Tutorial Sessions

Nonstandard Linear-Quadratic Decision Making

Abstract: Since the late 1950’s Linear-Quadratic-Gaussian (LQG) theory has been the dominating paradigm for feedback control design for linear systems under noisy state measurements with Gaussian statistics and quadratic performance index. Its salient feature of separation of estimation and control, allowing the optimal controller to be one of the optimal linear-quadratic regulator (LQR) with simply the state replaced by its conditional mean generated by the Kalman filter, made the optimal design easily implementable. Questions were raised though as to whether this attractive and appealing feature of the LQG theory is retained when some of the basic assumptions of the paradigm are violated, or takes variations around the basic model such as: (i) having distributed control inputs with decentralized information, (ii) having bandwidth constraints and/or sporadic failures on the channels that carry state information to the controller(s) and/or controller inputs to the plant (generally known as networked control), (iii) the plant or the channels carrying information being vulnerable to adversarial attacks (that is, worst case designs, captured via the framework of zero-sum dynamic games), (iv) having multiple agents with non-aligned objectives interacting over a network (that is, a nonzero-sum dynamic game framework), and (v) systems with delays. In this tutorial session, we will cover selected variations around the basic LQG model (including the Witsenhausen’s counter-example), identify the challenges one encounters in these variations, and discuss their resolutions.

Statistical Learning Theory for Identification and Control

Abstract: Machine learning methods are at an ever increasing pace being integrated into domains that have classically been within the purview of controls. There is a wide range of examples, including perception-based control, agile robotics, and autonomous driving and racing. As exciting as these developments may be, they have been most pronounced on the experimental and empirical sides. To deploy these systems safely, stably, and robustly into the real world, we argue that a principled and integrated theoretical understanding of a) fundamental limitations and b) statistical optimality is needed. This tutorial serves as a comprehensive reference for new researchers as to what the state-of-the-art techniques are in this field. In particular, we aim to provide a self-contained exposition reviewing the main results along with the most important proofs. An important goal is to make the proofs and presentation accessible to a wider audience, without requiring prior background on statistical learning theory.

Analysis and Design of Optimization Algorithms Using Tools from Control Theory

Abstract: First-order methods provide robust and efficient solutions to large-scale optimization problems. Recent advances in the analysis and design of first-order methods have been fueled by tools from controls, including integral quadratic constraints and multipliers from robust control. Similar advances have been made in the optimization community through the (related) performance estimation framework. Together, these tools have transformed the way in which we analyze and design optimization methods. In this tutorial session, we provide a high-level overview of these tools as well as describe some of the recent advances in the analysis of algorithms for robust and distributed optimization, the synthesis of novel algorithms, connections with interpolation, and the general structure of such proofs.

Control and Optimization for Autonomous Energy Systems

Abstract: Energy systems are undergoing rapid transformative changes and becoming increasingly heterogeneous due to the proliferation of solar, wind, energy storage, electric vehicles, and building automation. While this transformation is dramatically increasing the potential of future energy systems, their efficient and secure operation cannot be attained via classical control and optimization approaches. In fact, control, optimization, and monitoring tasks need to be performed in real time, requiring fast decision-making capabilities along with comprehensive situational awareness. As more players are added, the complexity of controlling and optimizing energy systems is rapidly growing which renders conventional methods ineffective under provisioned operational conditions. This tutorial session brings together leading researchers to overview topics at the forefront of optimization and control of autonomous energy systems. The covered topics include: (a) Online feedback optimization for optimal operation of power systems, (b) Control and optimization of grid-connected power electronics, (c) Unbalanced three-phase power flow modeling and ist application to optimal power flow, and (d) Optimal demand dispatch.