This book proposes a number of contributions that try to overcome the current limitations of the state-of-the-art to make the direct data-driven design technology competitive with model-based alternatives. Moreover, challenging modeling problems in modern engineering systems are addressed in a novel way to show both the methods and the implementation tricks that potentially make an application successful. The book is structured in two parts. The first part is dedicated to application-oriented system identification and proposes four contributions in which existing techniques are complemented with additional tools to deal with challenging real-world problems. The second part is devoted to data-driven design and deals with the estimation of application-oriented parameters as well as direct identification of controllers and filters within complex scenarios.

This chapter addresses the problem of nonparametric identification of Wiener systems using a Kernel-based approach. Salient features of the proposed framework are its ability to exploit both positive and negative samples, and the fact that it does not require prior knowledge of the dimension of the output of the linear subsystem. Thus, it can be considered as a generalization to dynamical systems of kernel-based nonlinear manifold embedding methods recently developed in the machine-learning field. The main result of the chapter shows that while in principle, the proposed approach results in a non-convex problem, a tractable convex relaxation can be obtained by using a combination of polynomial optimization and rank-minimization techniques. The main advantage of the proposed algorithm stems from the fact that, since it is based on kernel ideas, it uses scalar inner products of the observed data, rather than the data itself. Hence, it can comfortably handle cases involving systems with high dimensional outputs. A practical scenario where such situation arises is activity classification from video data, since here each data point is a frame in a video sequence, and hence its dimension is typically O(10³) even when using low resolution videos.

Aerospace structures are often submitted to air-load tests to check possible unstable structural modes that lead to failure. These tests induce structural oscillations stimulating the system with different wind velocities, known as flutter test. An alternative is assessing critical operating regimes through simulations. Although cheaper, modelbased flutter tests rely on an accurate simulation model of the structure under investigation. This chapter addresses the data-driven flutter modeling using state-space linear parameter varying (LPV) models. The estimation algorithm employs support vector machines to represent the functional dependence between the model coefficients and the scheduling signal, which values can be used to account for different operating conditions. Besides versatile, that model structure allows the formalization of the estimation task as a linear least-squares problem. The proposed method also exploits the ensemble concept, which consists of estimating multiple models from different data partitions. These models are merged into a final one, according to their ability to reproduce a validation data segment. A case study based on real data shows that this approach resulted in a more accurate model for the available data. The local stability of the identified LPV model is also investigated to provide insights about critical operating ranges as a function of the magnitude of the input and output signals.

This chapter presents the identification of a web-winding system as a linear parameter-varying (LPV) system with the reel radius as the time-varying parameter. This system is nonlinear, time-varying and input-output unstable. Two identification methods are considered: in the first one, an LPV model is estimated in a single step using a novel approach based on sparse identification and set membership optimality evaluation. In the second one, several local linear time-invariant (LTI) models are identified using classical identification algorithms, and the overall LPV model is constructed as a weighted sum of the local models. The two methods are applied to experimental data measured on a real web-winding machine.

The monitoring and control of battery systems can be enhanced by data collection and analysis that provide insight into the internal behavior of the battery. A well-known example is electrochemical impedance spectroscopy (EIS), which is equivalent to estimating the frequency response of the battery impedance at a particular operating condition. System identification provides a method for implementing EIS using hardware commonly found in advanced battery-management systems. In this chapter, a possible implementation of online system identification is discussed and illustrated using both simulation and experimental data.

In metrology, a given measurement technique has fundamental speed and accuracy limitations imposed by physical laws. Data processing allows us to overcome these limitations by using prior knowledge about the sensor dynamics. The prior knowledge considered in this paper is a model class to which the sensor dynamics belongs. We present methods that are applicable to linear time-invariant processes and are suitable for real-time implementation on a digital signal processor.

Iterative learning control (ILC) enables high control performance through learning from measured data using limited model knowledge, typically in the form of a nominal parametric model. Robust stability requires robustness to modeling errors, often due to deliberate undermodeling. The aim of this chapter is to outline a range of design approaches for multivariable ILC that is suited for engineering applications, with specific attention to addressing interaction using limited model knowledge. The proposed methods either address the interaction in the nominal model or as uncertainty, i.e., through robust stability. The result is a range of techniques, including the use of the structured singular value (SSV) and Gershgorin bounds, that provide a different trade-offbetween modeling requirements, i.e., modeling effort and cost, and achievable performance. This allows control engineers to select the approach that best fits the modeling budget and control requirements. This trade-offis demonstrated in case studies on industrial printers. Additionally, two learning approaches are presented that are compatible with, and provide extensions to, the developed multivariable design framework: model-free iterative learning and ILC for varying tasks.

In this chapter, the problem of estimating in a model-free manner the H_∞ norm of a linear dynamic system is discussed at a tutorial level. Two recently developed methods for addressing this problem are presented, namely the power iterations method and a class of multi-armed bandit (MAB) algorithms. Due to reasons of space, many details are omitted, but references are provided to complement this exposition.

