Carleman framework filtering of nonlinear noisy phase-locked loop system
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Prashant G. Medewar
,
Shambhu N. Sharma
Abstract
In control and communications, the phase-locked loop (PLL) is regarded as the demodulator. Under the presence of small noise, the PLL system fails to accomplish the locking condition resulting in the stochastic phase difference. As a result of this, the PLL becomes a nontrivial nonlinear stochastic system. To circumvent the curse of dimensionality and nonlinearity, we exploit the method of linearization in the Carleman framework in combination with the finite closure for the stochastic system considered here. We show that the Carleman linearization has proven useful to preserve the nonlinearity via bilinearization. The Carleman setup of the nonlinear stochastic differential system has the Markov property and the terms are manageable. Then, we filter the states of the PLL using the filtering theory of the homogeneous Markov process. Finally, the numerical simulations reveal the superiority of the proposed filtering in Carleman setting in contrasts with the celebrated extended Kalman filtering framework.
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Author contribution: All the authors have accepted responsibility for the entire content of this submitted manuscript and approved submission.
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Research funding: None declared.
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Conflict of interest statement: The authors declare no conflicts of interest regarding this article.
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Articles in the same Issue
- Frontmatter
- Original Research Articles
- Testing of logarithmic-law for the slip with friction boundary condition
- A new clique polynomial approach for fractional partial differential equations
- The modified Rusanov scheme for solving the phonon-Bose model
- Delta-shock for a class of strictly hyperbolic systems of conservation laws
- The Cădariu–Radu method for existence, uniqueness and Gauss Hypergeometric stability of a class of Ξ-Hilfer fractional differential equations
- Novel periodic and optical soliton solutions for Davey–Stewartson system by generalized Jacobi elliptic expansion method
- The simulation of two-dimensional plane problems using ordinary state-based peridynamics
- Reduced basis method for the nonlinear Poisson–Boltzmann equation regularized by the range-separated canonical tensor format
- Simulation of the crystallization processes by population balance model using a linear separation method
- PS and GW optimization of variable sliding gains mode control to stabilize a wind energy conversion system under the real wind in Adrar, Algeria
- Characteristics of internal flow of nozzle integrated with aircraft under transonic flow
- Magnetogasdynamic shock wave propagation using the method of group invariance in rotating medium with the flux of monochromatic radiation and azimuthal magnetic field
- The influence pulse-like near-field earthquakes on repairability index of reversible in mid-and short-rise buildings
- Intelligent controller for maximum power extraction of wind generation systems using ANN
- A new self-adaptive inertial CQ-algorithm for solving convex feasibility and monotone inclusion problems
- Existence and Hyers–Ulam stability of solutions for nonlinear three fractional sequential differential equations with nonlocal boundary conditions
- A study on solvability of the fourth-order nonlinear boundary value problems
- Adaptive control for position and force tracking of uncertain teleoperation with actuators saturation and asymmetric varying time delays
- Framing the hydrothermal significance of water-based hybrid nanofluid flow over a revolving disk
- Catalytic surface reaction on a vertical wavy surface placed in a non-Darcy porous medium
- Carleman framework filtering of nonlinear noisy phase-locked loop system
- Corrigendum
- Corrigendum to: numerical modeling of thermal influence to pollutant dispersion and dynamics of particles motion with various sizes in idealized street canyon
