Department of Mathematics and Statistics

Department of Mathematics and Statistics
Department of Mathematics and Statistics
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Control Theory Seminar

Control Theory - 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.