925 research outputs found
Neural-inspired sensors enable sparse, efficient classification of spatiotemporal data
Sparse sensor placement is a central challenge in the efficient
characterization of complex systems when the cost of acquiring and processing
data is high. Leading sparse sensing methods typically exploit either spatial
or temporal correlations, but rarely both. This work introduces a new sparse
sensor optimization that is designed to leverage the rich spatiotemporal
coherence exhibited by many systems. Our approach is inspired by the remarkable
performance of flying insects, which use a few embedded strain-sensitive
neurons to achieve rapid and robust flight control despite large gust
disturbances. Specifically, we draw on nature to identify targeted
neural-inspired sensors on a flapping wing to detect body rotation. This task
is particularly challenging as the rotational twisting mode is three
orders-of-magnitude smaller than the flapping modes. We show that nonlinear
filtering in time, built to mimic strain-sensitive neurons, is essential to
detect rotation, whereas instantaneous measurements fail. Optimized sparse
sensor placement results in efficient classification with approximately ten
sensors, achieving the same accuracy and noise robustness as full measurements
consisting of hundreds of sensors. Sparse sensing with neural inspired encoding
establishes a new paradigm in hyper-efficient, embodied sensing of
spatiotemporal data and sheds light on principles of biological sensing for
agile flight control.Comment: 21 pages, 19 figure
Koopman invariant subspaces and finite linear representations of nonlinear dynamical systems for control
In this work, we explore finite-dimensional linear representations of
nonlinear dynamical systems by restricting the Koopman operator to an invariant
subspace. The Koopman operator is an infinite-dimensional linear operator that
evolves observable functions of the state-space of a dynamical system [Koopman
1931, PNAS]. Dominant terms in the Koopman expansion are typically computed
using dynamic mode decomposition (DMD). DMD uses linear measurements of the
state variables, and it has recently been shown that this may be too
restrictive for nonlinear systems [Williams et al. 2015, JNLS]. Choosing
nonlinear observable functions to form an invariant subspace where it is
possible to obtain linear models, especially those that are useful for control,
is an open challenge.
Here, we investigate the choice of observable functions for Koopman analysis
that enable the use of optimal linear control techniques on nonlinear problems.
First, to include a cost on the state of the system, as in linear quadratic
regulator (LQR) control, it is helpful to include these states in the
observable subspace, as in DMD. However, we find that this is only possible
when there is a single isolated fixed point, as systems with multiple fixed
points or more complicated attractors are not globally topologically conjugate
to a finite-dimensional linear system, and cannot be represented by a
finite-dimensional linear Koopman subspace that includes the state. We then
present a data-driven strategy to identify relevant observable functions for
Koopman analysis using a new algorithm to determine terms in a dynamical system
by sparse regression of the data in a nonlinear function space [Brunton et al.
2015, arxiv]; we show how this algorithm is related to DMD. Finally, we
demonstrate how to design optimal control laws for nonlinear systems using
techniques from linear optimal control on Koopman invariant subspaces.Comment: 20 pages, 5 figures, 2 code
State-space model identification and feedback control of unsteady aerodynamic forces
Unsteady aerodynamic models are necessary to accurately simulate forces and
develop feedback controllers for wings in agile motion; however, these models
are often high dimensional or incompatible with modern control techniques.
Recently, reduced-order unsteady aerodynamic models have been developed for a
pitching and plunging airfoil by linearizing the discretized Navier-Stokes
equation with lift-force output. In this work, we extend these reduced-order
models to include multiple inputs (pitch, plunge, and surge) and explicit
parameterization by the pitch-axis location, inspired by Theodorsen's model.
Next, we investigate the na\"{\i}ve application of system identification
techniques to input--output data and the resulting pitfalls, such as unstable
or inaccurate models. Finally, robust feedback controllers are constructed
based on these low-dimensional state-space models for simulations of a rigid
flat plate at Reynolds number 100. Various controllers are implemented for
models linearized at base angles of attack , and . The resulting control laws are
able to track an aggressive reference lift trajectory while attenuating sensor
noise and compensating for strong nonlinearities.Comment: 20 pages, 13 figure
Ensemble-SINDy: Robust sparse model discovery in the low-data, high-noise limit, with active learning and control
Sparse model identification enables the discovery of nonlinear dynamical
systems purely from data; however, this approach is sensitive to noise,
especially in the low-data limit. In this work, we leverage the statistical
approach of bootstrap aggregating (bagging) to robustify the sparse
identification of nonlinear dynamics (SINDy) algorithm. First, an ensemble of
SINDy models is identified from subsets of limited and noisy data. The
aggregate model statistics are then used to produce inclusion probabilities of
the candidate functions, which enables uncertainty quantification and
probabilistic forecasts. We apply this ensemble-SINDy (E-SINDy) algorithm to
several synthetic and real-world data sets and demonstrate substantial
improvements to the accuracy and robustness of model discovery from extremely
noisy and limited data. For example, E-SINDy uncovers partial differential
equations models from data with more than twice as much measurement noise as
has been previously reported. Similarly, E-SINDy learns the Lotka Volterra
dynamics from remarkably limited data of yearly lynx and hare pelts collected
from 1900-1920. E-SINDy is computationally efficient, with similar scaling as
standard SINDy. Finally, we show that ensemble statistics from E-SINDy can be
exploited for active learning and improved model predictive control
Unsupervised decoding of long-term, naturalistic human neural recordings with automated video and audio annotations
Fully automated decoding of human activities and intentions from direct
neural recordings is a tantalizing challenge in brain-computer interfacing.
Most ongoing efforts have focused on training decoders on specific, stereotyped
tasks in laboratory settings. Implementing brain-computer interfaces (BCIs) in
natural settings requires adaptive strategies and scalable algorithms that
require minimal supervision. Here we propose an unsupervised approach to
decoding neural states from human brain recordings acquired in a naturalistic
context. We demonstrate our approach on continuous long-term
electrocorticographic (ECoG) data recorded over many days from the brain
surface of subjects in a hospital room, with simultaneous audio and video
recordings. We first discovered clusters in high-dimensional ECoG recordings
and then annotated coherent clusters using speech and movement labels extracted
automatically from audio and video recordings. To our knowledge, this
represents the first time techniques from computer vision and speech processing
have been used for natural ECoG decoding. Our results show that our
unsupervised approach can discover distinct behaviors from ECoG data, including
moving, speaking and resting. We verify the accuracy of our approach by
comparing to manual annotations. Projecting the discovered cluster centers back
onto the brain, this technique opens the door to automated functional brain
mapping in natural settings
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