Nitin Shyamkumar

Classical data-driven control typically follows the learn-then-stabilize scheme where first a model of the system of interest is identified from data and then a controller is constructed based on the learned model. However, learning a model from data is challenging since it can incur high training costs and the model quality critically depends on the available data. In this work, we address how well one needs to learn a model to derive a controller by formalizing the trade off between learning error and controller performance in the specific setting of robust H-infinity control. We propose a bound on the stability radius of a robust controller with respect to the error of the learned model. The proposed analysis suggests that tolerating an increased learning error leads to a small decrease in the performance objective of the controller. Numerical experiments with systems from aerospace engineering demonstrate that judiciously balancing learning error and control performance can indeed reduce the number of data points by one order of magnitude with less than 5% decrease in control performance as measured with the H-infinity stability radius.

Recently, Cardwell et. al. proposed the BBR algorithm to improve on TCP variants for congestion control. In contrast to packet loss based congestion control algorithms, BBR attempts to operate at the optimal operating point of a bandwidth constrained network where the delay is minimized and throughput is maximized. However, BBR is in its early stage and has numerous shortcomings. We examine poor performance on throughput in long latency networks in detail. We survey three different techniques from hybrid systems literature, including identifying Piecewise Affine systems, Max Min Plus Scaling systems, and the Min Plus service curve framework from the network calculus literature. We develop an analytical explanation of the performance degradation for longer latencies and design a steady state model for BBR in the network calculus framework. Our analytical explanation also suggests two possible fixes to improve BBR throughput in long latency networks.

Physics informed machine learning consists of various machine learning methods for learning partial differential equation (PDE) models and solutions. We empirically study three methods from this field for learning solutions to a PDE model, focusing on the Hamilton Jacobi Bellman PDE for continuous time control. We find that the methods learn accurate solutions for high dimensional linear systems. Although the methods have some shortcomings, they achieve promising results on the Cartpole task from nonlinear control.

An obstacle to understanding neural mechanisms of movement is the complex, distributed nature of the mammalian motor system. Here we present a novel behavioral paradigm for high-throughput dissection of neural circuits underlying mouse forelimb control. Custom touch-sensing joysticks were used to quantify mouse forelimb trajectories with micron-millisecond spatiotemporal resolution. Joysticks were integrated into computer-controlled, rack-mountable home cages, enabling batches of mice to be trained in parallel. Closed loop behavioral analysis enabled online control of reward delivery for automated training. We used this system to show that mice can learn, with no human handling, a direction-specific hold-still center-out reach task in which a mouse first held its right forepaw still before reaching out to learned spatial targets. Stabilogram diffusion analysis of submillimeter-scale micromovements produced during the hold demonstrate that an active control process, akin to upright balance, was implemented to maintain forepaw stability. Trajectory decomposition methods, previously used in primates, were used to segment hundreds of thousands of forelimb trajectories into millions of constituent kinematic primitives. This system enables rapid dissection of neural circuits for controlling motion primitives from which forelimb sequences are built.

We present a fast bidirectional algorithm for estimating a single element of the product of a matrix power and vector. This is an important primitive in many applications; in particular, we describe how it can be used to estimate a single element in the solution of a linear system Ax = b, with sublinear average-case running time guarantees for sparse systems. Our work combines the von Neumann-Ulam MCMC scheme for matrix multiplication with recent developments in bidirectional algorithms for estimating random-walk metrics. In particular, given a target additive-error threshold, we show how to combine a reverse local-variational technique with forward MCMC sampling, such that the resulting algorithm is order-wise faster than each individual approach.