In this chapter, we compare two approaches to the data-driven control (DDC) design problem. In this framework, the controllers are directly identified from data avoiding the plant identification step. The analyzed approaches are virtual reference feedback tuning (VRFT) and set-membership tuning (SMT) controller. They differ in the assumptions about the noise affecting the experimental data and the criteria to select an optimal controller. The former strategy assumes an stochastic description of the unknown signals, while the latter imposes an unknown but bounded (UBB) noise structure. Both methodologies are described and their main theoretical results are reported. The two approaches are evaluated on an experimental case study, consisting of the controller tuning for an active suspension (AS) system. Three Monte Carlo experiments are performed, where 100 controllers are derived from data affected by measurement noise using both methods, and their performance is evaluated on the experimental test-bench. Results show that both approaches offer a similar performance when the size of the dataset is much larger than the dimension of the controller parameters vector. However, for reduced datasets, the SMT approach gives consistent results while the VRFT method is not able to extract useful information. The same behavior is observed when the two approaches are applied to datasets affected by process disturbances. It is observed that the root mean squared error of the resulting loops can be up to 30 times lower using the set membership method for reduced datasets.

The Fisher information matrix (FIM) has long been of interest in statistics and other areas. It is widely used to measure the amount of information and calculate the lower bound for the variance for maximum likelihood estimation (MLE). In practice, we do not always know the actual FIM. This is often because obtaining the firstor second-order derivative of the log-likelihood function is difficult, or simply because the calculation of FIM is too formidable. In such cases, we need to utilize the approximation of FIM. In general, there are two ways to estimate FIM. One is to use the product of gradient and the transpose of itself, and the other is to calculate the Hessian matrix and then take negative sign. Mostly people use the latter method in practice. However, this is not necessarily the optimal way. To find out which of the two methods is better, we need to conduct a theoretical study to compare their efficiency. In this paper, we mainly focus on the case where the unknown parameter that needs to be estimated by MLE is scalar, and the random variables we have are independent. In this scenario, FIM is virtually Fisher information number (FIN). Using the Central Limit Theorem (CLT), we get asymptotic variances for the two methods, by which we compare their accuracy. Taylor expansion assists in estimating the two asymptotic variances. A numerical study is provided as an illustration of the conclusion. The next is a summary of limitations of this paper. We also enumerate several fields of interest for future study in the end of this paper.

Modeling is recognized to be one of the toughest and most time-consuming tasks in modern nonlinear control engineering applications. Linear parameter-varying (LPV) models deal with such complex problems in an effective way, by exploiting wellestablished tools for linear systems while, at the same time, being able to accurately describe highly nonlinear and time-varying plants. When LPV models are derived from experimental data, it is difficult to estimate a priori how modeling errors will affect the closed-loop performance. In this work, a method is proposed to directly map data onto LPV controllers. Specifically, a hierarchical structure is proposed both to maximize the system performance and to handle signal constraints. The effectiveness of the approach is illustrated via suitable simulation tests.

In this chapter, an innovative approach to fault detection for nonlinear dynamic systems is proposed, based on the recently introduced quasi-local set membership-identification method, overcoming some relevant issues proper of the “classical” techniques. The approach is based on the direct identification from experimental data of a suitable filter and related uncertainty bounds. These bounds are used to detect when a change (e.g., a fault) has occurred in the dynamics of the system of interest. The main advantage of the approach compared to the existing methods is that it avoids the utilization of complex modeling and filter design procedures, since the filter/observer is directly designed from data. Other advantages are that the approach does not require to choose any threshold (as typically done in many “classical” techniques), and it is not affected by under-modeling problems. An experimental study regarding fault detection for a drone actuator is finally presented to demonstrate the effectiveness of the proposed approach.

The frequency-domain methods that exist for investigating the behaviour of linear systems have become fundamental tools for the control systems engineer. However, due to the increasedperformance demands on today's industrial systems, the effects of certain nonlinearities can no longer be neglected in modern control applications; for such systems, direct application of these frequency-domain tools is not possible. In the current literature, however, frequency-domain methods exist where the underlying linear dynamics of a nonlinear system can be captured in an identification experiment; in this manner, the nonlinear system is replaced by a linear model with a noise source where a best linear approximation of the nonlinear system is obtained with an associated frequency-dependent uncertainty. With the frequency-domain data and uncertainty obtained from an identification experiment, robust control algorithms can then be used to ensure performance for the underlying linear system. This chapter presents a data-driven robust control strategy which implements a convex optimization algorithm to ensure the performance and closed-loop stability of a linear system that is subject to nonlinear distortions (by considering a model-reference objective). The effectiveness of the proposed data-driven method is illustrated by designing a controller for an inertial positioning system that possesses nonlinear torsional dynamics.