Stability Of Dynamical Systems Research Articles

Fixed-time synchronization of coupled neural networks under Hölder continuous nonlinear activation function

This paper investigates the fixed-time stability of dynamical systems and its application on the fixed-time synchronization (FTSYN) of the coupled neural networks (NNs). Firstly, a new theorem on fixed-time stability is established, along with an estimation of the settling time. Based on the new theorem and Lyapunov direct method, two different sufficient criteria are derived to ensure that the NNs in presence of Hölder continuity can achieve synchronization within fixed-time based on 1-norm and 2-norm, separately. Finally, two numerical simulations are conducted to demonstrate the validity and accuracy of the main findings.

The structure of the toric locus of a reaction network

Abstract We consider toric dynamical systems, which are also called complex-balanced mass-action systems. These are remarkably stable polynomial dynamical systems that arise from the analysis of mathematical models of reaction networks when, under the assumption of mass-action kinetics, they can give rise to complex-balanced equilibria. Given a reaction network, we study the set of parameter values for which the network gives rise to toric dynamical systems, also called the toric locus of the network. The toric locus is an algebraic variety, and we are especially interested in its topological properties. We show that complex-balanced equilibria depend continuously on the parameter values in the toric locus, and, using this result, we prove that the toric locus has a remarkable product structure: it is homeomorphic to the product of the set of complex-balanced flux vectors and the affine invariant polyhedron of the network. In particular, it follows that the toric locus is a contractible manifold. Finally, we show that the toric locus is invariant with respect to bijective affine transformations of the generating reaction network.

Stabilization of impulsive fuzzy dynamic systems involving Caputo short-memory fractional derivative

Stabilization of impulsive fuzzy dynamic systems involving Caputo short-memory fractional derivative

Effects of Air-ring Bearing Parameters on the Dynamic Stability of Rotor Air-ring Bearing System

Effects of Air-ring Bearing Parameters on the Dynamic Stability of Rotor Air-ring Bearing System

On Stabilization of Nonlinear Continuously-Discrete Dynamic Systems with a Constant Discretization Step

On Stabilization of Nonlinear Continuously-Discrete Dynamic Systems with a Constant Discretization Step

ҰЙЫТҚУЫ БАР ОРНЫҚСЫЗ ЖҮЙЕНІҢ ДИНАМИКАЛЫҚ СИПАТТАМАЛАРЫН ТАЛДАУ

This research addresses the issues of evaluating the stability and effectiveness of dynamic control systems and analyzing their transient processes. The study thoroughly analyzes the dynamic characteristics of control systems, system stability and sensitivity, as well as factors such as the duration and amplitude of transient processes. The findings of the study indicate that feedback mechanisms play a crucial role in ensuring system stability, highlighting the effectiveness of correctly selecting control parameters. Moreover, the significance of existing theoretical methods for studying transient processes in dynamic systems and optimizing control systems has been proven. The results allow for the application of effective methods for designing and optimizing control systems in various industries, such as transportation, energy, and healthcare. The obtained data point to the need for further research to fully understand and improve the dynamic features of the system. In conclusion, the findings of the study provide opportunities for exploring new theoretical methods and tools for designing control systems and applying them in real-world industrial settings.

Voltage regulation control of three-stage synchronous generator based on modified differential evolution algorithm

Abstract In modern aviation power systems, the dynamic stability of power generation systems has become a major challenge. To tackle issues such as slow response, poor voltage stability, and voltage oscillations in aircraft synchronous generators under sudden load changes, a Proportional-Integral-Derivative (PID) voltage regulator modified using the Differential Evolution (DE) algorithm has been developed. Additionally, the DE algorithm’s convergence speed and robustness are enhanced through the incorporation of directional search strategies and adaptive control parameters. Simulation results demonstrate that the optimized regulator delivers rapid response and minimal overshoot, thereby improving the accuracy and dynamic performance of the voltage regulator. The modified DE algorithm notably accelerates convergence compared to the traditional DE algorithm.

