1,641 research outputs found
Model Checking Tap Withdrawal in C. Elegans
We present what we believe to be the first formal verification of a
biologically realistic (nonlinear ODE) model of a neural circuit in a
multicellular organism: Tap Withdrawal (TW) in \emph{C. Elegans}, the common
roundworm. TW is a reflexive behavior exhibited by \emph{C. Elegans} in
response to vibrating the surface on which it is moving; the neural circuit
underlying this response is the subject of this investigation. Specifically, we
perform reachability analysis on the TW circuit model of Wicks et al. (1996),
which enables us to estimate key circuit parameters. Underlying our approach is
the use of Fan and Mitra's recently developed technique for automatically
computing local discrepancy (convergence and divergence rates) of general
nonlinear systems. We show that the results we obtain are in agreement with the
experimental results of Wicks et al. (1995). As opposed to the fixed parameters
found in most biological models, which can only produce the predominant
behavior, our techniques characterize ranges of parameters that produce (and do
not produce) all three observed behaviors: reversal of movement, acceleration,
and lack of response
Approximating Reachable Sets for Neural Network based Models in Real-Time via Optimal Control
In this paper, we present a data-driven framework for real-time estimation of
reachable sets for control systems where the plant is modeled using neural
networks (NNs). We utilize a running example of a quadrotor model that is
learned using trajectory data via NNs. The NN learned offline, can be excited
online to obtain linear approximations for reachability analysis. We use a
dynamic mode decomposition based approach to obtain linear liftings of the NN
model. The linear models thus obtained can utilize optimal control theory to
obtain polytopic approximations to the reachable sets in real-time. The
polytopic approximations can be tuned to arbitrary degrees of accuracy. The
proposed framework can be extended to other nonlinear models that utilize NNs
to estimate plant dynamics. We demonstrate the effectiveness of the proposed
framework using an illustrative simulation of quadrotor dynamics.Comment: 14 pages, 11 figures, journal paper that has been conditionally
accepte
Case Studies for Computing Density of Reachable States for Safe Autonomous Motion Planning
Density of the reachable states can help understand the risk of
safety-critical systems, especially in situations when worst-case reachability
is too conservative. Recent work provides a data-driven approach to compute the
density distribution of autonomous systems' forward reachable states online. In
this paper, we study the use of such approach in combination with model
predictive control for verifiable safe path planning under uncertainties. We
first use the learned density distribution to compute the risk of collision
online. If such risk exceeds the acceptable threshold, our method will plan for
a new path around the previous trajectory, with the risk of collision below the
threshold. Our method is well-suited to handle systems with uncertainties and
complicated dynamics as our data-driven approach does not need an analytical
form of the systems' dynamics and can estimate forward state density with an
arbitrary initial distribution of uncertainties. We design two challenging
scenarios (autonomous driving and hovercraft control) for safe motion planning
in environments with obstacles under system uncertainties. We first show that
our density estimation approach can reach a similar accuracy as the
Monte-Carlo-based method while using only 0.01X training samples. By leveraging
the estimated risk, our algorithm achieves the highest success rate in goal
reaching when enforcing the safety rate above 0.99.Comment: NASA Formal Methods 202
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