Department of Mathematics and Statistics

Department of Mathematics and Statistics
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Control Theory Seminar

Control Theory Seminar - Alex Olshevsky (Boston University)

Friday, July 19th, 2019

Time: 2:30 p.m Place: Jeffery 110

Speaker: Alex Olshevsky (Boston University)

Title: Convergence Rates in Decentralized Optimization

Abstract: The widespread availability of copious amounts of data has created a pressing need to develop optimization algorithms which can work in parallel when input data is unavailable at a single place but rather spread throughout multiple locations. In this talk, we consider the problem of optimizing a sum of convex (not necessarily differentiable) functions in a network where each node knows only one of the functions; this is a common model which includes as particular cases a number of distributed regression and classification problems. Our main result is a distributed subgradient method which simultaneously achieves the optimal scalings both with time and the network size for this problem.

Alex Olshevsky received the B.S. degree in applied mathematics and the B.S. degree in electrical engineering from the Georgia Institute of Technology, Atlanta, GA, USA, both in 2004, and the M.S. and Ph.D. degrees in electrical engineering and computer science from the Massachusetts Institute of Technology, Cambridge, MA, USA, in 2006 and 2010, respectively. He is currently an Associate Professor with the Department of Electrical and Computer Engineering, Boston University, Boston, MA, USA. Dr. Olshevsky is a recipient of the National Science Foundation CAREER Award, the Air Force Young Investigator Award, the INFORMS Computing Society Prize for the best paper on the interface of operations research and computer science, and a Society for Industrial and Applied Mathematics (SIAM) Award for annual paper from the SIAM Journal on Control and Optimization chosen to be reprinted in SIAM Review.

Control Theory Special Seminar - Behrouz Touri (UCSD)

Monday, June 17th, 2019

Time: 2:00 p.m Place: Jeffery Hall 319

Speaker: Behrouz Touri (University of California San Diego)

Title: Stochastic Adventures in Systems and Controls

Abstract: In this talk, we visit two systems and controls problems with stochastic components. The first problem relates to the control of safety critical systems. We provide a necessary and sufficient reachability result for an open and bounded safety set. In particular, we show that a stochastic system is controllable if and only if the expected system is controllable.

The second problem relates to control of large networked systems. We prove that a conjecture of Chris Godsil on controllability of graphs is true. The conjecture asserts that the number of binary symmetric matrices A that are controllable with all-one vector to the total number of binary matrices approaches one as the dimension of A approaches infinity. We also provide a result on universality of minimal controllability of networked systems.

Bio: Behrouz Touri is an Assistant Professor of the Electrical and Computer Engineering at the University of California San Diego and an Assistant Professor of the Electrical, Computer, and Energy Engineering Department at the University of Colorado Boulder (on leave). He received his B.Sc. degree in Electrical Engineering from Isfahan University of Technology, Isfahan, Iran in 2006, his M.Sc. degree in Communications, Systems, Electronics from Jacobs University, Bremen, Germany in 2008, and his Ph.D. degree in Industrial Engineering from the University of Illinois at Urbana-Champaign in 2011. Between 2011 and 2014, he was a postdoctoral researcher with the ECE departments of the University of Illinois and Georgia Institute of Technology. His research interests include applied probability theory, distributed optimization, control and estimation, population dynamics, and evolutionary game theory. He is a recipient of American Control Council's Donald P. Eckman Award in 2018 and AFOSR Young Investigator Award 2016.

Control Theory Seminar - Ali Pakniyat (University of Michigan)

Monday, May 27th, 2019

Time: 10:30 a.m Place: Jeffery 319

Speaker: Ali Pakniyat (University of Michigan)

