world data set with 11 PV plants, the accuracy of AutoPV is comparable to a model trained on two years of data and outperforms an incrementally trained model.

cs.LG↗

arXiv2022

Gaussian inference for data-driven state-feedback design of nonlinear systems

Data-driven control of nonlinear systems with rigorous guarantees is a challenging problem as it usually calls for nonconvex optimization and requires often knowledge of the true basis functions of the system dynamics. To tackle these drawbacks, this work is based on a data-driven polynomial representation of general nonlinear systems exploiting Taylor polynomials. Thereby, we design state-feedback laws that render a known equilibrium point globally asymptotically stable while operating with respect to a desired quadratic performance criterion. The calculation of the polynomial state feedback boils down to a single sum-ofsquares optimization problem, and hence to computationally tractable linear matrix inequalities. Moreover, we examine state-input data in presence of Gaussian noise by Bayesian inference to overcome the conservatism of deterministic noise characterizations from recent data-driven control approaches for Gaussian noise.

math.OC↗

arXiv2022

Accelerating LHC event generation with simplified pilot runs and fast PDFs

Poor computing efficiency of precision event generators for LHC physics has become a bottleneck for Monte-Carlo event simulation campaigns. We provide solutions to this problem by focusing on two major components of general-purpose event generators: The PDF evaluator and the matrix-element generator. For a typical production setup in the ATLAS experiment, we show that the two can consume about 80% of the total runtime. Using NLO simulations of $pp\to\ell^+\ell^-+\text{jets}$ and $pp\to t\bar{t}+\text{jets}$ as an example, we demonstrate that the computing footprint of LHAPDF and Sherpa can be reduced by factors of order 10, while maintaining the formal accuracy of the event sample. The improved codes are made publicly available.

hep-ph↗

arXiv2021

Concepts for Automated Machine Learning in Smart Grid Applications

Undoubtedly, the increase of available data and competitive machine learning algorithms has boosted the popularity of data-driven modeling in energy systems. Applications are forecasts for renewable energy generation and energy consumption. Forecasts are elementary for sector coupling, where energy-consuming sectors are interconnected with the power-generating sector to address electricity storage challenges by adding flexibility to the power system. However, the large-scale application of machine learning methods in energy systems is impaired by the need for expert knowledge, which covers machine learning expertise and a profound understanding of the application's process. The process knowledge is required for the problem formalization, as well as the model validation and application. The machine learning skills include the processing steps of i) data pre-processing, ii) feature engineering, extraction, and selection, iii) algorithm selection, iv) hyperparameter optimization, and possibly v) post-processing of the model's output. Tailoring a model for a particular application requires selecting the data, designing various candidate models and organizing the data flow between the processing steps, selecting the most suitable model, and monitoring the model during operation - an iterative and time-consuming procedure. Automated design and operation of machine learning aim to reduce the human effort to address the increasing demand for data-driven models. We define five levels of automation for forecasting in alignment with the SAE standard for autonomous vehicles, where manual design and application reflect Automation level 0.

cs.LG↗

arXiv2021

Data-driven system analysis of nonlinear systems using polynomial approximation

In the context of data-driven control of nonlinear systems, many approaches lack of rigorous guarantees, call for nonconvex optimization, or require knowledge of a function basis containing the system dynamics. To tackle these drawbacks, we establish a polynomial representation of nonlinear functions based on a polynomial sector by Taylor's theorem and a set-membership for Taylor polynomials. The latter is obtained from finite noisy samples. By incorporating the measurement noise, the error of polynomial approximation, and potentially given prior knowledge on the structure of the system dynamics, we achieve computationally tractable conditions by sum of squares relaxation to verify dissipativity and incremental dissipativity of nonlinear dynamical systems with rigorous guarantees. The framework is extended by combining multiple Taylor polynomial approximations which yields a less conservative piecewise polynomial system representation. The proposed approach is applied for numerical and experimental examples. There it is compared to a least-squares-error model including knowledge from first principle.

eess.SY↗

arXiv2021

Data-driven inference on optimal input-output properties of polynomial systems with focus on nonlinearity measures

In the context of dynamical systems, nonlinearity measures quantify the strength of nonlinearity by means of the distance of their input-output behaviour to a set of linear input-output mappings. In this paper, we establish a framework to determine nonlinearity measures and other optimal input-output properties for nonlinear polynomial systems without explicitly identifying a model but from a finite number of input-state measurements which are subject to noise. To this end, we deduce from data for the unidentified ground-truth system three possible set-membership representations, compare their accuracy, and prove that they are asymptotically consistent with respect to the amount of samples. Moreover, we leverage these representations to compute guaranteed upper bounds on nonlinearity measures and the corresponding optimal linear approximation model via semi-definite programming. Furthermore, we extend the established framework to determine optimal input-output properties described by time domain hard integral quadratic constraints.

eess.SY↗

arXiv2020

Dissipativity verification with guarantees for polynomial systems from noisy input-state data

In this paper, we investigate the verification of dissipativity properties for polynomial systems without an explicitly identified model but directly from noise-corrupted measurements. Contrary to most data-driven approaches for nonlinear systems, we determine dissipativity properties over all finite time horizons using noisy input-state data. To this end, we propose two noise characterizations to deduce two data-based set-membership representations of the ground-truth system. Each representation then serves as a framework to derive computationally tractable conditions to verify dissipativity properties with rigorous guarantees from noise-corrupted data using sum of squares (SOS) optimization.

eess.SY↗

arXiv2020

Iterative data-driven inference of nonlinearity measures via successive graph approximation

In this paper, we establish an iterative data-driven approach to derive guaranteed bounds on nonlinearity measures of unknown nonlinear systems. In this context, nonlinearity measures quantify the strength of the nonlinearity of a dynamical system by the distance of its input-output behaviour to a set of linear models. First, we compute a guaranteed upper bound of these measures by given input-output samples based on a data-based non-parametric set-membership representation of the ground-truth system and local inferences of nonlinearity measures. Second, we propose an algorithm to improve this bound iteratively by further samples of the unknown input-output behaviour.

eess.SY↗

arXiv2016

Probing Collective Effects in Hadronisation with the Extremes of the Underlying Event

We define a new set of observables to probe the structure of the underlying event in hadron collisions. We use the conventional definition of the `transverse region' in jet events and, for a fixed window in jet $p_\perp$, propose to measure several discriminating quantities as a function of the level of activity in the transverse region. The measurement of these observables in LHC data would reveal whether, e.g., the properties of `low-UE' events are compatible with equivalent measurements in $e^+e^-$ collisions (jet universality), and whether the scaling behaviour towards `high-UE' events exhibits properties of non-trivial soft-QCD dynamics, such as colour re-connections or other collective phenomena. We illustrate at $\sqrt{s} = 13$ TeV that significant discriminatory power is obtained in comparisons between MC models with varying treatments of collective effects, including Pythia 8, EPOS, and Dipsy.

hep-ph↗