Control Theory: A Mathematical Perspective on Cyber-Physical Systems

Control theory is an interdisciplinary field that is located at the crossroads of pure and applied mathematics with systems engineering and the sciences. Recently the control field is facing new challenges motivated by application domains that involve networks of systems. Examples are interacting robots, networks of autonomous cars or the smart grid. In order to address the new challenges posed by these application disciplines, the special focus of this workshop has been on the currently very active field of Cyber-Physical Systems, which forms the underlying basis for many network control applications. A series of lectures in this workshop was devoted to give an overview on current theoretical developments in Cyber-Physical Systems, emphasizing in particular the mathematical aspects of the field. Special focus was on the dynamics and control of networks of systems, distributed optimization and formation control, fundamentals of nonlinear interconnected systems, as well as open problems in control

Active Information Acquisition With Mobile Robots

The recent proliferation of sensors and robots has potential to transform fields as diverse as environmental monitoring, security and surveillance, localization and mapping, and structure inspection. One of the great technical challenges in these scenarios is to control the sensors and robots in order to extract accurate information about various physical phenomena autonomously. The goal of this dissertation is to provide a unified approach for active information acquisition with a team of sensing robots. We formulate a decision problem for maximizing relevant information measures, constrained by the motion capabilities and sensing modalities of the robots, and focus on the design of a scalable control strategy for the robot team. The first part of the dissertation studies the active information acquisition problem in the special case of linear Gaussian sensing and mobility models. We show that the classical principle of separation between estimation and control holds in this case. It enables us to reduce the original stochastic optimal control problem to a deterministic version and to provide an optimal centralized solution. Unfortunately, the complexity of obtaining the optimal solution scales exponentially with the length of the planning horizon and the number of robots. We develop approximation algorithms to manage the complexity in both of these factors and provide theoretical performance guarantees. Applications in gas concentration mapping, joint localization and vehicle tracking in sensor networks, and active multi-robot localization and mapping are presented. Coupled with linearization and model predictive control, our algorithms can even generate adaptive control policies for nonlinear sensing and mobility models. Linear Gaussian information seeking, however, cannot be applied directly in the presence of sensing nuisances such as missed detections, false alarms, and ambiguous data association or when some sensor observations are discrete (e.g., object classes, medical alarms) or, even worse, when the sensing and target models are entirely unknown. The second part of the dissertation considers these complications in the context of two applications: active localization from semantic observations (e.g, recognized objects) and radio signal source seeking. The complexity of the target inference problem forces us to resort to greedy planning of the sensor trajectories. Non-greedy closed-loop information acquisition with general discrete models is achieved in the final part of the dissertation via dynamic programming and Monte Carlo tree search algorithms. Applications in active object recognition and pose estimation are presented. The techniques developed in this thesis offer an effective and scalable approach for controlled information acquisition with multiple sensing robots and have broad applications to environmental monitoring, search and rescue, security and surveillance, localization and mapping, precision agriculture, and structure inspection