Asian Journal of Control最新文献

This manuscript focuses on solving the nonlinear time-fractional Navier–Stokes equations with Rosenblatt process and bounded delay in Hilbert space. Firstly, this work aims to reformulate the nonlinear partial differential equation using stochastic calculus, Stokes operator and Helmholtz–Hodge projection operator. By applying Mittag-Leffler functions, Schauder's fixed point theorem and stochastic analysis, the existence of mild solution is obtained. Under suitable assumptions, optimal control results are obtained for the proposed system through Balder's theorem. Finally, numerical examples are presented with and without delay, which ensures the obtained theoretical results.

Wind farms constantly inject varying power into the traditional power grid, affecting its operation and resulting in power quality and stability issues. Multivariable-based control strategies for pitch angle control are most widely utilized to stabilize the fluctuations in the output wind power. In this research work, Fractional Order PID (FOPID) and Model Reference Neural Network (MR-NN) controllers are proposed for controlling the pitch angle of a squirrel-cage induction generator (SCIG)-based wind turbine to stabilize the output active power under varying wind speeds. For comparison purposes, an Integer Order PI (IOPI) controller is also designed and implemented. Particle Swarm Optimization, Artificial Bee Colony (ABC), and Genetic Algorithm have been used to optimize the tuning parameters of both the IOPI and FOPID controllers. All the optimizing algorithms and controllers have been designed and realized in MATLAB. A comparative analysis of all the optimized variants of IOPI and FOPI controllers with MR-NN controllers has been performed. The FOPID controller using the ABC algorithm outperforms all other control techniques in both steady-state and transient-state performance. The FOPID-ABC controller achieved the fastest settling time (27.3 s) and the lowest steady-state error (−0.0006), demonstrating superior stability and precision in power regulation.

This paper addresses the challenge of designing observers for nonlinear tempered fractional-order (TFO) systems, which are characterized by their tempered fractional derivatives and Mittag–Leffler stability properties. We propose novel observer frameworks for systems with Lipschitz, one-sided Lipschitz (OSL), and quasi-OSL nonlinearities, leveraging Lyapunov stability theory and tempered fractional calculus. By integrating practical stability concepts with tempered Mittag–Leffler functions, we establish sufficient conditions for the practical stability of error dynamics under bounded disturbances. Numerical simulations validate the efficacy of the observers in tracking system states despite nonlinearities and disturbances. The results extend existing observer design methodologies to tempered fractional-order systems, offering broader applicability in control engineering.

In this work, we analyze a class of Hilfer fractional neutral stochastic differential equations with finite delay in a non-dense domain. We establish existence and uniqueness results using analytical tools from fractional calculus, semigroup theory, stochastic analysis, and fixed-point techniques. A set of assumptions is introduced to guarantee the existence and uniqueness of solutions. Furthermore, a set of hypotheses is provided to examine the approximate controllability of the system. An illustrative example is provided to highlight the theoretical developments.

This research paper focuses on analyzing the stability of fractional-order systems that use a specific type of fractional derivative, called the k-Caputo derivative. It presents a new theorem for determining stability of such systems, which is a generalized version of the Mittag–Leffler theorem. Additionally, it introduces the first observer design, for k-Caputo fractional-order systems. The paper concludes by demonstrating the effectiveness of these new findings, through a numerical simulation.

This study introduces a linear feedback control methodology for achieving synchronization in fractional-order (FO) time-delayed chaotic systems, establishing an order- and delay-dependent synchronization criterion through linear matrix inequality (LMI) formulations. First, an efficient linear control strategy is introduced aimed at synchronizing FO chaotic systems. This strategy is engineered for facile implementation in circuits and practical deployment in engineering contexts. Second, leveraging LMI techniques, the order- and delay-dependent criterion facilitates the derivation of the synchronization control gain matrix. Apart from theoretical analysis, an analog experimental circuit is designed specifically for FO time-delayed chaotic systems in this paper. Notably, the circuit design replaces conventional delay analog filter modules with all-pass filter configurations, simplifying electronic component requirements. Furthermore, the paper utilizes an effective approximation method for equivalently modeling arbitrary FO chaotic systems using standardized electronic components, thereby enabling physical circuit realizations. Finally, numerical simulations and analog circuit experiments are conducted to verify the theoretical framework.

This work investigates the existence and optimal control results for higher order Caputo fractional dynamical systems with damping. The first step is to use the standard Laplace transform and the concept of the $��(�\kappa �,�\gamma �)�$-regularized family of operators to define a mild solution for this system. Following that, we use the Banach fixed point theorem to discuss the existence and uniqueness results. This approach ensures that we can establish not only whether solution exist but also that they are unique, which is crucial for the predictability of the control system being studied. Finally, we present an example to validate the theoretical results.

The aim of this work is to discuss the existence and uniqueness of pseudo almost periodic solutions with measures for a class of two-term fractional differential equations, in Banach space, where the nonlinear perturbation is of measure pseudo almost periodic type. Finally, to illustrate our main results, we present two examples of fractional order delay relaxation oscillation equations.

The study of swelling soils is of considerable importance in geotechnical engineering and soil mechanics due to their capacity to undergo significant volumetric changes in response to moisture variation. These volumetric changes can affect the mechanical stability of structures such as foundations, retaining walls, and pavements. Traditional thermoelastic models often fall short in capturing the complex interaction between thermal, mechanical, and poroelastic effects in such materials, especially when memory and hereditary behavior are prominent. This necessitates the development of more sophisticated models that integrate porous effects with nonlocal time operators such as fractional derivatives. In this paper, we consider a fractional thermoelastic swelling system consisting of two-wave equations in one-dimensional argument with a heat conduction equation based on Fourier's law. The coupling occurs with the first component of the system, describing the displacement of the fluid. We prove that the system is Mittag-Leffler is stable under the usual physical condition on the coefficients of the system and the only dissipation resulting from the heat. Our result is obtained by using the multiplier method and some properties in fractional calculus.