23,986 research outputs found
Constrained optimal controller for linear systems with state and control dependent disturbance
The problem is posed with the additional constraints that the dynamic controller uses only noise-corrupted outputs, and that its dimension is significantly lower than that of a Kalman filter. The unknown disturbance is viewed as an adversary which tries to maximize a performance criterion: a criterion that the controller gains attempt to minimize. The optimal controller gains are determined by solving a nonlinear matrix two-point boundary value problem
Nonlinear Relaxation Dynamics in Elastic Networks and Design Principles of Molecular Machines
Analyzing nonlinear conformational relaxation dynamics in elastic networks
corresponding to two classical motor proteins, we find that they respond by
well-defined internal mechanical motions to various initial deformations and
that these motions are robust against external perturbations. We show that this
behavior is not characteristic for random elastic networks. However, special
network architectures with such properties can be designed by evolutionary
optimization methods. Using them, an example of an artificial elastic network,
operating as a cyclic machine powered by ligand binding, is constructed.Comment: 12 pages, 9 figure
A geometrically controlled rigidity transition in a model for confluent 3D tissues
The origin of rigidity in disordered materials is an outstanding open problem
in statistical physics. Previously, a class of 2D cellular models has been
shown to undergo a rigidity transition controlled by a mechanical parameter
that specifies cell shapes. Here, we generalize this model to 3D and find a
rigidity transition that is similarly controlled by the preferred surface area:
the model is solid-like below a dimensionless surface area of
, and fluid-like above this value. We demonstrate that,
unlike jamming in soft spheres, residual stresses are necessary to create
rigidity. These stresses occur precisely when cells are unable to obtain their
desired geometry, and we conjecture that there is a well-defined minimal
surface area possible for disordered cellular structures. We show that the
behavior of this minimal surface induces a linear scaling of the shear modulus
with the control parameter at the transition point, which is different from the
scaling observed in particulate matter. The existence of such a minimal surface
may be relevant for biological tissues and foams, and helps explain why cell
shapes are a good structural order parameter for rigidity transitions in
biological tissues.Comment: 6 pages main text + 13 pages appendix, 3 main text figures + 6
appendix figure
Survivability of Deterministic Dynamical Systems
The notion of a part of phase space containing desired (or allowed) states of
a dynamical system is important in a wide range of complex systems research. It
has been called the safe operating space, the viability kernel or the sunny
region. In this paper we define the notion of survivability: Given a random
initial condition, what is the likelihood that the transient behaviour of a
deterministic system does not leave a region of desirable states. We
demonstrate the utility of this novel stability measure by considering models
from climate science, neuronal networks and power grids. We also show that a
semi-analytic lower bound for the survivability of linear systems allows a
numerically very efficient survivability analysis in realistic models of power
grids. Our numerical and semi-analytic work underlines that the type of
stability measured by survivability is not captured by common asymptotic
stability measures.Comment: 21 pages, 6 figure
- …