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We address several issues that are important for developing a comprehensive understanding of the problems of control over networks. Proceeding from bottom to top, we describe theoretical frameworks to study the following issues, and present some answers: (i) Network information theory: Are there limits to information transfer over wireless networks? How should nodes in a network cooperate to achieve information transfer? (ii) In-network information processing: How should data from distributed sensors be fused over a wireless network? Can one classify functions of sensor data vis-a-vis how difficult they are to compute over a wireless network? (iii) Real-time scheduling over wireless networks: How should packets with hard deadlines be scheduled for transmission over unreliable nodes? What QoS guarantees can be provided with respect to latencies and throughputs? (iv) Clock synchronization over wireless networks: What are the ultimate limits to synchronization error? How should clocks be synchronized? (v) System level guarantees in networked control: How can one provide overall guarantees on of networked control systems that take into account hybrid behavior, real-time interactions, and distributed aspects? (vi) Abstractions and architecture: What are appropriate abstractions, and what is an appropriate architecture, to simplify networked control system design and deployment?
It is widely recognized that many of the most important challenges faced by control engineers involve the development of methods to design and analyze systems having components most naturally described by differential equations interacting with components best modeled using sequential logic. This situation can arise both in the development of high volume, cost sensitive, consumer products and in the design and certification of one of a kind, complex and expensive systems. The response of the control community to this challenge includes work on limited communication control, learning control, control languages, and various efforts on hybrid systems. This work has led to important new ideas but progress has been modest and the more interesting results seem to lack the kind of unity that would lead to a broadly inclusive theory. In this talk we describe an approach to problems of this type based on sample path descriptions of finite state Markov processes and suitable adaptations of known results about linear systems. The result is an insightful design technique yielding finite state controllers for systems governed by differential equations. We illustrate with concrete examples.
Networked embedded sensing and control systems are increasingly becoming ubiquitous in applications from manufacturing, chemical processes and autonomous robotic space, air and ground vehicles, to medicine and biology. They offer significant advantages, but present serious challenges to information processing, communication and decision-making. This area, called cyber-physical systems, which has been brought to the forefront primarily because of advances in technology that make it possible to place computational intelligence out of the control room and in the field, is the latest challenge in systems and control, where our quest for higher degrees of autonomy has brought us, over the centuries, from the ancient water clock to autonomous spacecrafts. Our quest for autonomy leads to consideration of increasingly complex systems with ever more demanding performance specifications, and to mathematical representations beyond time-driven continuous linear and nonlinear systems, to event-driven and to hybrid systems; and to interdisciplinary research in areas at the intersection of control, computer science, networking, driven by application needs in physics, chemistry, biology, finance. After an introduction to some of the main research and education issues we need to address and a brief description of lessons learned in hybrid systems research, we shall discuss recent methodologies we are currently working on to meet stability and performance specifications in networked control systems, which use passivity, model-based control and intermittent feedback control.
A gray-box model is one that has a known structure (generally constrained to a strict subset of the class of models it is drawn from) but has unknown parameters. Such models typically embody or reflect the underlying physical or mechanistic understanding we have about the system, as well as structural features such as the delineation of subsystems and their interconnections. The unknown parameters in the gray-box model then become the focus of our system identification efforts.
In a variety of application domains, ranging from biology and medicine to power systems, the gray-box models that practitioners accept --- as plausible representations of the reality they deal with every day --- have been built up over decades of study, and are large, detailed and complex. In addition to being difficult to simulate or compute or design with, a significant feature of these models is the uncertainty associated with many or most of the parameters in the model. The data that one collects from the associated system is rarely rich enough to allow reliable identification of all these parameters, yet there are good reasons to not be satisfied with direct black-box identification of a reduced-order model. The challenge then is to develop meaningful reduced-order gray-box models that reflect the detailed, hard-won knowledge one has about the system, while being better suited to identification and simulation and control design than the original large model.
Practitioners generally seem to have an intuitive understanding of what aspects of the original model structure, and which variables and parameters, should be retained in a physically or mechanistically meaningful reduced-order model for whatever aspect of the system behavior they are dealing with at a particular time. Can we capture and perhaps improve on what they are doing when they develop their (often informal) reduced models?
This talk will illustrate and elaborate on the above themes. Examples will be presented of approaches and tools that might be used to explore and expose structure in a detailed gray-box model, to guide gray-box reduction.
Most individuals form their opinions about the quality of products, social trends and political issues via their interactions in social and economic networks. While the role of social networks as a conduit for information is as old as humanity, recent social and technological developments, such as Facebook, Blogs and Tweeter, have added further to the complexity of network interactions. Despite the ubiquity of social networks and their importance in communication, we know relatively little about how opinions form and information is transmitted in such networks. For example, does a large social network of individuals holding disperse information aggregate it efficiently? Can falsehoods, misinformation and rumors spread over networks? Do social networks, empowered by our modern communication means, support the wisdom of crowds or their ignorance? Systematic analysis of these questions necessitate a combination of tools and insights from game theory, the study of multiagent systems, and control theory. Game theory is central for studying both the selfish decisions and actions of individuals and the information that they reveal or communicate. Control theory is essential for a holistic study of networks and developing the tools for optimization over networks. In this talk, I report recent work on combining game theoretic and control theoretic approaches to the analysis of social learning over networks.
Over the past decade, game theorists have made substantial progress in identifying simple learning heuristics that lead to equilibrium behavior without making unrealistic demands on agents information or computational abilities, as is the case in the perfect rationality approach to game theory. Recent research shows that very complex, interactive systems can equilibrate even when agents have virtually no knowledge of the environment in which they are embedded. This talk will survey different approaches to the problem of learning in games, show the various senses in which learning rules converge to equilibrium, and sketch the theoretical limits to what is achievable.
The analysis of signals into constituent harmonics and the estimation of their power distribution are considered fundamental to systems engineering. Due to its significance in modeling and identification, spectral analysis is in fact a "hidden technology" in a wide range of application areas, and a variety of sensor technologies, ranging from radar to medical imaging, rely critically upon efficient ways to estimate the power distribution from recorded signals. Robustness and accuracy are of at most importance, yet there is no universal agreement on how these are to be quantified. Thus, in this talk, we will motivate the need for ways to compare power spectral distributions.
Metrics, in any field of scientific endeavor, must relate to physically meaningful properties of the objects under consideration. In this spirit, we will discuss certain natural notions of distance between power spectral densities. These will be motivated by problems in prediction theory and related properties of time-series. Analogies will be drawn with an old subject of a similar vein, that of quantifying distances between probability distributions, which has given rise to information geometry. The contrast and similarities between metrics will be highlighted by analyzing mechanical vibrations, speech, and visual tracking.