Title: The Quest for Missing Component: Dualities in Hybrid Optimal Control

Abstract: We revisit the notion of feedback as a ubiquitous policy structure in systems and control theory, and argue that a feedback law purely in state is not necessarily optimal. By studying examples of deterministic and stochastic hybrid systems, we remark that a general control policy depends on both the past information and future predictions about the process and, hence, a reduction to feedback structure jointly in the state and a "dual" variable requires the pair to summarize both the past and the future. Viewing the two fundamental results in optimal control theory from a duality perspective, we show that duality relationship holds in the Minimum Principle (MP) between the finite dimensional spaces of state variations and of co-state (adjoint) processes, and in Dynamic Programming (DP) between the infinite dimensional spaces of measures and of continuous functions. We present new version of the MP and DP for deterministic and stochastic hybrid systems and illustrate their implementation on analytic and practical examples. For numerical solution methodologies, we study the three classes of (a) generally nonlinear, (b) linear quadratic, and (c) polynomial systems where, for the latter case in particular, we can employ sum-of-squares techniques.

Control Theory Seminar - Prof. Melkior Ornik (UIUC)

Friday, May 17th, 2019

Time: 10:30 a.m Place: Jeffery 110

Speaker: Prof. Melkior Ornik (University of Illinois at Urbana-Champaign)

Title: Deception and Unpredictability in Stochastic Control

Abstract: In a number of adversarial scenarios, the success of an agent at achieving its objective rests on its use of a deceptive strategy: a strategy that enables the agent to progress towards its objective while manipulating the beliefs of the agent’s adversary about the nature of the agent. For instance, the agent may wish to instill incorrect beliefs about its location, identity, or objective, or it may simply wish to act seemingly unpredictably while still progressing towards its objective. In this talk, I will outline recent work on formalizing the notions of deception and unpredictability within the setting of Markov decision processes. I will begin by describing a basic approach that encodes deception through introducing a belief space for an adversary and a belief-induced reward objective, thus expressing deceptive strategies as control policies on a product state space. I will then discuss notions of unpredictability, deception, and counter-deception in scenarios with a temporal logic objective. I will relate unpredictability of an agent to the total Shannon entropy of its paths, and show that maximal unpredictability is achieved by following a policy that results in maximal total entropy of the induced Markov chain. Finally, I will express the notion of deception for temporal logic objectives using Kullback-Leibler divergence and show that optimal deceptive (for the agent) and counter-deceptive (for the adversary) policies can be synthesized as solutions of a convex optimization problem and a non-convex min-max problem, respectively. I will conclude with a brief discussion of open problems in the area of deceptive planning.

Control Theory Seminar - Prof. Jon Sensinger (UNB)

Monday, April 29th, 2019

Time: 10:30 a.m Place: Jeffery 110

Speaker: Prof. Jon Sensinger (UNB)

Title: Bottlenecks in rehabilitation human-machine interfaces: from mechanisms to control to human-machine interaction

Abstract: Humans can do amazing things compared with many robots. When humans interact with machines, it often leads to high expectations. These expectations are particularly high of human machine interfaces that try to assist (such as exoskeletons and prostheses) or rehabilitate (e.g., for stroke). Humans are complex, and the tasks they often wish to do require unique mechanisms and insightful control strategies. My personal bias is that solutions to these problems are often best solved using a control-theoretic framework.

This talk will highlight some of the mechanical and control bottlenecks that have limited the field, along with our contributions to help solve those problems. It will then turn to the field of computational motor control - a promising field that has used optimal stochastic feedback control theory to offer a compelling explanation for why humans move the way they do. The talk will briefly discuss the idea and some of the recent contributions by our group and others. From an engineering perspective, I will propose a holistic approach of including the person’s own capabilities, control strategies, and even level of interest, in the closed-loop design process. I will survey initial success of applying this approach to augmented sensory feedback, and lay out a vision for applying it to feedforward control as well. The talk will end by diving deeper into our most recent work developing a simple model of human adaptation. We've developed an inductive outcome measure that probes can infer from trial-by-trial data how confident people are in their feed-forward control. Challenges, limitations, and next steps will be discussed.

