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This talk will present models for the evolution of opinions, interpersonal influences, and social power in a group of individuals. I will present empirical data and mathematical models for the opinion formation process in deliberative groups, including concepts of self-weight and social power. I will then focus on groups who discuss and form opinions along sequences of judgmental, intellective, and resource allocation issues. I will show how the natural dynamical evolution of interpersonal influence structures is shaped by the psychological phenomenon of reflected appraisal. Multi-agent models and analysis results are grounded in influence networks from mathematical sociology, replicator dynamics from evolutionary games, and transactive memory systems from organization science. (Joint work with: Noah E. Friedkin, Peng Jia, and Ge Chen)
The interactions of dynamical systems communicating over a networked environment lead to intriguing synchronization behaviors with applications in Internet of Things, formations, satellite control, and human societal behaviors. This talk studies the relation between local controls design and communication graph restrictions. The distinctions between stability and optimality on graphs are explored. An optimal design method for local feedback controllers is given that decouples the control design from the graph structural properties. In the case of continuous-time systems, the optimal design method guarantees synchronization on any graph with suitable connectedness properties. In the case of discrete-time systems, a condition for synchronization is that the Mahler measure of unstable eigenvalues of the local systems be restricted by the condition number of the graph. Thus, graphs with better topologies can tolerate a higher degree of inherent instability in the individual node dynamics. A theory of duality between controllers and observers on communication graphs is given, including methods for cooperative output feedback control based on cooperative regulator designs. In second part of the talk, we discuss graphical games. Standard differential multi-agent game theory has a centralized dynamics affected by the control policies of multiple agent players. We give a new formulation for games on communication graphs. Standard definitions of Nash equilibrium are not useful for graphical games since, though in Nash equilibrium, all agents may not achieve synchronization. A strengthened definition of Interactive Nash equilibrium is given that guarantees that all agents are participants in the same game, and that all agents achieve synchronization while optimizing their own value functions.
This tutorial will describe the design of stable observers for nonlinear systems. The design methodology utilizes tools that include Lyapunov analysis, the Circle Criterion and the S-procedure Lemma. The observer stability conditions are typically obtained as linear or bilinear matrix inequalities from which the observer gains can be computed. The tutorial will start with a dynamic system in which the process dynamics has Lipschitz nonlinearities. This will later be generalized to allow for either Lipschitz, bounded Jacobian or sector bounded nonlinearities in both the process dynamics and the measurement equations. Simple programs to solve LMIs in Matlab and obtain the observer gains will also be presented. The lecture will conclude with the application of the developed methodology to automotive slip angle estimation in the presence of nonlinear tire force models.
With the increasing trend towards system downsizing and the growing stringency of requirements, constraint handling and limit protection are becoming increasingly important for engineered systems. Constraints can reflect actuator limits, safety requirements (e.g., process temperatures and pressures must not exceed safe values) or obstacle avoidance requirements. Reference governors are control schemes that can be augmented to already existing control systems in order to provide constraint handling/limit protection capabilities. These add-on schemes exploit prediction and optimization or invariance/strong returnability properties to supervise and minimally modify operator (e.g., pilot or driver) commands, or other closed-loop signals, whenever there is a danger of future constraint violations. The presentation will introduce the basic reference governor schemes along with the existing theory. Several recent extensions and new variants of these schemes will be highlighted. Selected aerospace and automotive applications will be described. Opportunities for future research will be mentioned.
High-gain observers play an important role in the design of feedback control for nonlinear systems. This lecture overviews the essentials of this technique. A motivating example is used to illustrate the main features of high-gain observers, with emphasis on the peaking phenomenon and the role of control saturation in dealing with it. The use of the observer in feedback control is discussed and a nonlinear separation principle is presented. The use of an extended high-gain observer as a disturbance estimator is covered. Challenges in implementing high-gain observers are discussed, with the effect of measurement noise as the most serious one. Techniques to cope with measurement noise are presented. The lecture ends by listing examples of experimental testing of high-gain observers.
In this talk we address the problem of designing nonlinear observers that possess robustness to output measurement errors. To this end, we introduce a novel concept of quasi-Disturbance-to-Error Stable (qDES) observer. In essence, an observer is qDES if its error dynamics are input-to-state stable (ISS) with respect to the disturbance as long as the plant's input and state remain bounded. We develop Lyapunov-based sufficient conditions for checking the qDES property for both full-order and reduced-order observers. This relates to a novel "asymptotic ratio" characterization of ISS which is of interest in its own right. When combined with a state feedback law robust to state estimation errors in the ISS sense, a qDES observer can be used to achieve output feedback control design with robustness to measurement disturbances. As an application of this idea, we treat a problem of stabilization by quantized output feedback. Applications to synchronization of electric power generators and of chaotic systems in the presence of measurement errors will also be discussed.
