4,675 research outputs found
On Fractional Model Reference Adaptive Control
This paper extends the conventional Model Reference Adaptive Control systems to fractional ones based on the theory of fractional calculus. A control law and an incommensurate fractional adaptation law are designed for the fractional plant and the fractional reference model. The stability and
tracking convergence are analyzed using the frequency distributed fractional integrator model and Lyapunov theory. Moreover, numerical simulations of
both linear and nonlinear systems are performed to exhibit the viability and effectiveness of the proposed methodology
Pseudo-State Sliding Mode Control of Fractional SISO Nonlinear Systems
This paper deals with the problem of pseudo-state sliding mode
control of fractional SISO nonlinear systems with model inaccuracies. Firstly,
a stable fractional sliding mode surface is constructed based on the Routh-Hurwitz conditions for fractional differential equations. Secondly, a sliding
mode control law is designed using the theory of Mittag-Leffler stability. Further,
we utilize the control methodology to synchronize two fractional chaotic
systems, which serves as an example of verifying the viability and effectiveness
of the proposed technique
Hidden Conformal Symmetry for Vector Field on Various Black Hole Backgrounds
Hidden conformal symmetries of scalar field on various black hole backgrounds
have been investigated for years, but whether those features holds for other
fields are still open questions. Recently, with proper assumptions, Lunin
achieves to the separation of variables for Maxwell equations on Kerr
background. In this paper, with that equation, we find that hidden conformal
symmetry appears at near region under low frequency limit. We also extended
those results to vector field on Kerr-(A)dS and Kerr-NUT-(A)dS backgrounds,
then hidden conformal symmetry also appears if we focusing on the near-horizon
region at low frequency limit.Comment: 18 pages, no figure, matches the published versio
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