Data-based Methods for Interconnected Systems: Theory and Algorithms

Organisers

  • Anne Koch
  • Maria Prandini

Speakers

  • Hakan Hjalmarsson, KTH, Stockholm, Sweden
  • Alessandro Chiuso, University of Padova, Padova, Italy
  • Shen Zeng, Washington University, St. Louis, USA
  • Sebastian Trimpe, Max Planck Institute, Stuttgart, Germany
  • Nikolai Matni, University of Pennsylvania, Philadelphia, US
  • Florian Dörfler, ETH Zürich, Switzerland
  • Alessandro Falsone, Politecnico di Milano, Milano, Italy
  • Hideaki Ishii, Tokyo Institute of Technology, Tokyo, Japan

Summary

We propose a one-day workshop to highlight recent developments in data-based analysis and design that have been motivated by emerging applications involving multiple interconnected systems. This poses new challenges to traditional data-based approaches and calls for further theoretical and algorithmic developments.
The goal of the workshop is to provide a wide coverage of the field, including modeling, analysis, control and optimization, while offering new vistas. To this purpose, we bring together outstanding researchers from leading institutions worldwide. Target audience comprises graduate level control engineers, as well as researchers with a strong interest in data-based approaches.

Programme

Learning of interconnected dynamical systems, Hakan Hjalmarsson

Key issues in data-driven learning of interconnected dynamical systems include topology detection, identifiability analysis, and identification of the dynamics, both of entire interconnected systems as well as individual modules. We present an overview of these topics together with state-of-the art results. Central to our exposition are statistical considerations. Both non-parametric (kernel based) and parametric methods are discussed. The thrust is on linear time-invariant models but we also provide excursions into the more diverse non-linear landscape.


Dynamic networks: representation and identification, Alessandro Chiuso

In this talk we shall discuss representation and  identification of interconnected dynamic systems. First several notions of dynamic networks shall be introduced and their relation discussed. In the context of internally stable interconnections, we shall focus on a canonical representation  that is identifiable without additional structural assumptions. Algorithmic and statistical issues related to the network identification problem will then be discussed in the context of sparse estimation. Extensions and applications will conclude the presentation.


Uncovering novel systems analysis and design principles through particle-based considerations, Shen Zeng

In the past decades, modeling and control were mostly concerned with exclusively one dynamical system with relatively mild complexity, which allowed for a highly successful systems theoretic treatment by purely analytical methods. However, recent years have witnessed a significant shift towards far more complex and large-scale dynamical systems in virtually all of the applied sciences, in which a traditional analytical approach is infeasible. This trend highlights the need for the exploration and development of novel systems analysis and design principles that are specifically applicable to complex and large-scale dynamical systems. In this talk, I will first introduce the very fruitful approach associated with viewing a complex dynamical system in a more global fashion, i.e. in terms of its macroscopic behavior. After providing a rapid review of the corresponding theory of transport operators (which are the  adjoints of the Koopman operators), I will describe recent developments of employing sample-based approaches to efficiently elucidate and compute important dynamical features in complex systems, such as invariant sets and measures, isochrons, as well as more systems theoretic features, such as global observability measures for nonlinear systems. In contrast to parametric approaches employing function libraries for describing the spatio-temporal patters to be computed, sample-based, or, nonparametric, approaches are often more flexible and computationally more efficient.


Event-triggered learning, Sebastian Trimpe

The ability to learn is an essential aspect of autonomous systems facing uncertain and changing environments. However, the process of learning a new model or behavior often does not come for free, but involves a certain cost.  For example, gathering informative data can be challenging due to physical limitations, or updating models can require substantial computation.  Moreover, learning for autonomous agents often requires exploring new behavior and thus typically means deviating from nominal or desired behavior. Hence, the question of "when to learn?" is essential for the efficient and intelligent operation of autonomous systems. We have recently proposed the concept of event-triggered learning (ETL) for making principled decisions on when to learn new dynamics models.  Building on the core idea of learning only when necessary, we have developed concrete triggers and theory for different domains.  In the context of networked and interconnected systems, ETL leads to superior communication savings over standard event-triggered control.  For linear quadratic control, ETL automatically detects inaccurate models and yields improved control performance under changing dynamics.  In this talk, we present the concept, theoretical results, and experimental applications of ETL.


On the Sample Complexity of Distributed Linear Optimal Controllers, Nikolai Matni

We propose a robust control based approach to designing distributed controllers for unknown-but-sparse linear and time invariant systems. By leveraging modern techniques in sparse system identification and distributed robust controller synthesis, we show that near-optimal distributed controllers can be learned with sub-linear sample complexity and computed with near-linear computational complexity, both measured with respect to the dimension of the full system. In particular, we provide end-to-end Probably Approximately Correct (PAC) bounds on the stability and performance of the designed distributed controller, and prove that for sparse systems, the number of samples needed to guarantee robust and near optimal performance can be much smaller than the dimension of the full system. Although the proposed optimization problem is quasi-convex, we show that it can be solved to global optimality by iteratively solving a series of small quadratic programs. We end with a demonstration of our results on a large-scale power-system inspired example.


Data-enabled predictive control (DeePC), Florian Dörfler

We consider the problem of optimal and constrained control for unknown systems. A novel data-enabled predictive control (DeePC) algorithm is presented that computes optimal and safe control policies using real-time feedback driving the unknown system along a desired trajectory while satisfying system constraints. Using a finite number of data samples from the unknown system, our proposed algorithm uses a behavioral systems theory approach to learn a non-parametric system model used to predict future trajectories. We show that, in the case of deterministic linear time-invariant systems, the DeePC algorithm is equivalent to the widely adopted Model Predictive Control (MPC), but it generally outperforms subsequent system identification and model-based control. To cope with nonlinear and stochastic systems, we propose salient regularizations to the DeePC algorithm. Using techniques from distributionally robust stochastic optimization, we prove that these regularization indeed robustify DeePC against corrupted data. We illustrate our results with nonlinear and noisy simulations and experiments from aerial robotics, power electronics, and power systems.


A distributed data-based approach to multi-agent decision-making, Alessandro Falsone

We consider multi-agent decision-making problems that can be formulated as  optimization programs where each agent introduces its own constraints on the optimization vector, and the constraints of all agents depend on a common source of uncertainty. We suppose that uncertainty is known locally to each agent through a private set of data, and that each agent enforces its data-based constraints to the solution of the multi-agent optimization problem. Our goal is to assess the feasibility properties of the corresponding multi-agent data-based solution and provide distributed resolution algorithms that can cope with heterogeneity of the agents, privacy of their local data, and combinatorial complexity when discrete decision variables are involved. Possible application to energy systems are presented to showcase our results.


Resilience and privacy issues in distributed algorithms, Hideaki Ishii

The wide use of networking has enabled various cyber-physical devices  to be connected for carrying out collaborative computation for control and estimation purposes. At the same time, however, risks of cyber attacks have drastically increased, which can result not only in having important and private data to be stolen, but also devices to be remotely manipulated in a stealthy manner by adversaries. In this talk, we present how to protect distributed algorithms from malicious attackers by raising the security levels in terms of their resilience and privacy preservation. Particular attention will be given to the multi-agent consensus problem. We will see how false data injection type attacks as well as eavesdropping type attacks can harm the system. Then, we provide several solutions for addressing such issues. We will further discuss that cyber security of distributed algorithms is in fact an interesting area for interdisciplinary research, connecting systems control with computer science.