246 research outputs found
Correlation Clustering with Low-Rank Matrices
Correlation clustering is a technique for aggregating data based on
qualitative information about which pairs of objects are labeled 'similar' or
'dissimilar.' Because the optimization problem is NP-hard, much of the previous
literature focuses on finding approximation algorithms. In this paper we
explore how to solve the correlation clustering objective exactly when the data
to be clustered can be represented by a low-rank matrix. We prove in particular
that correlation clustering can be solved in polynomial time when the
underlying matrix is positive semidefinite with small constant rank, but that
the task remains NP-hard in the presence of even one negative eigenvalue. Based
on our theoretical results, we develop an algorithm for efficiently "solving"
low-rank positive semidefinite correlation clustering by employing a procedure
for zonotope vertex enumeration. We demonstrate the effectiveness and speed of
our algorithm by using it to solve several clustering problems on both
synthetic and real-world data
Suspended Load Path Tracking Control Using a Tilt-rotor UAV Based on Zonotopic State Estimation
This work addresses the problem of path tracking control of a suspended load
using a tilt-rotor UAV. The main challenge in controlling this kind of system
arises from the dynamic behavior imposed by the load, which is usually coupled
to the UAV by means of a rope, adding unactuated degrees of freedom to the
whole system. Furthermore, to perform the load transportation it is often
needed the knowledge of the load position to accomplish the task. Since
available sensors are commonly embedded in the mobile platform, information on
the load position may not be directly available. To solve this problem in this
work, initially, the kinematics of the multi-body mechanical system are
formulated from the load's perspective, from which a detailed dynamic model is
derived using the Euler-Lagrange approach, yielding a highly coupled, nonlinear
state-space representation of the system, affine in the inputs, with the load's
position and orientation directly represented by state variables. A zonotopic
state estimator is proposed to solve the problem of estimating the load
position and orientation, which is formulated based on sensors located at the
aircraft, with different sampling times, and unknown-but-bounded measurement
noise. To solve the path tracking problem, a discrete-time mixed
controller with pole-placement constraints
is designed with guaranteed time-response properties and robust to unmodeled
dynamics, parametric uncertainties, and external disturbances. Results from
numerical experiments, performed in a platform based on the Gazebo simulator
and on a Computer Aided Design (CAD) model of the system, are presented to
corroborate the performance of the zonotopic state estimator along with the
designed controller
A Provable Defense for Deep Residual Networks
We present a training system, which can provably defend significantly larger
neural networks than previously possible, including ResNet-34 and DenseNet-100.
Our approach is based on differentiable abstract interpretation and introduces
two novel concepts: (i) abstract layers for fine-tuning the precision and
scalability of the abstraction, (ii) a flexible domain specific language (DSL)
for describing training objectives that combine abstract and concrete losses
with arbitrary specifications. Our training method is implemented in the DiffAI
system
Robust explicit model predictive control for hybrid linear systems with parameter uncertainties
Explicit model-predictive control (MPC) is a widely used control design
method that employs optimization tools to find control policies offline;
commonly it is posed as a semi-definite program (SDP) or as a mixed-integer SDP
in the case of hybrid systems. However, mixed-integer SDPs are computationally
expensive, motivating alternative formulations, such as zonotope-based MPC
(zonotopes are a special type of symmetric polytopes). In this paper, we
propose a robust explicit MPC method applicable to hybrid systems. More
precisely, we extend existing zonotope-based MPC methods to account for
multiplicative parametric uncertainty. Additionally, we propose a convex
zonotope order reduction method that takes advantage of the iterative structure
of the zonotope propagation problem to promote diagonal blocks in the zonotope
generators and lower the number of decision variables. Finally, we developed a
quasi-time-free policy choice algorithm, allowing the system to start from any
point on the trajectory and avoid chattering associated with discrete switching
of linear control policies based on the current state's membership in
state-space regions. Last but not least, we verify the validity of the proposed
methods on two experimental setups, varying physical parameters between
experiments
Zonotopic set-membership state estimation for discrete-time descriptor LPV systems
© 2018 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.This technical note proposes a novel set-membership state estimation approach based on zonotopes for discrete-time descriptor linear parameter-varying systems. The consistency test between the system model and measured outputs is implemented to construct a parameterized intersection zonotope with respect to a correction matrix. With a defined zonotope minimization criterion, we propose a novel offline optimization problem to obtain the optimal correction matrix. In addition, with the proposed approach, an adaptive bound of the radius of the intersection zonotope is also provided. Finally, a case study with a truck-trailer system is shown to illustrate the proposed approach.Peer ReviewedPostprint (author's final draft
Reachability Analysis and Safety Verification of Neural Feedback Systems via Hybrid Zonotopes
Hybrid zonotopes generalize constrained zonotopes by introducing additional
binary variables and possess some unique properties that make them convenient
to represent nonconvex sets. This paper presents novel hybrid zonotope-based
methods for the reachability analysis and safety verification of neural
feedback systems. Algorithms are proposed to compute the input-output
relationship of each layer of a feedforward neural network, as well as the
exact reachable sets of neural feedback systems. In addition, a sufficient and
necessary condition is formulated as a mixed-integer linear program to certify
whether the trajectories of a neural feedback system can avoid unsafe regions.
The proposed approach is shown to yield a formulation that provides the
tightest convex relaxation for the reachable sets of the neural feedback
system. Complexity reduction techniques for the reachable sets are developed to
balance the computation efficiency and approximation accuracy. Two numerical
examples demonstrate the superior performance of the proposed approach compared
to other existing methods.Comment: 8 pages, 4 figure
- …