During the past decades model predictive control (MPC) has become a preferred control strategy for the control of a large number of industrial processes. Computational issues, application aspects and systems theoretic properties of MPC (like stability and robustness) are rather well understood by now. For many application disciplines a significant shift in the typical control tasks to be solved can, however, be witnessed at present. This concerns for example robot control, autonomous mobility, or industrial production processes. This will be examplarily discussed with the vision of the smart factory of the future, often termed Industry 4.0, where the involved control tasks, are undergoing a fundamental new orientation. In particular the stabilization of predetermined setpoints does not play the same role as it has in the past. In this talk we will first give an introduction to and an overview over the field of model predictive control. Then new challenges and opportunities for the field of control are discussed with Industry 4.0 as an example. We will in particular investigate the potential impact of Model Predictive Control for the fourth industrial revolution and will argue that some new developments in MPC, especially connected to distributed and economic model predictive control, appear to be ideally suited for addressing some of the new challenges.
Geometric mechanics is useful in developing a compact description of the motion of a rigid body in three-dimensional space which is singularity-free, unique, does not limit the motion to small angles, and enables a single control law to be obtained even in the presence of translational/rotational coupling. Such a description, which is based on the Lie group SE(3) and its corresponding "exponential coordinates", is especially useful for spacecraft and other types of autonomous vehicles undergoing fast rotations and tumbling motions. This talk will explore various coordinates for rigid body attitude along with their pros and cons (including the phenomenon of unwinding when using a quaternion attitude description) as well as the use of the SE(3) framework in multi-vehicle consensus control design in which it is desired to achieve leader-follower formations along with attitude synchronization. The case of four formation flying spacecraft in a Molniya orbit will serve as an illustrative example.
As the characteristic size of a flying robot decreases, the challenges for successful flight revert to basic questions of fabrication, actuation, fluid mechanics, stabilization, and power — whereas such questions have in general been answered for larger aircraft. When developing a robot on the scale of a housefly, all hardware must be developed from scratch as there is nothing “off-the-shelf” which can be used for mechanisms, sensors, or computation that would satisfy the extreme mass and power limitations. With these challenges in mind, this talk will present progress in the essential technologies for insect-scale robots and the latest flight experiments with robotic insects.
The term capacity has natural connotations about fundamental limits and robustness to disruptions. For engineered systems, a rigorous characterization of capacity also provides insight into algorithms with universal performance guarantees and informs optimal strategic resource allocation. We present analysis and optimization of capacity and related performance metrics for societal cyber-physical systems (including traffic, mobility, and power networks) in canonical settings. At the macroscopic scale, we extend static network flow formulations to several flow dynamics and control settings (including cascading failure). The tractability of the resulting nonlinear analysis and optimization is facilitated by the spatial sparsity of dynamics and invariance of key input-output properties, such as monotonicity, across multiple resolutions in the network. At the microscopic scale, we consider spatial queues with state-dependent service rate; for example, such problems arise in networks of dynamically coupled vehicles. While this dependence is complex in general, we provide tight characterization in limiting cases, for instance large queue length, which leads to tight throughput estimates. Case studies are provided to evaluate the effectiveness of the proposed frameworks.
With its thin atmosphere, uncertain wind and terrain, and ever-increasing science requirements, robotic missions to the surface of Mars have presented enormous challenges to the Entry, Descent, and Landing (EDL) and Guidance, Navigation, and Control (GN&C) engineers. Throughout the years, these challenges have been met with a series of landing architectures that spawned different degrees of passive and active control, from the ballistic airbag landers in the Mars Pathfinder and Spirit and Opportunity Rovers, to the guided-entry, SkyCrane-delivered Curiosity. Landing on Europa (the Jovian moon that may have the conditions to harbor life) presents a different set of challenges over a Martian landing. While Europa’s lack of atmosphere relieves the landing engineer from the complexities of heatshields and parachutes and the vagaries of an atmosphere, they now face the enormous challenges of bringing large amounts of fuel and powerful propulsion to do the job the atmosphere does on Mars, while dealing with an extremely uncertain surface topography and radiation environment. These challenges are being addressed with increased automation based on new GN&C sensors and algorithms. In this talk, I will describe the challenges of both Mars and Europa landings, and the intellectual journey trod by engineers in meeting them.
General anesthesia is a drug-induced, reversible condition comprised of five behavioral states: unconsciousness, amnesia (loss of memory), analgesia (loss of pain sensation), akinesia (immobility), and maintenance of physiological stability and control of the stress response. As a consequence, every time an anesthesiologist administers anesthesia he/she creates a control system with a human in the loop. Our work shows that a primary mechanism through which anesthetics create these altered states of arousal is by initiating and maintaining highly structured oscillations. These oscillations impair communication among brain regions. We show how these dynamics change systematically with different anesthetic classes, anesthetic dose and with age. As a consequence, we have developed a principled, neuroscience-based paradigm for using the EEG to monitor the brain states of patients receiving general anesthesia and for implementing formal control strategies for maintaining anesthetic state. We will illustrate these strategies with results from actual control experiments.
