MAE Seminar – Control of Underactuated Autonomous Systems on Probability Densities

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MAE Seminar – Control of Underactuated Autonomous Systems on Probability Densities

Tuesday, February 6, 2024, at 12:50pm, Location: MAE-A 303

Dr. Karthik Elamvazhuthi, Postdoctoral Scholar, Department of Mechanical Engineering, University of California, Riverside

Abstract
Whether it’s a single satellite or a swarm of them, can we use a common framework for the design of controllers? In this talk, I will discuss the problem of controlling autonomous systems to target probability densities, a problem relevant to multi-agent control, control under uncertainties, and generative modeling in machine learning. Unlike classical control methods for multi-agent systems, the probabilistic approach provides globally stabilizing control laws, allowing for both nonlinearity of dynamics and non-convexity of the state-space. Using the same probabilistic framework, we propose a method for feedback control under uncertainty using Denoising Diffusion Probabilistic Models (DDPMs), the state-of-the-art method in generative modeling, employed by commercial tools like Dall-E and Midjourney. By conceptualizing feedback control of an autonomous system as a generative process, we show how one can steer a system towards desired target sets. I will then discuss how in each of these methods the well-posedness of the density control problem is influenced by geometric control and spectral theoretic properties of related partial differential operators. To validate this framework, I will present some simulation experiments verifying the proposed control methodologies on some examples from robotics such as sensor coverage, path planning of wheeled robots, and distributed environmental mapping.

Biography
Karthik Elamvazhuthi is a postdoctoral scholar in the Department of Mechanical Engineering, University of California, Riverside. Prior to that he was a CAM (Computational and Applied Mathematics) Assistant Adjunct Professor in the Department of Mathematics, University of California, Los Angeles. He completed his Ph.D. and M.S. degrees in mechanical engineering from Arizona State University, Tempe, AZ, USA, in 2019 and 2014, respectively. His research interests lie at the intersection of control theory, robotics and machine learning. Specifically, he is interested in optimal transport of nonlinear systems, control of robotic swarms, and understanding approximation capabilities of deep neural networks, using methods from partial differential equations and geometric control theory.

MAE Faculty Host: John Schueller