A novel artificial intelligence based multistage controller for load frequency control in power systems

The imbalance between generated power and load demand often causes unwanted fluctuations in the frequency and tie-line power changes within a power system. To address this issue, a control process known as load frequency control (LFC) is essential. This study aims to optimize the parameters of the LFC controller for a two-area power system that includes a reheat thermal generator and a photovoltaic (PV) power plant. An innovative multi-stage TDn(1 + PI) controller is introduced to reduce the oscillations in frequency and tie-line power changes. This controller combines a tilt-derivative with an N filter (TDn) with a proportional-integral (PI) controller, which improves the system’s response by correcting both steady-state errors and the rate of change. This design enhances the stability and speed of dynamic control systems. A new meta-heuristic optimization technique called bio-dynamic grasshopper optimization algorithm (BDGOA) is used for the first time to fine-tune the parameters of the proposed controller and improve its performance. The effectiveness of the controller is evaluated under various load demands, parameter variations, and nonlinearities. Comparisons with other controllers and optimization algorithms show that the BDGOA-TDn(1 + PI) controller significantly reduces overshoot in system frequency and tie-line power changes and achieves faster settling times for these oscillations. Simulation results demonstrate that the BDGOA-TDn(1 + PI) controller significantly outperforms conventional controllers, achieving a reduction in overshoot by 75%, faster settling times by 60%, and a lower integral of time-weighted absolute error by 50% under diverse operating conditions, including parameter variations and nonlinearities such as time delays and governor deadband effects.

Stability and bifurcation analysis of a 2DOF dynamical system with piezoelectric device and feedback control

This study aims to demonstrate the behaviors of a two degree-of-freedom (DOF) dynamical system consisting of attached mass to a nonlinear damped harmonic spring pendulum with a piezoelectric device. Such a system is influenced by a parametric excitation force on the direction of the spring’s elongation and an operating moment at the supported point. A negative-velocity-feedback (NVF) controller is inserted into the main system to reduce the undesired vibrations that affect the system’s efficiency, especially at the resonance state. The equations of motion (EOM) are derived by using Lagrangian equations. Through the use of the multiple-scales-strategy (MSS), approximate solutions (AS) are investigated up to the third order. The accuracy of the AS is verified by comparing them to the obtained numerical solutions (NS) through the fourth-order Runge-Kutta Method (RK-4). The study delves into resonance cases and solvability conditions to provide the modulation equations (ME). Graphical representations showing the time histories of the obtained solutions and frequency responses are presented utilizing Wolfram Mathematica 13.2 in addition to MATLAB software. Additionally, discusses the bifurcation diagrams, Poincaré maps, and Lyapunov exponent spectrums to show the various behavior patterns of the system. To convert vibrating motion into electrical power, a piezoelectric sensor is connected to the dynamical model, which is just one of the energy harvesting (EH) technologies with extensive applications in the commercial, industrial, aerospace, automotive, and medical industries. Moreover, the time histories of the obtained solutions with and without control are analyzed graphically. Finally, resonance curves are used to discuss stability analysis and steady-state solutions.

Fractional-Order Modeling and Stochastic Dynamics Analysis of a Nonlinear Rubbing Overhung Rotor System

To study the nonlinear dynamic behavior and system stability of a rubbing overhung rotor with viscoelastic and memory-effect damping and random uncertain parameters, this paper introduces a fractional-order modeling and stochastic dynamic analysis method for the nonlinear overhung rotor system with frictional impact faults. Firstly, the dynamic equations of the overhung rotor considering friction effect and fractional damping effect are established based on the transfer matrix method and fractional order derivative. Then, the time-domain response of the fractional-order dynamic equations is solved by combining the Runge–Kutta method and the continuous fractional expansion, and the steady-state response characteristics of different fractional damping are analyzed in the deterministic case. Finally, to analyze the response of the system under the effect of stochastic parameters, the sparse grid-based PCE metamodel of the system response is developed. Statistical moments, probability distributions, and sensitivity indices of the response of stochastic systems are revealed. The results of this paper provide a theoretical basis for efficient and accurate prediction of the stochastic response of nonlinear rubbing overhung rotor systems.

Improved General Relativity Search Algorithm (IGRSA) for Designing Power System Stabilizers

This paper proposes a novel optimization algorithm for designing power system stabilizers (PSSs). The prospect of attaining higher stability motivated the authors to creat a new optimization algorithm for this study. A novel algorithm named the Improved General. Relativity Search Algorithm (IGRSA) was also developed by cloud theory to improve the performance of GRSA. The supremacy of the proposed approach is tested by comparing it with an introduced objective function in a medium multi-machine power system. The nonlinear simulation results and eigenvalues analysis has demonstrated that the proposed approach in this study is highly effective in enhancing the dynamic stability of the power system.