Feedback is as ubiquitous in nature as it is in design. So control theory can help us understand both natural and designed systems. Even better, generalized models abstracted from nature give us a mathematical means to connect control theoretic explanations of nature with opportunities in control design. Control theory is enriched by the language, questions, and perspectives of fields as diverse as animal behavior, cognitive science, and dance. I will present a model for multi-agent dynamics that is informed by these fields. The model derives from principles of symmetry and bifurcation, which exploit instability to recover the remarkable capacity of natural groups to trade off flexibility and stability.
In many application domains, including systems and control theory, the optimization problems that appear are seldom "generic" but instead they often have well-defined structural features. Depending on the situation, such structure may be described algebraically (e.g., by transformations under which the problem is invariant, like linearity or time-invariance), geometrically (by restricting the feasible set to a given manifold/variety), or graphically (e.g., by a graph summarizing the interactions among decision variables). Exploiting this structure is crucial for practical efficiency. In this talk we will provide a gentle introduction to these ideas, surveying the basic notions as well as describing algorithmic techniques to detect and exploit these properties. In particular, we will discuss some recent developments, including dimension/symmetry reduction techniques for SDPs, and chordal networks. As we will illustrate through applications, algorithms that automatically exploit structure can significantly outperform existing techniques.
The 25th anniversary of the commercialization of lithium-ion batteries marks their wide-spread use in handheld consumer electronics and coincides with a period of intense efforts for powering electric vehicles. Managing the potent brew of lithium ions in the large quantities necessary for vehicle propulsion is anything but straightforward. Designing the complex conductive structure, choosing the electrode material for locking the energy in high potential states and synthesizing the interfaces for releasing the chemical energy at fast but controllable rates has been the focus of the electrochemists and material scientists. But from the Rosetta-Philae spacecraft landing three billion miles away from Earth to the daily commute of a hybrid electric automobile, the control engineers behind the battery management system (BMS) have been the unsung heroes. The BMS is the brain of the battery system and is responsible for State of Charge (SOC), State of Health (SOH) and State of Power (SOP) estimation while protecting the cell by limiting its power. The BMS relies on accurate prediction of complex electrochemical, thermal and mechanical phenomena. This raises the question of model and parameter accuracy. Moreover, if the cells are aging, which parameters should we adapt after leveraging limited sensor information from the measured terminal voltage and sparse surface temperatures? With such a frugal sensor set, what is the optimal sensor placement? To this end, control techniques and novel sensors that measure the cell swelling during lithium intercalation and thermal expansion will be presented. We will conclude by highlighting the fundamental difficulties that keep every battery control engineer awake, namely predicting local hot spots, detecting internal shorts, and managing the overwhelming energy released during a thermal runaway.
Recent work on Model Predictive Control has refocused attention on the role of future disturbance uncertainty. One way of dealing with this issue is to use policy rather than sequence optimization. However, this comes at a significant increase in computational burden. In this talk we will outline strategies for dealing with the computational issue, including using quantized scenarios to represent the future disturbances. The related issue of providing performance guarantees in the face of high uncertainty will also be discussed. The ideas will be illustrated by the development of a new treatment strategy for Type 1 diabetes mellitus.
What is model reference adaptive control? Why does one prefer using a model reference adaptive controller? How can we design and analyze a model reference adaptive controller? In this FoRCE video, we answer these fundamental questions related to model reference adaptive control theory and beyond.
More information provided here.
The area of polynomial optimization has been actively studied in computer science, operations research, applied mathematics and engineering, where the goal is to find a high-quality solution using an efficient computational method. This area has attracted much attention in the control community since several long-standing control problems could be converted to polynomial optimization problems. The current researches on this area have been mostly focused on various important questions: i) how does the underlying structure of an optimization problem affect its complexity? Ii) how does sparsity help? iii) how to find a near globally optimal solution whenever it is hard to find a global minimum? iv) how to design an efficient numerical algorithm for large-scale non-convex optimization problems? v) how to deal with problems with a mix of continuous and discrete variables? In this talk, we will develop a unified mathematical framework to study the above problems. Our framework rests on recent advances in graph theory and optimization, including the notions of OS-vertex sequence and treewidth, matrix completion, semidefinite programming, and low-rank optimization. We will also apply our results to two areas of power systems and distributed control. In particular, we will discuss how our results could be used to address several hard problems for power systems such as optimal power flow (OPF), security-constrained OPF, state estimation, and unit commitment.
The number of unmanned aerial vehicles or drones has grown exponentially over the last three decades. Yet we are only now seeing autonomous flying robots that can operate in three-dimensional indoor environments and in outdoor environments without GPS. I will discuss the need for smaller, safer, smarter, and faster flying robots and the challenges in control, planning, and coordinating swarms of robots with applications to search and rescue, first response and precision farming. Publications and videos are available at kumarrobotics.org.
