Abstract: Entropy and information are crucial notions in stochastic communications theory. However, they have not been as central in control, which has a rich tradition of non-probabilistic models and techniques. This tutorial session gives an introduction to recent non-probabilistic entropy and information concepts for state estimation and control. In the first half, the basic elements of a recent theory of nonstochastic information are described. Motivated by worst-case estimation and control, this framework allows non-statistical analogues of mutual independence, Markovness, information, and directed information to be rigorously defined. This yields information-theoretic tools for finding fundamental bounds in worst- case networked control systems. In the second half, the focus is on deterministic notions of entropy for nonlinear control systems. These notions are related to topological entropy in dynamical systems theory, and give the minimal feedback bit rates sufficient for achieving set-invariance. These developments for control systems are seen sometimes in analogy, and sometimes in contrast, to those for dynamical systems. Furthermore, a number of open problems in this field will be elucidated. Taken together, the ideas discussed in this session give a way to use information and entropy ideas in control, without having to adopt a stochastic formulation.

Session Structure:

• Nonstochastic Information Concepts for Estimation and Control (60 min)
  Nair, Girish N. (Univ. of Melbourne)
• Entropy Properties of Deterministic Control Systems (60 min)
  Colonius, Fritz (Univ. of Augsburg)

Abstract: The purpose of this tutorial is to analyze circuit models of neurons from a control perspective. A first objective of the tutorial is to review the basic modeling principles of neurophysiology: neurons are modeled as nonlinear electrical circuits and those circuits exhibit the fundamental behavioral property of excitability. The particular architecture of the circuits is key to the tractability of their analysis. A second objective of the tutorial is to review central questions from experimental neurophysiology, emphasizing the relevance and the methodological challenges of sensitivity analysis of neuronal behaviors. A third objective of the tutorial is to illustrate recent work by the authors. This work suggests that the localization properties of excitable behaviors are key for the tractability of systems and control questions including sensitivity, robustness, and regulation of neuronal behaviors.

Session Structure:

• Neuronal Behaviors: A Control Perspective
  Drion, Guillaume (Univ. of Liege), O'Leary, Timothy (Brandeis Univ.), Dethier, Julie (Univ. of Liege), Franci, Alessio (Univ. Nacional Autonoma de Mexico (UNAM)), Sepulchre, Rodolphe (Univ. of Cambridge)

Abstract: Passivity is one of the most physically appealing concepts in systems and control theory. The stored internal energy in a passive system is bounded from above by the externally supplied energy. It is well known that this energy dissipation property has important implications for closed-loop stability. Additionally, the passivity property is preserved with respect to feedback and parallel interconnections of passive systems. This composability property of passive systems is crucial in designing and analyzing highly networked systems. Due to these desirable features, the passivity paradigm has been widely utilized to achieve outstanding success in robot control, which is the main focus of the session. The tutorial session starts with a historical perspective on passivity-based robot control and its broad applicability to several important problems in robotics. Despite the long history, passivity-based robot control is being actively utilized in addressing emerging problems in robot control. Hence, the remainder of the session presents application of passivity-based robot control to address important research issues in bilateral teleoperation, visual feedback estimation and robot control, cooperative robot control, and mixed human-robot teams.

Session Structure:

• Passivity-Based Control of Robots: Historical Perspective and Contemporary Issues (5min)
  Hatanaka, Takeshi (Tokyo Inst. of Tech.), Chopra, Nikhil (Univ. of Maryland, Coll. Park), Spong, Mark W. (Univ. of Texas at Dallas)
• Historical Perspective (40 min)
  Spong, Mark W. (Univ. of Texas at Dallas)
• Distributed Synchronization of Networked Robotic Systems with Applications to Bilateral Teleoperation (40 min)
  Chopra, Nikhil (Univ. of Maryland, Coll. Park)
• Passivity-Based 3-D Rigid Motion Coordination, Visual Feedback Estimation/Control and More Advanced Issues (35 min)
  Hatanaka, Takeshi (Tokyo Inst. of Tech.)

Abstract: Stochastic hybrid systems are driven by random processes and have states that can both flow continuously and jump instantaneously. Many classes of stochastic hybrid systems, with different modeling strengths, have been considered in the literature. In this tutorial we first consider perhaps the simplest class of stochastic hybrid systems: those that admit unique solutions and that do not permit state conditions that force jumps. Several examples are given to illustrate the utility of this simple modeling class and Lyapunov-based sufficient conditions for various stability properties are given. The second half of the tutorial addresses a recent, more general stochastic hybrid systems modeling framework that permits state conditions to trigger jumps and that allows for non-unique solutions, via stochastic differential and difference inclusions and possibly overlapping flow and jump sets. Examples are provided to show the relevance of models that admit non-unique solutions and forced jumps. Lyapunov-based sufficient conditions for various stability properties for this class of stochastic hybrid systems are also provided.