Empirical Stability Criteria for 3D Hierarchical Triple Systems. I. Circumbinary Planets

In this work we revisit the problem of the dynamical stability of hierarchical triple systems with applications to circumbinary planetary orbits. We derive critical semimajor axes based on simulating and analyzing the dynamical behavior of 3 × 108 binary star–planet configurations. For the first time, three-dimensional and eccentric planetary orbits are considered. We explore systems with a variety of binary and planetary mass ratios, binary and planetary eccentricities from 0 to 0.9, and orbital mutual inclinations ranging from 0° to 180°. Planetary masses range between the size of Mercury and the lower fusion boundary (approximately 13 Jupiter masses). The stability of each system is monitored over 106 planetary orbital periods. We provide empirical expressions in the form of multidimensional, parameterized fits for two borders that separate dynamically stable, unstable, and mixed zones. In addition, we offer a machine learning model trained on our data set as an alternative tool for predicting the stability of circumbinary planets. Both the empirical fits and the machine learning model are tested for their predictive capabilities against randomly generated circumbinary systems with very good results. The empirical formulae are also applied to the Kepler and TESS circumbinary systems, confirming that many planets orbit their host stars close to the stability limit of those systems. Finally, we present a REST application programming interface with a web-based application for convenient access to our simulation data set.

Improved Sliding Mode Control of a Wind Turbine System Based on a Developed Permanent Magnet Synchronous Generator

Wind energy conversion systems (WECS) are emerging as among the most reliable alternative energy sources, requiring innovative control strategies to improve performance and reduce operating costs. The objective of this paper is the implementation of sliding mode control (SMC) for a permanent magnet synchronous generator (PMSG) to optimize the dynamical response and wind turbine system (WTS) stability. The control architecture comprises the PMSG, an AC-DC power converter, and a DC bus link, with a particular focus on extracting the optimum wind turbine power during variable wind speeds. A complete system model was developed and tested in MATLAB for a PMSG of 2 MW subjected to uncertain fluctuations in wind speed. The simulation results confirm that the SMC technique significantly improves speed-tracking accuracy, minimizes current ripple, and improves overall system stability. In addition, the proposed method ensures robust performance under non-linear and uncertain conditions, making it a viable solution for large-scale wind applications. These results highlight the potential of SMC to enhance the accuracy and efficiency of the WECS.

Optimizing size and location of UPFC for enhanced system dynamic stability using hybrid approach

This paper proposed a novel hybrid optimization technique, combining the Enhanced Multi-Strategic Sparrow Search Algorithm (EMSA) and White Shark Optimizer (WSO), to determine the optimal location and size of a Unified Power Flow Controller (UPFC) for enhancing power system dynamic stability. The proposed method offers improved search capabilities, reduced randomness, and lower computational complexity compared to existing approaches. Generator faults can significantly impact system dynamic stability constraints, including voltage and power loss. EMSA algorithm is employed to identify optimal location for UPFC placement by selecting bus with minimum power loss. Subsequently, WSO algorithm is used to optimize UPFC's capacity, ensuring that affected system parameters and dynamic stability constraints are restored within safe limits. Optimized UPFC is then installed at identified location, and system's power flow is analyzed. Proposed method is implemented in MATLAB/Simulink environment and tested on both IEEE 30 and IEEE 14 standard benchmark systems. Proposed method's performance is evaluated by comparison with existing methods.

Controllability and Optimal Fast Operation of Nonlinear Systems

A new method for solving the problem of controllability and optimal transient behavior of nonlinear systems subject to boundary conditions and constraints on control values was proposed. Unlike existing methods, this new approach is based on constructing a general solution of the integral equation for a linear controlled system, followed by transforming the original problem into a special initial optimal control problem. We propose a new method for studying the global asymptotic stability of dynamical systems with a cylindrical phase space with a countable equilibrium position based on a non-singular transformation of the equation of motion and estimation of improper integrals along the solution of the system. Conditions for global asymptotic stability were obtained without involving any periodic Lyapunov function, as well as the frequency theorem. The effectiveness of the proposed method is shown with an example.

