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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.
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.
