1,595 research outputs found
Coverage and Field Estimation on Bounded Domains by Diffusive Swarms
In this paper, we consider stochastic coverage of bounded domains by a
diffusing swarm of robots that take local measurements of an underlying scalar
field. We introduce three control methodologies with diffusion, advection, and
reaction as independent control inputs. We analyze the diffusion-based control
strategy using standard operator semigroup-theoretic arguments. We show that
the diffusion coefficient can be chosen to be dependent only on the robots'
local measurements to ensure that the swarm density converges to a function
proportional to the scalar field. The boundedness of the domain precludes the
need to impose assumptions on decaying properties of the scalar field at
infinity. Moreover, exponential convergence of the swarm density to the
equilibrium follows from properties of the spectrum of the semigroup generator.
In addition, we use the proposed coverage method to construct a
time-inhomogenous diffusion process and apply the observability of the heat
equation to reconstruct the scalar field over the entire domain from
observations of the robots' random motion over a small subset of the domain. We
verify our results through simulations of the coverage scenario on a 2D domain
and the field estimation scenario on a 1D domain.Comment: To appear in the proceedings of the 55th IEEE Conference on Decision
and Control (CDC 2016
Controllability of the one-dimensional fractional heat equation under positivity constraints
This is a pre-copy-editing, author-produced PDF of an article accepted for publication in Communications on Pure and Applied Analysis following peer review. The definitive publisher-authenticated version Biccari, U., Warma, M., & Zuazua, E. (2020). Controllability of the one-dimensional fractional heat equation under positivity constraints. Communications on Pure & Applied Analysis, 19(4), 1949-1978.
is available online at https://www.aimsciences.org/article/doi/10.3934/cpaa.2020086In this paper, we analyze the controllability properties under positivity constraints on the control or the state of a one-dimensional heat equation involving the fractional Laplacian (−dx2)s (0 < s < 1) on the interval (−1, 1). We prove the existence of a minimal (strictly positive) time Tmin such that the fractional heat dynamics can be controlled from any initial datum in L2(−1, 1) to a positive trajectory through the action of a positive control, when s > 1/2. Moreover, we show that in this minimal time constrained controllability is achieved by means of a control that belongs to a certain space of Radon measures. We also give some numerical simulations that confirm our theoretical resultsThis project has received funding from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme (grant agreement NO. 694126-DyCon). The work of the three authors is partially supported by the Air Force Office of Scientific Research under Award NO: FA9550-18-1-0242. The work of the first and of the third author was partially supported by the Grant MTM2017-92996-C2-1-R COSNET of MINECO (Spain) and by the ELKARTEK project KK-2018/00083 ROAD2DC of the Basque Government. The work of the third author was partially supported by the Alexander von Humboldt-Professorship program, the European Union’s Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement NO. 765579-ConFlex, and by the Grant ICON-ANR-16-ACHN-0014 of the French AN
Recovering Linear Controllability of an Underactuated Spacecraft by Exploiting Solar Radiation Pressure
Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/140657/1/1.G001446.pd
Spectral control for ecological stability
A system made up of N interacting species is considered. Self-reaction terms
are assumed of the logistic type. Pairwise interactions take place among
species according to different modalities, thus yielding a complex asymmetric
disordered graph. A mathematical procedure is introduced and tested to
stabilise the ecosystem via an {\it ad hoc} rewiring of the underlying
couplings. The method implements minimal modifications to the spectrum of the
Jacobian matrix which sets the stability of the fixed point and traces these
changes back to species-species interactions. Resilience of the equilibrium
state appear to be favoured by predator-prey interactions
Water Management in PEM Fuel Cells: Controllability Analysis and Steady-state Optimization for Temperature Control
This paper presents a controllability study of the water management inside anode channel by
regulating the stack temperature for PEM fuel cell systems with dead-ended anode. Moreover, this work
includes the design of a steady-state target optimizer which calculates the temperature set-point profiles
that minimize the stack degradation and the hydrogen leaks. The control architecture is successfully
simulated and the results show promising performanc
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