Stability Analysis and Stabilization of General Conformable Polynomial Fuzzy Models with Time Delay

This paper introduces a sum-of-squares (S-O-S) approach to Stability Analysis and Stabilization (SAS) of nonlinear dynamical systems described by General Conformable Polynomial Fuzzy (GCPF) models with a time delay. First, we present GCPF models, which are more general compared to the widely recognized Takagi–Sugeno Fuzzy (T-SF) models. Then, we establish SAS conditions for these models using a Lyapunov–Krasovskii functional and the S-O-S approach, making the SAS conditions in this work less conservative than the Linear Matrix Inequalities (LMI)-based approach to the T-SF models. In addition, the SAS conditions are found by satisfying S-O-S conditions dependent on membership functions that are reliant on the polynomial fitting approximation algorithm. These S-O-S conditions can be solved numerically using the recently developed SOSTOOLS. To demonstrate the effectiveness and practicality of our approach, two numerical examples are provided to demonstrate the effectiveness and practicality of our approach.

Dynamical systems theory applied to short walking trials

Human walking is an extremely complex neuromuscular activity whose simplicity disappears when an attempt is made to provide a quantitative description of the process. The dynamical systems theory provides a framework for analyzing the stability and chaotic nature of dynamical systems, employing Floquet multipliers (FM) and long and short-term Lyapunov exponents (LE), respectively. This report compares FM and LE from three methods: method A (false nearest neighbors and numerical approximation), method B (false nearest neighbors and semi-analytical technique) and method C (singular value decomposition and semi-analytical technique). Data from 33 healthy older adults with no history of falls were used to explain the dynamic system. A surrogate center of mass trajectory was calculated for the analysis of sway in the transverse plane. Results revealed methodological differences in LE and FM calculations with semi-analytical solutions providing closer approximations to observed gait behavior. The long-term LE from Methods A and B were similar, but other LE pairings differed. Method A’s short-term LE indicated chaotic gaits for all subjects, while long-term LE from Methods A and B indicated chaos for half the subjects. Method C showed non-chaotic gait for most subjects. Method B’s FM indicated over 30% of subjects had unstable gait. Method C yielded values of LE and FM that most closely matched the subjects’ gait patterns. This study offers a methodological foundation for gait analysis using short time-series data, facilitating deeper insights into both stability and chaos within gait dynamics.

Control Method for Ultra-Low Frequency Oscillation and Frequency Control Performance in Hydro–Wind Power Sending System

In a hydropower-dominated power grid, the primary frequency regulation (PFR) capability of hydropower units is typically compromised to suppress ultra-low frequency oscillations (ULFOs). However, as renewable wind power is further integrated, a practicable solution to damp ULFOs has emerged, which is to adjust the frequency control parameters of wind turbine (WT) units. Driven by the goals of overall damping enhancement and ULFO suppression, this paper first establishes an extended unified frequency model (EUFM) of a hydro–wind power sending system. Based on EUFM, the damping torque of the hydro–wind power sending system is derived, and the specific impact of WT control parameters on ULFOs and PFR characteristics is investigated. Then, a novel optimization objective function considering damping in the ultra-low frequency band and PFR is formulated and solved using an intelligence algorithm. By optimizing the parameters of the WT to suppress ULFOs, the PFR capability of hydropower units can be released. Finally, simulation results verify that the optimized WT parameters can simultaneously address the ULFO problem and guarantee PFR performance, thereby enhancing the frequency dynamic stability of the sending system.

On the structure of the matrix in Sturm algorithm for determining the number of zeros in the open unit disk for a real polynomial

In 1984, C.W Schelin presented a numerical method for calculating the number of zeros of a real polynomial inside the unit disk using the argument principle and Cauchy index on [-1, 1] inspired by sturm’s algorithm [3], this method is based on calculation of the generalized Sturm sequence in Chebyshev form, however in some cases this algorithm does not efficient for this reason, it has been modified in another works [1], [2]. There are other numerical algorithms for calculating the number of zeros of a polynomial in the unit disk like shur -Cohn and Marden-Cohn but the numerical method presented in this study [1] is more efficient in cost of elementary operations (o (n2)). In this paper, we propose to improve this algorithm [1], to do this we study the matrix structure involved in the calculation of chebychev polynomials, for there on we prove that is a Toeplitz matrix which is known for their important properties in the complexity of calculations and we calculate its last line which is necessary to define the whole matrix to solve the linear system for calculating polynomials which are necessary to obtain Chebyshev sequence, this result will reduce calculation steps in this method [1]. This numerical algorithm may operate to study the stability of dynamical systems [2].

Output feedback stabilization of logical dynamical systems with state‐dependent control constraints

Output feedback stabilization of logical dynamical systems with state‐dependent control constraints