# List of abstracts – talks

## Monday September 25

### Florian Dörfler, ETH Zürich: Data-Driven Control Based on Behavioral Systems Theory

We consider the problem of optimal and constrained control for unknown systems. A novel data-enabled predictive control method is presented that computes optimal and safe control policies. Using a finite number of data samples from the unknown system, our method uses a behavioral systems theory approach to learn a nonparametric system model used to predict future trajectories. To cope with nonlinearities and stochasticities, we propose salient regularizations to our problem formulation. Using techniques from optimal transport and distributionally robust optimization, we prove that these regularization indeed robustify our method. We show that, in the case of deterministic linear time-invariant systems, our method is equivalent to the widely adopted model predictive control, but it can also outperform subsequent system identification and model-based control. We illustrate our results with nonlinear and noisy simulations and experiments from robotics, power electronics, and power systems.

### Alessandro Chiuso, University of Padova: Data Driven Control - the thin line between model based and model free

In this presentation I will discuss an optimal, receding horizon, predictive control problem in a data drivencontext. The optimal solution will be derived, in a Bayesian framework, under very mild high-level assumptions on the unknown data generating mechanism. It will be shown that well known procedures recently introduced in the literature such as DeePC/$\gamma$-DDPC and their variants, where regularization is introduced ad-hoc to counter the effect of noise, are suboptimal special cases of our procedure. The Bayesian framework provides a convenient mean to link so called model-free and model-based procedures.

### Alexandre Proutiere, KTH Royal Institute of Technology: Finite-time Analysis of Linear System Identification: Sample Complexity Lower Bounds and Optimal Algorithms

This talk is based on joint work with Yassir Jedra (KTH). We survey recent advances in the finite-time analysis of linear system identification. This analysis is performed in the so-called fixed-budget and fixed confidence settings. In the fixed budget setting, the learner aims at estimating the state transition and the state-action transition matrices from a random system trajectory of fixed length, whereas in the fixed confidence setting, the learner further controls the length of the observed trajectory – she can stop when she believes that enough information has been gathered. In both settings, we analyze the sample complexity in the PAC framework defined as the length of the observed trajectory required to identify the system parameters with prescribed accuracy and confidence levels (epsilon, delta). The first part of the talk is devoted to the introduction of versatile information-theoretical techniques leading to instance-specific sample complexity lower bounds. By instance-specific, we mean that the lower bounds explicitly depend on the system to be identified, and hence, unlike the classical minimax bounds, really captures the identification hardness specific to the system. In the second part of the talk, we present a few results from random matrix theory that are instrumental in the finite-time performance analysis of classical estimation algorithms such as the Least Squares Estimator (LSE). Based on this analysis, we discuss scenarios where the optimality of the LSE can be established (in those scenarios, its performance matches our instancespecific sample complexity lower bounds).

### Vikram Krishnamurthy, Cornell University: Social sensing and reinforcement learning

This seminar is in two related parts. The first part discusses models for sequential decision making involving social learning. We also discuss sequential detection involving multi-agent decision makers and rational inattention models. The second part of the talk discusses inverse reinforcement learning (IRL) - namely how to estimate the utility function of a decision maker given its decisions. We discuss revealed preferences and Afriat's theorem from microeconomics for IRL, and also Bayesian IRL methods to detect the presence of a sequential detector from its decisions. As an illustrative example we discuss multimedia user engagement.

## Tuesday September 26

### Gianluigi Pillonetto, Aleksandr Aravkin, Daniel Gedon, Lennart Ljung, Antônio H. Ribeiro, Thomas B. Schön University of Padova, Washington University, Uppsala University, Linköping University, Uppsala University, Uppsala University: Deep networks for system identification: a survey

