A Sum-of-Squares Approach to the Analysis of Zeno Stability in Polynomial Hybrid Systems

Hybrid dynamical systems can exhibit many unique phenomena, such as Zeno behavior. Zeno behavior is the occurrence of infinite discrete transitions in finite time. Zeno behavior has been likened to a form of finite-time asymptotic stability, and corresponding Lyapunov theorems have been developed. In this paper, we propose a method to construct Lyapunov functions to prove Zeno stability of compact sets in cyclic hybrid systems with parametric uncertainties in the vector fields, domains and guard sets, and reset maps utilizing sum-of-squares programming. This technique can easily be applied to cyclic hybrid systems without parametric uncertainties as well. Examples illustrating the use of the proposed technique are also provided

ANALYSIS OF ZENO STABILITY IN HYBRID SYSTEMS USING SUM-OF-SQUARES PROGRAMMING

Hybrid dynamical systems are systems that combine continuous dynamics with discrete transitions. Such systems can exhibit many unique phenomena, such as Zeno behavior. Zeno behavior is the occurrence of infinite discrete transitions in finite time. This phenomenon has been likened to a form of finite-time asymptotic stability, wherein trajectories converge asymptotically to compact sets in finite time whilst undergoing infinite transitions. Corresponding Lyapunov theorems have been developed. The main objective of our research was to develop computational techniques to determine whether or not a given hybrid system exhibits this Zeno phenomenon. In this thesis, we propose a method to algorithmically construct Lyapunov functions to prove Zeno stability of compact sets in hybrid systems. We use sum-of-squares programming to construct Lyapunov functions that allow us to prove Zeno stability of compact sets for hybrid systems with polynomial vector fields. Examples illustrating the use of the proposed technique are also provided. Finally, we provide a method using sum-of-squares programming to show Zeno stability of compact sets for systems with parametric uncertainties in the vector field, guard sets and domains, and transition maps. We then discuss potential applications of the proposed methods, along with examples.M.S. in Electrical Engineering, December 201

Optimizing DNN Architectures for High Speed Autonomous Navigation in GPS Denied Environments on Edge Devices

We address the challenge of high speed autonomous navigation of micro aerial vehicles (MAVs) using DNNs in GPS-denied environments with limited computational resources; specifically, we use the ODROID XU4 and the Raspberry Pi 3. The high computation costs of using DNNs for inference, particularly in the absence of powerful GPUs, necessitates negotiating a tradeoff between accuracy and inference. We address this tradeoff by employing sparsified neural networks. To obtain such architectures, we propose a novel algorithm to find sparse “sub networks” of existing pre trained models. Contrary to existing pruning-only strategies, our proposal includes a novel exploration step that efficiently searches for a different, but identically sparse, architecture with better generalization abilities. We derive learning theoretic bounds that reinforce our empirical findings that the optimized network achieves comparable generalization to the original network. We show that using our algorithm it is possible to discover models which, on average, have upto 19x fewer parameters than those obtained using existing state of the art pruning methods on autonomous navigation datasets, and achieve upto 6x improvements on inference time compared to existing state of the art shallow models on the ODROID XU4 and Raspberry Pi 3. Last, we demonstrate that our sparsified models can complete autonomous navigation missions with speeds upto 4 m/s using the ODROID XU4, which existing state of the art methods fail to do

Integration of Process Improvement (sequence unknown), IPRO 304 - Deliverables: IPRO 304 Poster F09

A. Finkl and Sons require an effective way of detecting carbide inserts on the steel milling machine. These inserts break off due to stress and shape of metal and need to be replaced immediately to avoid further damage to the machine and the steel to be milled.Sponsorship: A. Finkl and SonaDeliverables for IPRO 304: Integration of Process Improvements for the fall 2009 semester

Integration of Process Improvement (sequence unknown), IPRO 304 - Deliverables: IPRO 304 IPRO Day Presentation F09

A. Finkl and Sons require an effective way of detecting carbide inserts on the steel milling machine. These inserts break off due to stress and shape of metal and need to be replaced immediately to avoid further damage to the machine and the steel to be milled.Sponsorship: A. Finkl and SonaDeliverables for IPRO 304: Integration of Process Improvements for the fall 2009 semester

Integration of Process Improvement (sequence unknown), IPRO 304 - Deliverables: IPRO 304 Brochure F09

A. Finkl and Sons require an effective way of detecting carbide inserts on the steel milling machine. These inserts break off due to stress and shape of metal and need to be replaced immediately to avoid further damage to the machine and the steel to be milled.Sponsorship: A. Finkl and SonaDeliverables for IPRO 304: Integration of Process Improvements for the fall 2009 semester

Integration of Process Improvement (sequence unknown), IPRO 304 - Deliverables: 304

A. Finkl and Sons require an effective way of detecting carbide inserts on the steel milling machine. These inserts break off due to stress and shape of metal and need to be replaced immediately to avoid further damage to the machine and the steel to be milled.Sponsorship: A. Finkl and SonaDeliverables for IPRO 304: Integration of Process Improvements for the fall 2009 semester

Integration of Process Improvement (sequence unknown), IPRO 304 - Deliverables

A. Finkl and Sons require an effective way of detecting carbide inserts on the steel milling machine. These inserts break off due to stress and shape of metal and need to be replaced immediately to avoid further damage to the machine and the steel to be milled.Sponsorship: A. Finkl and SonaDeliverables for IPRO 304: Integration of Process Improvements for the fall 2009 semester