Session Structure:

• Stochastic Hybrid Systems: A Modeling and Stability Theory Tutorial (5 min)
  Teel, Andrew R. (Univ. of California at Santa Barbara), Hespanha, Joao P. (Univ. of California, Santa Barbara)
• Stochastic Hybrid Systems: Time-Triggered and Event-Triggered Jumps (55 min)
  Hespanha, Joao P. (Univ. of California, Santa Barbara)
• Stochastic Hybrid Inclusions (60 min)
  Teel, Andrew R. (Univ. of California at Santa Barbara)

Abstract: Battery systems are becoming increasingly prevalent as a source of power for applications across domains from consumer electronics to automotive, due to a range of factors such as portability and environmental considerations. The relatively high cost of batteries leads to a natural tradeoff in their use to ensure the lifetime of the battery is not unduly compromised while still delivering good performance.
    Similar tradeoffs have been successfully dealt with in other systems using model based control and estimation techniques, and this motivates their use for battery systems. Complicating this process is the complex nature of the physics-based models describing the operation of a battery cell, as these consist of a large number of partial differential equations spanning multiple, coupled domains.
    This tutorial session will consist of three presentations that will review the existing physics-based battery models, and introduce recent approaches that have been used to develop simplified models based on the original high-fidelity model. The assumptions underpinning the model simplification will be presented and discussed. The simplified models will then be utilized in several challenging problems related to the use of batteries to demonstrate their efficacy. The opportunities for future research will also be discussed.

Session Structure:

• Estimation and Control of Battery Electrochemistry Models: A Tutorial (40 min)
  Moura, Scott (Univ. of California, Berkeley)
• Simplification Techniques for PDE-Based Li-Ion Battery Models (40 min)
  Manzie, Chris (The Univ. of Melbourne), Zou, Changfu (Univ. of Melbourne), Nesic, Dragan (Univ. of Melbourne)
• A Comparison of Model Order Reduction Techniques for Electrochemical Characterization of Lithium-Ion Batteries (40 min)
  Canova, Marcello (The Ohio State Univ.), Pan, Ke (Center for Automotive Res.), Fan, Guodong (Center for Automotive Res.)

Abstract: Many modern control and signal processing applications rely on solving a sequence of optimization problems, which are updated with measurements of an uncertain process that evolves in time. The solutions of these optimization problems are then used to make decisions, update inputs of the physical system and/or update a mathematical model of the process. We give here a tutorial introduction to some of the fundamental questions and implementation issues that arise in real-time optimization applications. We will concentrate on some of the decisions that have to be made when designing the computing architecture and algorithm and argue that the choice of one informs the other. The session will start with an introduction to real-time optimization, with a focus on the nature and structure of problems arising in control and estimation applications. This will be followed with an introduction to computer architecture fundamentals and recent research on methods for hardware-algorithm co-design for real-time optimization. The session will include an in-depth look at structured linear algebra parallelization strategies for solving large-scale nonlinear programming problems on high performance computing platforms. We will conclude with a discussion on future computer architectures and open research problems.

Session Structure:

• Computer Architectures to Close the Loop in Real-Time Optimization (5 min)
  Kerrigan, Eric C. (Imperial Coll. London), Constantinides, George A. (Imperial Coll. London), Suardi, Andrea (Imperial Coll. London), Picciau, Andrea (Imperial Coll. London), Khusainov, Bulat (Imperial Coll. London)
• Real-Time Optimization (15 min)
  Kerrigan, Eric C. (Imperial Coll. London)
• Current Computer Architectures (20 min)
  Suardi, Andrea (Imperial Coll. London)
• Co-Design of Algorithms and Hardware (20 min)
  Khusainov, Bulat (Imperial Coll. London)
• Nonlinear Programming Strategies on High-Performance Computers (40 min)
  Kang, Jia (Texas A&M Univ.), Chiang, Naiyuan (Argonne National Lab.), Laird, Carl Damon (Purdue Univ.), Zavala, Victor (Univ. of Wisconsin-Madison)
• Future Computer Architectures (20 min)
  Kerrigan, Eric C. (Imperial Coll. London)