Deep learning is a topic of considerable current interest. The availability of massive data collections and powerful software resources has led to an impressive amount of results in many application areas that reveal essential but hidden properties of the observations. System identification learns mathematical descriptions of dynamic systems from input-output data and can thus benefit from the advances of deep neural networks to enrich the possible range of models to choose from. For this reason, we provide a survey of deep learning from a system identification perspective. We cover a wide spectrum of topics to enable researchers to understand the methods, providing rigorous practical and theoretical insights into the benefits and challenges of using them. The main aim of the identified model is to predict new data from previous observations. This can be achieved with different deep learning based modelling techniques and we discuss architectures commonly adopted in the literature, like feedforward, convolutional, and recurrent networks. Their parameters have to be estimated from past data trying to optimize the prediction performance. For this purpose, we discuss a specific set of first-order optimization tools that is emerged as efficient. The survey then draws connections to the well-studied area of kernel-based methods. They control the data fit by regularization terms that penalize models not in line with prior assumptions. We illustrate how to cast them in deep architectures to obtain deep kernel-based methods. The success of deep learning also resulted in surprising empirical observations, like the counter-intuitive behaviour of models with many parameters. We discuss the role of overparameterized models, including their connection to kernels, as well as implicit regularization mechanisms which affect generalization, specifically the interesting phenomena of benign overfitting.

### Paul Van den Hof, Karthik Ramaswamy, Stefanie Fonken, Shengling Shi, Eindhoven University of Technology: Identification of local models in interconnected systems – confounding variables, data-informativity and MATLAB toolbox

Identification of a local model in an interconnected system through prediction error methods requires the appropriate selection of a predictor model, consisting of predictor inputs and predicted outputs. In this setting several conditions need to be satisfied in order to guarantee accurate –consistent- model estimates, including the handling of confounding variables and the conditions for data-informativity. Generically these conditions can be satisfied through path-based conditions on the graph of the network model. An update of recent results will be presented, showing that data-informativity cannot simply be obtained by adding a sufficient number of excitation signals, but requires the appropriate selection of inputs and outputs in the predictor model. The results will be illustrated through the recently released MATLAB Toolbox for identification in dynamic networks.

### Mingzhou Yin, Roy S. Smith, ETH Zürich: Error Bounds for Kernel-Based Linear System Identification with Unknown Hyperparameters

Applying regularization in reproducing kernel Hilbert spaces has been successful in linear system identification using stable kernel designs. From a Gaussian process perspective, it automatically provides probabilistic error bounds for the identified models from the posterior covariance, which are useful in robust and stochastic control. However, the error bounds require knowledge of the true hyperparameters in the kernel design. They can be inaccurate with estimated hyperparameters for lightly damped systems or in the presence of high noise. In this work, we provide reliable quantification of the estimation error when the hyperparameters are unknown. The bounds are obtained by first constructing a high-probability set for the true hyperparameters from the marginal likelihood function. Then the worst-case posterior covariance is found within the set. The proposed bound is proven to contain the true model with a high probability and its validity is demonstrated in numerical simulation.

## Wednesday September 27

### Brandon O’Connell, Elizabeth Cross and Timothy Rogers, University of Sheffield: A Bayesian View on Stochastic Subspace Identification with Extension to Statistical Robustness

The family of Stochastic Subspace Identification (SSI) methods is one of the most popular and effective methods for system identification. Within structural dynamics, it is considered to be the state-of-the-art approach for operational modal analysis (output-only/blind system identification). This is due to it's robustness to noise, ease of model order selection and empirically strong results. Development of SSI can be shown via a set of orthogonal or oblique projections onto a linear subspace (hence the naming) or it can be viewed as performing Canonical Correlation Analysis (CCA) between the "past" and "future" Hankel matrices formed by a time-delay embedding of the measured responses. Following the view of CCA, it can be noted that the decomposition (along with other matrix factorisations, e.g, Principal Component Analysis, PCA) has an interpretation as a probabilistic latent variable model. Armed with this representation, it can be shown that classical SSI is a maximum likelihood solution to this probabilistic model and the door to a Bayesian treatment is open. The journey through this door is the contribution of this talk. As well as recovery of posterior uncertainty over the system properties via Bayesian inference, it will be shown how the probabilistic interpretation is amenable to powerful extensions. One shown here will statistical robustness to outlying data in the measured time-series through the application of a Student's-T prior in the latent space of the model. It will be presented how this novel robust Bayesian is able to avoid misidentification which is seen in the classical SSI algorithm when presented with intentionally corrupted data designed to mimic realistic issues encountered in field recordings, e.g. sensor dropout.

