Two MURI groups will be reporting on the 1st year progress.
Location: CSL 301. The building will be open 8am-8pm; take elevator or stairs to the third floor. Alternatively, join by zoom.
Video recordings of the proceedings: morning session, afternoon session.
| Topic | Speaker | |
|---|---|---|
| 8:40-8:50 | Opening Remarks | Leve |
| 8:50-9:15 | Geometry, Topology, and Symmetry of Open Smooth and Hybrid Systems | Bloch |
| 9:15-9:40 | Propagation of Geometric Structures in Smooth Hybrid Systems | Clark |
| 9:40-10:05 | Stochastic Hybrid Systems | Lee |
| 10:05-10:30 | Modeling, Control, and Trajectory Optimization by Exploiting Lie Group Symmetry | Ghaffari |
| 10:30-10:50 | Break1Coffee shop in the neighboring building (across the lawn). | |
| 10:50-11:15 | Identifying Regions of Attraction in High Dimensional Systems | Mischaikow |
| 11:15-11:40 | Identifying Switching Behavior and Bifurcations in Interaction Networks | Kalies |
| 11:40-12:05 | Towards a Categorical Framework for Open Hybrid Systems | Guralnik |
| 12:05-12:30 | Bringing the Heat: Swift Trajectory Planning with Spatial-Pseudospectral Techniques | Vasudevan |
| 12:30-2:00 | Lunch2See below for lunch opportunities. | |
| 2:00-2:30 | Spaces of Trajectories: Obstacles and Cuts3I will focus on the spaces of trajectories: first as a unifying theme of this MURI, and then on several specific results: I will describe how the topology of the phase space and the topology of the space of executed trajectories force discontinuities (unavoidable guards) in any realization. Further, I will adderess several new results of the space of paths avoiding obstacles when some slacks are afforded. | Baryshnikov |
| 2:30-2:55 | Localization and mapping with coarse information 4In this talk we examine information requirements for control-enabling tasks such as state estimation, model detection, localization and mapping in an unknown environment. We discuss the role of topological entropy in determining data rates necessary for solving these tasks. Through examples, we study simultaneous localization and mapping (SLAM) based on a binary signal generated by an unknown landmark. We look in some detail into the problem of characterizing states that cannot be distinguished based on such information, and employ the Kalman observability decomposition and related geometric concepts to construct an algorithm for computing indistinguishable sets. Towards the end, we briefly touch on the problem of reconstructing possible configurations of multiple unknown landmarks (signal sources) from the total signal that they provide. | Liberzon |
| 2:55-3:20 | Hybrid systems with rough observations: Indistinguishable sets and perception contracts5We study a class of open hybrid control systems where the plant state is available to the controller through “rough” measurements. These measurements are influenced by uncontrolled environmental quantities like landmarks and often have discrete and low-dimensional information structures. In this talk, we discuss initial results on simultaneous algorithmic design of controllers and observers for such open hybrid systems. First, we will discuss a variation of the simultaneous localization and mapping (SLAM) problem with discrete measurements from this point of view. A notion of indistinduishable relations define the limits of solving this SLAM problem and we discuss algorithms for computing such indistinguishability relations. In the second half, we will introduce the notion of perception contracts as an assume-guarantee method for analyzing hybrid systems with rough measurements and discuss how they can be used to identify sufficient safe environments. | Mitra |
| 3:20-3:50 | Break6Coffee shop in the neighboring building (across the lawn). | |
| 3:50-4:15 | Hybrid Anchoring and Anchorability7Collapse of dimension — the consequence of an attracting invariant submanifold — commands a central focus in the folklore and practice of applied dynamical systems theory, particularly in biology. For example in organismal biology, its interpretation as a low degree of freedom (DoF) behavioral “template” to be “anchored” in the high DoF animal body has won substantial popularity over the past quarter century in addressing Bernstein’s century old “DoFProblem.” In classical engineering applications, the question of how to synthesize such closed loop behaviors seems amenable to techniques for assessing stabilizability in open loop systems and the study of “perplexity” – topological obstructions to desired attracting sets – in the resulting closed loop. However, in the hybrid setting, this agenda is hindered from the start by the lack of a broadly applicable model of what it might mean to posit an “open” hybrid system that includes the locus of the guard sets within the purview of the controller’s input affordance. This talk will review recent progress within a robotics research agenda that has sought to bypass the need to formalize the concept of an “open” hybrid system by recourse to behavior synthesis via parallel and sequential compositions of pre-synthesized anchored templates. After reviewing work in progress advancing the formal analysis and empirical construction of spatial anchors for bioinspired sagittal plane locomotion templates, the discussion will shift to describe parallel progress in a data mining pipeline for discovering new such constructions from animal motion capture data. The talk concludes with some brief speculative remarks bearing on a reconsideration of how to frame the characterization of hybrid guardset affordance in the robotics setting. | Koditschek |
| 4:15-4:40 | Categorical Synthesis8In this talk I will describe our progress on the following controller synthesis problem: given a specification system S and a plant P, when does there exist (and how to compute) and controller C so that the composition of C with P is “equivalent” to S. I will review the discussions within our team about this problem and how they led to a different notion of “equivalence” and its categorical formalization. In doing so, I will also establish bridges with other work being done in our team. I will conclude with a working version of a result relating this controller synthesis problem to stabilizability of a certain sub-object of an open hybrid systems. | Tabuada |
| 4:40-5:05 | A categorical approach to Lyapunov stability9Lyapunov functions characterize stability for dynamical systems, and Lyapunov analysis forms the foundations for modern nonlinear control. We present a categorical framework for Lyapunov theory, generalizing stability analysis through Lyapunov functions. Core to our approach is the axioms underlying a setting for stability, which give the necessary ingredients for “doing Lyapunov theory” in a category of interest. With these minimal assumptions we define stability, formulate Lyapunov morphisms, and demonstrate that the existence of Lyapunov morphisms imply stability. This is applied to systems, framed as coalgebras, wherein we recover the classic Lyapunov conditions for stability and asymptotic stability. | Moeller |
| 5:05-5:30 | Wrap up |
Lunch opportunities abound: on Green, Wright and 6th Streets, within 7 minutes walk.
