57 research outputs found
The Exponentially Faster Stick-Slip Dynamics of the Peeling of an Adhesive Tape
The stick-slip dynamics is considered from the nonlinear
differential-algebraic equation (DAE) point of view and the peeling dynamics is
shown to be a switching differential index DAE model. In the stick-slip regime
with bifurcations, the differential index can be arbitrarily high. The time
scale of the peeling velocity, the algebraic variable, in this regime is shown
to be exponentially faster compared to the angular velocity of the spool and/or
the stretch rate of the tape. A homogenization scheme for the peeling velocity
which is characterized by the bifurcations is discussed and is illustrated with
numerical examples.Comment: 7 figures, 24 page
Rollover Preventive Force Synthesis at Active Suspensions in a Vehicle Performing a Severe Maneuver with Wheels Lifted off
Among the intelligent safety technologies for road vehicles, active
suspensions controlled by embedded computing elements for preventing rollover
have received a lot of attention. The existing models for synthesizing and
allocating forces in such suspensions are conservatively based on the
constraint that no wheels lift off the ground. However, in practice,
smart/active suspensions are more necessary in the situation where the wheels
have just lifted off the ground. The difficulty in computing control in the
last situation is that the problem requires satisfying disjunctive constraints
on the dynamics. To the authors',knowledge, no efficient solution method is
available for the simulation of dynamics with disjunctive constraints and thus
hardware realizable and accurate force allocation in an active suspension tends
to be a difficulty. In this work we give an algorithm for and simulate
numerical solutions of the force allocation problem as an optimal control
problem constrained by dynamics with disjunctive constraints. In particular we
study the allocation and synthesis of time-dependent active suspension forces
in terms of sensor output data in order to stabilize the roll motion of the
road vehicle. An equivalent constraint in the form of a convex combination
(hull) is proposed to satisfy the disjunctive constraints. The validated
numerical simulations show that it is possible to allocate and synthesize
control forces at the active suspensions from sensor output data such that the
forces stabilize the roll moment of the vehicle with its wheels just lifted off
the ground during arbitrary fish-hook maneuvers
Reinforcing POD-based model reduction techniques in reaction-diffusion complex networks using stochastic filtering and pattern recognition
Complex networks are used to model many real-world systems. However, the
dimensionality of these systems can make them challenging to analyze.
Dimensionality reduction techniques like POD can be used in such cases.
However, these models are susceptible to perturbations in the input data. We
propose an algorithmic framework that combines techniques from pattern
recognition (PR) and stochastic filtering theory to enhance the output of such
models. The results of our study show that our method can improve the accuracy
of the surrogate model under perturbed inputs. Deep Neural Networks (DNNs) are
susceptible to adversarial attacks. However, recent research has revealed that
Neural Ordinary Differential Equations (neural ODEs) exhibit robustness in
specific applications. We benchmark our algorithmic framework with the neural
ODE-based approach as a reference.Comment: 19 pages, 6 figure
Explicitly Constrained Stochastic Differential Equations on Manifolds
In this manuscript we consider Intrinsic Stochastic Differential Equations on
manifolds and constrain it to a level set of a smooth function. Such type of
constraints are known as explicit algebraic constraints. The system of
differential equation and the algebraic constraints is, in combination, called
the Stochastic Differential Algebraic Equations (SDAEs). We consider these
equations on manifolds and present methods for computing the solution of SDAEs.Comment: 13 pages, 2 Algorithm
Data driven approach to sparsification of reaction diffusion complex network systems
Graph sparsification is an area of interest in computer science and applied
mathematics. Sparsification of a graph, in general, aims to reduce the number
of edges in the network while preserving specific properties of the graph, like
cuts and subgraph counts. Computing the sparsest cuts of a graph is known to be
NP-hard, and sparsification routines exists for generating linear sized
sparsifiers in almost quadratic running time .
Consequently, obtaining a sparsifier can be a computationally demanding task
and the complexity varies based on the level of sparsity required. In this
study, we extend the concept of sparsification to the realm of
reaction-diffusion complex systems. We aim to address the challenge of reducing
the number of edges in the network while preserving the underlying flow
dynamics. To tackle this problem, we adopt a relaxed approach considering only
a subset of trajectories. We map the network sparsification problem to a data
assimilation problem on a Reduced Order Model (ROM) space with constraints
targeted at preserving the eigenmodes of the Laplacian matrix under
perturbations. The Laplacian matrix () is the difference between the
diagonal matrix of degrees () and the graph's adjacency matrix (). We
propose approximations to the eigenvalues and eigenvectors of the Laplacian
matrix subject to perturbations for computational feasibility and include a
custom function based on these approximations as a constraint on the data
assimilation framework. We demonstrate the extension of our framework to
achieve sparsity in parameter sets for Neural Ordinary Differential Equations
(neural ODEs)
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