The use of electrical stimulation as a therapeutic modality is rapidly expanding its reach into all disciplines in medicine. These electroceuticals are being used to combat everything from Parkinsonian tremors, epilepsy to depression and inflammatory bowel disease. Compared to the field of pharmaceuticals where much is known about the pharmacodynamics and kinetics of molecular compounds, very little is known in this field regarding the electrical dynamics and kinetics of complex neurological networks. Most research done in this field has been through the use of rudimentary rectangular biphasic stimulus waveforms. In this talk, I will review some of the computational strategies that have been used to optimize the shape of the stimulus waveform, and I will discuss some potential ideas for future exploration.
Joshua Chang is an assistant professor of the Departments of Neurology and Population Health at Dell Medical School at The University of Texas at Austin. He received his B.S. and M.Eng at MIT in Electrical Engineering and Computer Science, with a focusing on signal processing, control theory and artificial intelligence. After working a couple years as a software engineer and IT consultant, he pursued an MD/PhD at the University of Massachusetts Medical School, where he completed his thesis in Quantitative Health Sciences under the supervision of Dr. David Paydarfar in the design and development of evolutionary algorithms to optimize stimulus waveforms for implantable electrical devices. He continues his research here as an investigator of the Clayton Foundation for Research.
As multi-agent systems grow and become increasingly data-driven, more and more personal data can be shared with unknown or unintended recipients. For example, self-driving cars may share position information for collision avoidance, and smart power grids may share power consumption data to optimize power generation. Even seemingly innocuous data can be very revealing about users, and new data-driven technologies must therefore protect sensitive user data while still allowing networks of agents to function. To address this need, I will present a differentially private implementation for multi-agent tracking control. This talk will use the classic linear-quadratic (LQ) tracking problem to give a broadly applicable problem formulation, and I will cover a recent privacy implementation that integrates a centralized cloud computer into an otherwise decentralized network. The agents add noise to all data sent to the cloud in order to enforce differential privacy, which gives each agent strong, rigorous privacy guarantees. In contrast to some existing approaches, the cloud does not need to be trusted and instead receives only private information from users, which it then uses to generate control values for them. Functions of private data are therefore fed back into the system. To characterize privacy in feedback, I will present numerical bounds on how difficult it is to compute control values using private user data. The end result of this work is a privacy implementation coupled with a method for quantitatively trading off individual privacy and aggregate performance in networks.
Matthew Hale is an Assistant Professor of Mechanical and Aerospace Engineering at the University of Florida. He received his BSE in Electrical Engineering from the University of Pennsylvania in 2012, and his MS and PhD in Electrical and Computer Engineering from the Georgia Institute of Technology in 2015 and 2017, respectively. His research broadly pertains to designing coordination strategies for multi-agent systems under challenging conditions. Current research interests include privacy in control, asynchronous coordination of networks, and graph theory. He directs the Control, Optimization, and Robotics Engineering (CORE) Lab at the University of Florida, which houses a swarm robotics testbed for testing and validating algorithms developed by his group.
In the framework of steady-state diffusion problems, we show how the ideas of static condensation and hybridization lead to the introduction of the hybridizable discontinuous Galerkin methods.
Professor Cockburn received his Ph.D from University of Chicago in 1986 under the direction of Jim Douglas, Jr. He has spent all his academic career at University of Minnesota where he is now Distinguished McKnight University Professor. His research interests include the development of Discontinuous Galerkin methods for nonlinear conservation laws, second-order elliptic problems, electro-magnetism, wave propagation and elasticity.
Autonomous systems use closed-loop feedback of sensed or communicated information to meet desired objectives. Meeting such objectives is more challenging when autonomous systems are tasked with operating in uncertain complex environments with intermittent feedback. This presentation explores different analysis methods that quantify the effects of intermittent feedback with respect to stability and performance of the autonomous agent. Various scenarios are considered where the intermittency results from natural phenomena or adversarial actors, including purposeful intermittency to enable new capabilities. Specific examples include intermittency due to occlusions in image-based feedback and intermittency resulting from various network control problems.
Prof. Warren Dixon received his Ph.D. in 2000 from the Department of Electrical and Computer Engineering from Clemson University. He worked as a research staff member and Eugene P. Wigner Fellow at Oak Ridge National Laboratory (ORNL) until 2004, when he joined the University of Florida in the Mechanical and Aerospace Engineering Department where he currently holds the Newton C. Ebaugh professorship. His main research interest has been the development and application of Lyapunov-based control techniques for uncertain nonlinear systems. His work has been recognized by a number of early career, best paper, and student mentoring awards. He is a Fellow of ASME and IEEE for his contributions to control of uncertain nonlinear systems.
We discuss some recent developments in solution algorithms for the linear algebra problems that arise from parameter-dependent partial differential equations (PDEs). In this setting, there is a need to solve large coupled algebraic systems (which come from stochastic Galerkin methods), or large numbers of standard spatially discrete systems (arising from Monte Carlo or stochastic collocation methods). The ultimate goal is surrogate approximations to the PDE solutions that can be evaluated cheaply for multiple values of the parameters, which can be used effectively for simulation or uncertainty quantification. Our focus is on representing parameterized solutions in reduced-basis or low-rank matrix formats. We show that efficient solution algorithms can be built from multigrid methods designed for the underlying discrete PDE, in combination with methods for truncating the ranks of iterates, which reduce both cost and storage requirements of solution algorithms. These ideas can be applied to the systems arising from many ways of treating the parameter spaces, including stochastic Galerkin and collocation. In addition, we present new approaches for solving the dense systems that arise from reduced-order models by preconditioned iterative methods and we show that such approaches can also be combined with empirical interpolation methods to solve the algebraic systems that arise from nonlinear PDEs.
Topology optimization is able to provide unintuitive and innovative design solutions and a performance improvement (e.g. weight savings) in excess of 50% is not uncommonly demonstrated in a wide range of engineering design problems. With the rise of advance materials and additive manufacturing, topology optimization is attracting much attention in the recent years. This presentation will introduce topology optimization in structural design, fiber composites and architected material. It will also include more recent advances topology optimization, multiscale design optimization breaking down the barrier between material and structural designs. Another direction of interests in large-scale topology optimization using the latest sparse data structures tailored to novel level set method. We have demonstrated an order of magnitude improvements on both the memory footage and the computation time. These efforts represent a pathway to applying topology optimization for complex multiphysics multifunctional structures, which may be too complex to rely on designers’ intuition.
Dr. H Alicia Kim is Jacobs Scholar Chair Professor in the Structural Engineering Department of the University of California, San Diego and leads the Multiscale Multiphysics Design Optimization (M2DO) lab. Her interests are in design optimization for structures including level set topology optimization, multiscale optimization, coupled multi physics optimization, modeling and optimization of composite materials and multifunctional structures. She has published around 200 journal and conference papers in these fields including award winning papers at the AIAA conferences and World Congresses on Structural and Multidisciplinary Optimization. Her research in topology optimization began in the 90’s at the University of Sydney, Australia where she developed one of the first boundary based topology optimization methods. She continued her research at the University of Warwick and the University of Bath, UK before moving to the current position in 2015.