3,371 research outputs found
Optimal sampled-data control, and generalizations on time scales
In this paper, we derive a version of the Pontryagin maximum principle for
general finite-dimensional nonlinear optimal sampled-data control problems. Our
framework is actually much more general, and we treat optimal control problems
for which the state variable evolves on a given time scale (arbitrary non-empty
closed subset of R), and the control variable evolves on a smaller time scale.
Sampled-data systems are then a particular case. Our proof is based on the
construction of appropriate needle-like variations and on the Ekeland
variational principle.Comment: arXiv admin note: text overlap with arXiv:1302.351
Maximum Hands-Off Control: A Paradigm of Control Effort Minimization
In this paper, we propose a new paradigm of control, called a maximum
hands-off control. A hands-off control is defined as a control that has a short
support per unit time. The maximum hands-off control is the minimum support (or
sparsest) per unit time among all controls that achieve control objectives. For
finite horizon control, we show the equivalence between the maximum hands-off
control and L1-optimal control under a uniqueness assumption called normality.
This result rationalizes the use of L1 optimality in computing a maximum
hands-off control. We also propose an L1/L2-optimal control to obtain a smooth
hands-off control. Furthermore, we give a self-triggered feedback control
algorithm for linear time-invariant systems, which achieves a given sparsity
rate and practical stability in the case of plant disturbances. An example is
included to illustrate the effectiveness of the proposed control.Comment: IEEE Transactions on Automatic Control, 2015 (to appear
Projection operator formalism and entropy
The entropy definition is deduced by means of (re)deriving the generalized
non-linear Langevin equation using Zwanzig projector operator formalism. It is
shown to be necessarily related to an invariant measure which, in classical
mechanics, can always be taken to be the Liouville measure. It is not true that
one is free to choose a ``relevant'' probability density independently as is
done in other flavors of projection operator formalism. This observation
induces an entropy expression which is valid also outside the thermodynamic
limit and in far from equilibrium situations. The Zwanzig projection operator
formalism therefore gives a deductive derivation of non-equilibrium, and
equilibrium, thermodynamics. The entropy definition found is closely related to
the (generalized) microcanonical Boltzmann-Planck definition but with some
subtle differences. No ``shell thickness'' arguments are needed, nor desirable,
for a rigorous definition. The entropy expression depends on the choice of
macroscopic variables and does not exactly transform as a scalar quantity. The
relation with expressions used in the GENERIC formalism are discussed
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