12,712 research outputs found
Backstepping PDE Design: A Convex Optimization Approach
Abstract\u2014Backstepping design for boundary linear PDE is
formulated as a convex optimization problem. Some classes of
parabolic PDEs and a first-order hyperbolic PDE are studied,
with particular attention to non-strict feedback structures. Based
on the compactness of the Volterra and Fredholm-type operators
involved, their Kernels are approximated via polynomial
functions. The resulting Kernel-PDEs are optimized using Sumof-
Squares (SOS) decomposition and solved via semidefinite
programming, with sufficient precision to guarantee the stability
of the system in the L2-norm. This formulation allows optimizing
extra degrees of freedom where the Kernel-PDEs are included
as constraints. Uniqueness and invertibility of the Fredholm-type
transformation are proved for polynomial Kernels in the space
of continuous functions. The effectiveness and limitations of the
approach proposed are illustrated by numerical solutions of some
Kernel-PDEs
Enlarged Controllability of Riemann-Liouville Fractional Differential Equations
We investigate exact enlarged controllability for time fractional diffusion
systems of Riemann-Liouville type. The Hilbert uniqueness method is used to
prove exact enlarged controllability for both cases of zone and pointwise
actuators. A penalization method is given and the minimum energy control is
characterized.Comment: This is a preprint of a paper whose final and definite form is with
'Journal of Computational and Nonlinear Dynamics', ISSN 1555-1415, eISSN
1555-1423, CODEN JCNDDM, available at
[http://computationalnonlinear.asmedigitalcollection.asme.org]. Submitted
10-Aug-2017; Revised 28-Sept-2017 and 24-Oct-2017; Accepted 05-Nov-201
Norm Optimal Iterative Learning Control with Application to Problems in Accelerator based Free Electron Lasers and Rehabilitation Robotics
This paper gives an overview of the theoretical basis of the norm optimal approach to iterative learning control followed by results that describe more recent work which has experimentally benchmarking the performance that can be achieved. The remainder of then paper then describes its actual application to a physical process and a very novel application in stroke rehabilitation
Quantum Trajectories, State Diffusion and Time Asymmetric Eventum Mechanics
We show that the quantum stochastic unitary dynamics Langevin model for
continuous in time measurements provides an exact formulation of the Heisenberg
uncertainty error-disturbance principle. Moreover, as it was shown in the 80's,
this Markov model induces all stochastic linear and non-linear equations of the
phenomenological "quantum trajectories" such as quantum state diffusion and
spontaneous localization by a simple quantum filtering method. Here we prove
that the quantum Langevin equation is equivalent to a Dirac type boundary-value
problem for the second-quantized input "offer waves from future" in one extra
dimension, and to a reduction of the algebra of the consistent histories of
past events to an Abelian subalgebra for the "trajectories of the output
particles". This result supports the wave-particle duality in the form of the
thesis of Eventum Mechanics that everything in the future is constituted by
quantized waves, everything in the past by trajectories of the recorded
particles. We demonstrate how this time arrow can be derived from the principle
of quantum causality for nondemolition continuous in time measurements.Comment: 21 pages. See also relevant publications at
http://www.maths.nott.ac.uk/personal/vpb/publications.htm
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