### Gerben I. Beintema, Maarten Schoukens, Roland Tóth, Eindhoven University of Technology: Meta-state-space learning: A Novel Approach for the Identification of Stochastic Dynamic Systems

The available methods for identifying stochastic dynamical systems from input-output data impose restricting structural assumptions on either the noise structure or the state probability distributions. This presentation introduces a novel identification method for nonlinear stochastic systems without making major structural assumptions. The method is formulated by first deriving a novel and exact representation of stochastic systems called meta-state-space representation. In this representation, the meta-state can be interpreted as a parameterization of the state probability function space. The meta-state-space representation is uniquely suited for identification since the meta-state transition function is deterministic allowing the adaptation of conventional identification methods with relatively little modifications. We also propose a neural meta-state-space model and identification method that is computationally tractable and that uses neural networks as universal function approximators. Using simulation and benchmark studies, we demonstrate that this identification method can obtain models with a log-likelihood close to the theoretical limit, even for highly nonlinear, highly stochastic systems.

### Mohammad Khosravi, Delft University of Technology: Representer Theorem for Learning Koopman Operators

In this work, we consider the problem of learning the Koopman operator for discrete-time autonomous systems. The learning problem is formulated as a generic constrained regularized empirical loss minimization in the infinite-dimensional space of linear operators. We show that a representer theorem holds for the introduced learning problem under certain but general conditions, which allows convex reformulation of the problem in a specific finite-dimensional space without any approximation and loss of precision. We discuss the inclusion of various forms of regularization and constraints in the learning problem, such as the operator norm, the Frobenius norm, the operator rank, the nuclear norm, and the stability. Subsequently, we derive the corresponding equivalent finite-dimensional problem. Furthermore, we demonstrate the connection between the proposed formulation and the extended dynamic mode decomposition. We present several numerical examples to illustrate the theoretical results and verify the performance of regularized learning of the Koopman operators.

### Matteo Scandella, Michelangelo Bin, Thomas Parisini, Imperial College London, University of Bologna, Imperial College London: Kernel methods for identification of nonlinear systems

Identifying dynamical systems possessing specific stability properties is of crucial importance in applications. Existing results mainly focus on linear systems or some limited classes of nonlinear systems, and a systematic procedure to identify nonlinear systems characterized by specific stability properties is still an open problem. In this presentation, we propose a kernel-based nonlinear identification methodology to directly and systematically identify stable nonlinear discrete-time systems. To achieve this aim, we build on the regularized regression in the reproducing kernel Hilbert spaces, which is modified by including stability constraints in the kernel properties and in the hyperparameters' selection algorithm. The proposed method can be used to enforce, on the identified model, bounded-input-bounded-state stability, asymptotic gain, and input-to-state stability properties, as well as their incremental versions. Once the methodology is detailed, and sufficient conditions for stability are singled out, the presentation reviews some widely used kernels and their applicability within the proposed methodology.

### Tomas McKelvey, Chalmers University of Technology: Radar platform tracking for airborne bistatic systems

For a receiver in a bistatic radar system, the relative position and velocity of the transmitter need to be known to the processor. In this presentation, we describe a clutter model and a method that over time tracks the transmitter position and velocity using the ground clutter response. For a given bistatic range the ground clutter response sensed by the receiver originates from ground scatterers located around an ellipsis. Each point on the ellipsis will correspond to a specific angle and Doppler frequency that depends on the relative geometry between the transmitter and receiver, and the velocities of both platforms. Assuming clutter response from one coherent processing interval (CPI), the position and velocity of the transmitter can be estimated by combining data for all relevant range bins and solving the associated maximum likelihood problem. The estimate is improved by incorporating a motion model and performing sequential filtering, i.e., tracking. In numerical simulations, the estimate from the tracking is compared with the maximum likelihood estimate. The numerical simulations clearly show that the estimate of the position and velocity from the tracker has lower variance and RMSE than themaximum likelihood estimate.