Dr. Jon Sensinger is the acting director of the Institute of Biomedical Engineering (IBME) at the University of New Brunswick and an associate professor in Electrical and Computer Engineering. Trained as a biomedical engineer and a clinical prosthetist, he directed the prosthesis design and control lab at the Rehabilitation Institute of Chicago and Northwestern University prior to coming to UNB. He has licenced several patents and is a cofounder of Coapt LLC, the first company to commercialize pattern recognition in the field of prostheses. He has a strong interest in seeing clinical problems through the lens of math - fusing theoretical paradigm shifts that result in meaningful clinical applications. As the acting director of IBME he directs a broad team comprising clinicians, scientists, engineers, professors, and graduate students who all share a passion to improve the lives of persons with disability. IBME has a 50+ year legacy of innovation in the field of prostheses and rehabilitation engineering, and Dr. Sensinger strives to maintain that focus as the field pushes the boundaries of rehabilitation engineering.

Control Theory Seminar - Prof. Andy Lamperski

Monday, December 3rd, 2018

Time: 10:00 a.m Place: TBA

Speaker: Prof. Andy Lamperski

Title: Optimal Control with Noisy Time and Communicative Actions

Abstract: This talk will cover two topics: 1) Control and estimation with noisy time, and 2) communication via control actions. 

In most control analysis, time is assumed to be perfectly known.  However, in many important scenarios ranging from robotics, biological motor control, and transportation systems, timing information is not known perfectly. In the first part of the talk, we will examine problems of optimal control and estimation when time is imperfectly measured. For optimal control, we will show that under some clock noise models, dynamic programming principles can be obtained. In the linear quadratic case, explicit solutions can be computed. For estimation, we will present the problem of estimating time from sensor data. In particular, we will examine how control can influence the accuracy of time estimates, and we will discuss the estimation of time from multiple sensors with inaccurate time-stamps. 

The second part of the talk will focus on communication with control actions. This communication strategy is known as signaling. While most signaling problems are mathematically challenging, humans routinely signal during cooperative movements. The second part of the talk will present a tractable problem that models salient features of human signaling strategies. The problem consists of a signaler that reaches towards an unspecified target, and an observer that decides on the target location based on movement measurements. The optimal control scheme reproduces qualitative phenomena observed in human reaching experiments.

Control Theory - Prof. Ashutosh Nayyar (USC)

Thursday, November 20th, 2018

Time: 10:00 a.m Place: Jeffery Hall 319

Speaker: Prof. Ashutosh Nayyar (USC)

Title: Decentralized control over unreliable communication links

Abstract: Decentralized control problems have been a topic of significant research interest due to their relevance to multi-agent systems and large-scale distributed systems.The design of optimal decentralized control strategies has been investigated under various models for inter-controller communication such as graph-based communication models and communication with delays. A common feature of much of the prior work is that the underlying communication structure of the decentralized system is assumed to be fixed and unchanging. For example, several works assume a fixed communication graph among controllers whose edges describe perfect communication links between controllers. Similarly, when the communication graph incorporates delays, the delays are assumed to be fixed and known. This is a key limitation since in many situations communication among controllers may suffer from imperfections such as random packet loss and random packet delays. These imperfections introduce a new layer of uncertainty in the information structure that is not present in the models considered in prior work. In this talk, we will describe a decentralized LQG control problem where some of the communication links suffer from random packet loss. We will first identify optimal decentralized control strategies for finite horizon version of our problem. We will then discuss the infinite horizon problem and show that there are critical thresholds for packet loss probabilities above which no strategy can achieve finite cost and below which optimal strategies can be explicitly identified.

Control Theory - Christoph Kawan (University of Passau)

Thursday, September 27th, 2018

Time: 9:00-10:30 a.m Place: Jeffery Hall 319

Speaker: Christoph Kawan (University of Passau)

Title: Robust estimation under information constraints for deterministic non-linear systems

Abstract: A fundamental problem in information-based control is to estimate the state of a dynamical system using information sent through a rate-limited channel. In this talk, we explain the concept of restoration entropy, introduced by Matveev and Pogromsky, which characterizes the smallest channel capacity above which a robust coding and estimation policy with arbitrarily small estimation error can be implemented. In particular, we provide a characterization of restoration entropy that involves no asymptotic quantities and leads to nearly optimal policies.