221,842 research outputs found
A Fast Eigen Solution for Homogeneous Quadratic Minimization with at most Three Constraints
We propose an eigenvalue based technique to solve the Homogeneous Quadratic
Constrained Quadratic Programming problem (HQCQP) with at most 3 constraints
which arise in many signal processing problems. Semi-Definite Relaxation (SDR)
is the only known approach and is computationally intensive. We study the
performance of the proposed fast eigen approach through simulations in the
context of MIMO relays and show that the solution converges to the solution
obtained using the SDR approach with significant reduction in complexity.Comment: 15 pages, The same content without appendices is accepted and is to
be published in IEEE Signal Processing Letter
Optimal entanglement witnesses for continuous-variable systems
This paper is concerned with all tests for continuous-variable entanglement
that arise from linear combinations of second moments or variances of canonical
coordinates, as they are commonly used in experiments to detect entanglement.
All such tests for bi-partite and multi-partite entanglement correspond to
hyperplanes in the set of second moments. It is shown that all optimal tests,
those that are most robust against imperfections with respect to some figure of
merit for a given state, can be constructed from solutions to semi-definite
optimization problems. Moreover, we show that for each such test, referred to
as entanglement witness based on second moments, there is a one-to-one
correspondence between the witness and a stronger product criterion, which
amounts to a non-linear witness, based on the same measurements. This
generalizes the known product criteria. The presented tests are all applicable
also to non-Gaussian states. To provide a service to the community, we present
the documentation of two numerical routines, FULLYWIT and MULTIWIT, which have
been made publicly available.Comment: 14 pages LaTeX, 1 figure, presentation improved, references update
H∞ control of nonlinear systems: a convex characterization
The nonlinear H∞-control problem is considered with an emphasis on developing machinery with promising computational properties. The solutions to H∞-control problems for a class of nonlinear systems are characterized in terms of nonlinear matrix inequalities which result in convex problems. The computational implications for the characterization are discussed
Constraining Attacker Capabilities Through Actuator Saturation
For LTI control systems, we provide mathematical tools - in terms of Linear
Matrix Inequalities - for computing outer ellipsoidal bounds on the reachable
sets that attacks can induce in the system when they are subject to the
physical limits of the actuators. Next, for a given set of dangerous states,
states that (if reached) compromise the integrity or safe operation of the
system, we provide tools for designing new artificial limits on the actuators
(smaller than their physical bounds) such that the new ellipsoidal bounds (and
thus the new reachable sets) are as large as possible (in terms of volume)
while guaranteeing that the dangerous states are not reachable. This guarantees
that the new bounds cut as little as possible from the original reachable set
to minimize the loss of system performance. Computer simulations using a
platoon of vehicles are presented to illustrate the performance of our tools
Generalized ℓ2 synthesis
A framework for optimal controller design with generalized ℓ2 objectives is presented. The allowable disturbances are constrained to be in a pre-specified set; the design objective is to ensure that the resulting output errors do not belong to another pre-specified set. The solution takes the form of an affine matrix inequality (AMI), which is both a necessary
and sufficient condition for the posed problem to have a solution. In the simplest case, the resulting optimization reduces to standard ℋ∞ synthesis
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