Abstract.
While recent years have shown rapid progress of learning-based and data-driven methods to effectively utilize data for control tasks, providing rigorous theoretical guarantees for such methods is challenging and an active field of research. This talk will give an overview of the state of the art of the recently developed framework for data-driven model predictive control (MPC) of unknown systems. In this framework no mathematical model is required for the MPC controller and only input-output data is needed. As a big advantageous feature, this framework admits rigorous theoretical guarantees for the closed loop. The proposed approach relies on the Fundamental Lemma of Willems et al. which parametrizes trajectories of unknown linear systems using data. First, we cover MPC schemes for linear systems with a focus on theoretical guarantees for the closed loop, which can be derived even if the data are noisy. Building on these results, we then move towards the general, nonlinear case. Specifically, we present a data-driven MPC approach which updates the data used for prediction online at every time step and, thereby, stabilizes unknown nonlinear systems using only input-output data. In addition to introducing the framework and the theoretical results, we also discuss successful applications of the proposed framework in simulation and real-world experiments.

Abstract.
Perhaps the most challenging aspect of research on multi-agent dynamical systems, formulated as non-cooperative stochastic differential/dynamic games (SDGs) with asymmetric dynamic information structures, is the presence of strategic interactions among agents, with each one developing beliefs on others in the absence of shared information. This belief generation process involves what is known as second-guessing phenomenon, which generally entails infinite recursions, thus compounding the difficulty of obtaining (and arriving at) an equilibrium. This difficulty is somewhat alleviated when there is a high population of agents (players), in which case strategic interactions at the level of each agent become much less pronounced. With some structural specifications, this leads to what is known as mean field games (MFGs), which have been the subject of intense research activity during the last fifteen years or so. The talk will first provide a general overview of fundamentals of MFGs approach to decision making in multi-agent dynamical systems in both model-based and model-free settings, and discuss connections to finite-population games. Following this general introduction, the talk will focus, for concrete results, on the structured setting of discrete-time infinite-horizon linear-quadratic-Gaussian dynamic games, where the players are partitioned into finitely-many populations with an underlying graph topology—a framework motivated by paradigms where consensus and dissensus co-exist. In this formulation, each population has a high number of indistinguishable agents, but there is no indistinguishability across different populations. It is possible to characterize the Nash equilibrium (NE) of the underlying game when the number of agents in each population goes to infinity, the so-called mean-field equilibrium (MFE), with only local state information for each agent, which can then be shown to lead to an approximate NE when the population sizes are finite, with a precise quantification of the approximation as a function of population sizes. For the model-free versions of such games, a reinforcement learning algorithm will be introduced based on zero-order stochastic optimization, for computation of the MFE, along with guaranteed convergence. The talk will also address derivation of a finite-sample bound, quantifying the estimation error as a function of the number of samples, and will conclude with a discussion of some extensions of the general setting and future research directions.

Abstract.
Network systems are mathematical models for the study of cooperation, propagation, synchronization and other dynamical phenomena that arise among interconnected agents. Network systems are widespread in science as they are fundamental modeling tools, e.g., in sociology and epidemiology. They also play a key growing role in technology, e.g., in the design of power grids, cooperative robotic behaviors and distributed computing algorithms. Their study pervades applied mathematics. This talk will review established and emerging frameworks for modeling, analysis and design of network systems.  I will survey the available comprehensive theory for linear network systems and then highlight selected nonlinear concepts.  Next, I will focus on recent developments by my group on a rigorous and comprehensive framework for the analysis of security, transmission capacity, and multistability for active power flow in power networks.

Abstract. Our motivation for the research to be described is derived from the following fact: The expected value of a random variable X, denoted E(X), is often inconsistent with what human beings may actually expect based on psychological considerations. This is particularly important when predictions involving life-threatening situations arise. To bring this issue into sharp focus, this seminar begins with a set of questions related to the recent rampage of Hurricane Irma from the Gulf of Mexico into in the State of Florida. When the use of empirical data leads to an expected value forecast of storm surge wave height which is unduly pessimistic, will the “boy who cried wolf” effect be in play the next time a hurricane approaches the mainland? On the other hand, if the formally calculated expected wave height is too optimistic, might it be the case that many will take inadequate protective measures? Based on such considerations, we define a new alternative to E(X) which we believe is quite useful for “mission critical” situations with downside risk being of paramount concern. We call this new metric the Conservative Expected Value and denote it by CEV(X). In this talk, we provide the technical definition of the CEV, compare it with the classical expected value and describe some aspects of the rich mathematical theory which accompanies it. We also include a description of some of the studies we have conducted using the CEV to evaluate historical data. This talk is dedicated to the memory of Roberto Tempo.