2,395 research outputs found
A survey on fuzzy fractional differential and optimal control nonlocal evolution equations
We survey some representative results on fuzzy fractional differential
equations, controllability, approximate controllability, optimal control, and
optimal feedback control for several different kinds of fractional evolution
equations. Optimality and relaxation of multiple control problems, described by
nonlinear fractional differential equations with nonlocal control conditions in
Banach spaces, are considered.Comment: This is a preprint of a paper whose final and definite form is with
'Journal of Computational and Applied Mathematics', ISSN: 0377-0427.
Submitted 17-July-2017; Revised 18-Sept-2017; Accepted for publication
20-Sept-2017. arXiv admin note: text overlap with arXiv:1504.0515
Partial complete controllability of deterministic semilinear systems
In this paper the concept of partial complete controllability for deterministic semilinear control systems in separable Hilbert spaces is investigated. Some important systems can be expressed as a first order differential equation only by enlarging the state space. Therefore, the ordinary controllability concepts for them are too strong. This motivates the partial controllability concepts, which are directed to the original state space. Based on generalized contraction mapping theorem, a sufficient condition for the partial complete controllability of a semilinear deterministic control system is obtained in this paper. The result is demonstrated through appropriate examples.Publisher's Versio
Approximate controllability of Sobolev type fractional stochastic nonlocal nonlinear differential equations in Hilbert spaces
We introduce a new notion called fractional stochastic nonlocal condition, and then we study approximate controllability of class of fractional stochastic nonlinear differential equations of Sobolev type in Hilbert spaces. We use Hölder's inequality, fixed point technique, fractional calculus, stochastic analysis and methods adopted directly from deterministic control problems for the main results. A new set of sufficient conditions is formulated and proved for the fractional stochastic control system to be approximately controllable. An example is given to illustrate the abstract results
Approximate Controllability of Delayed Fractional Stochastic Differential Systems with Mixed Noise and Impulsive Effects
We herein report a new class of impulsive fractional stochastic differential
systems driven by mixed fractional Brownian motions with infinite delay and
Hurst parameter . Using fixed point techniques, a
-resolvent family, and fractional calculus, we discuss the existence of a
piecewise continuous mild solution for the proposed system. Moreover, under
appropriate conditions, we investigate the approximate controllability of the
considered system. Finally, the main results are demonstrated with an
illustrative example.Comment: Please cite this paper as follows: Hakkar, N.; Dhayal, R.; Debbouche,
A.; Torres, D.F.M. Approximate Controllability of Delayed Fractional
Stochastic Differential Systems with Mixed Noise and Impulsive Effects.
Fractal Fract. 2023, 7, 104. https://doi.org/10.3390/fractalfract702010
Behavioral Theory for Stochastic Systems? A Data-driven Journey from Willems to Wiener and Back Again
The fundamental lemma by Jan C. Willems and co-workers, which is deeply
rooted in behavioral systems theory, has become one of the supporting pillars
of the recent progress on data-driven control and system analysis. This
tutorial-style paper combines recent insights into stochastic and
descriptor-system formulations of the lemma to further extend and broaden the
formal basis for behavioral theory of stochastic linear systems. We show that
series expansions -- in particular Polynomial Chaos Expansions (PCE) of
-random variables, which date back to Norbert Wiener's seminal work --
enable equivalent behavioral characterizations of linear stochastic systems.
Specifically, we prove that under mild assumptions the behavior of the dynamics
of the -random variables is equivalent to the behavior of the dynamics of
the series expansion coefficients and that it entails the behavior composed of
sampled realization trajectories. We also illustrate the short-comings of the
behavior associated to the time-evolution of the statistical moments. The paper
culminates in the formulation of the stochastic fundamental lemma for linear
(descriptor) systems, which in turn enables numerically tractable formulations
of data-driven stochastic optimal control combining Hankel matrices in
realization data (i.e. in measurements) with PCE concepts.Comment: 30 pages, 8 figure
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