Search Results (132)

This article concerns a Cournot duopoly game with homogeneous expectations. The cost functions of the two players are assumed to be asymmetric to capture possible asymmetries in firms’ technologies or firms’ input costs. Large values of the speed of adjustment of the players destabilize the Nash Equilibrium (N.E.) and cause the appearance of a chaotic trajectory in the Discrete Dynamical System (D.D.S.). The scope of this article is to control the chaotic dynamics that appear outside the stability field, assuming asymmetric cost functions of the two players. Specifically, one player uses linear costs, while the other uses nonlinear costs (quadratic or cubic). The cubic cost functions are widely used in the Economic Dispatch Problem. The delayed feedback control method is applied by introducing a new control parameter at the D.D.S. It is shown that larger values of the control parameter keep the N.E. locally asymptotically stable even for higher values of the speed of adjustment. Full article

This paper proposes a Distributed Adaptive Regularization Algorithm (DARN) for solving composite non-convex and non-smooth optimization problems in multi-agent systems. The algorithm employs a three-phase iterative framework to achieve efficient collaborative optimization: (1) a local regularized optimization step, which utilizes proximal mappings to enforce strong convexity of weakly convex objectives and ensure subproblem well-posedness; (2) a consensus update based on doubly stochastic matrices, guaranteeing asymptotic convergence of agent states to a global consensus point; and (3) an innovative adaptive regularization mechanism that dynamically adjusts regularization strength using local function value variations to balance stability and convergence speed. Theoretical analysis demonstrates that the algorithm maintains strict monotonic descent under non-convex and non-smooth conditions by constructing a mixed time-scale Lyapunov function, achieving a sublinear convergence rate. Notably, we prove that the projection-based update rule for regularization parameters preserves lower-bound constraints, while spectral decay properties of consensus errors and perturbations from local updates are globally governed by the Lyapunov function. Numerical experiments validate the algorithm’s superiority in sparse principal component analysis and robust matrix completion tasks, showing a 6.6% improvement in convergence speed and a 51.7% reduction in consensus error compared to fixed-regularization methods. This work provides theoretical guarantees and an efficient framework for distributed non-convex optimization in heterogeneous networks. Full article

This paper introduces a novel field-oriented control (FOC) strategy for an open-end stator three-phase winding induction motor (OEW-TP-IM) using dual space vector modulation-pulse width modulation (SVM-PWM) inverters. This configuration reduces common mode voltage at the motor’s terminals, enhancing efficiency and reliability. The study presents a backstepping control approach combined with a mean value theorem (MVT)-based observer to improve control accuracy and stability. Stability analysis of the backstepping controller for key control loops, including flux, speed, and currents, is conducted, achieving asymptotic stability as confirmed through Lyapunov’s methods. An advanced observer using sector nonlinearity (SNL) and time-varying parameters from convex theory is developed to manage state observer error dynamics effectively. Stability conditions, defined as linear matrix inequalities (LMIs), are solved using MATLAB R2016b to optimize the observer’s estimator gains. This approach simplifies system complexity by measuring only two line currents, enhancing responsiveness. Comprehensive simulations validate the system’s performance under various conditions, confirming its robustness and effectiveness. This strategy improves the operational dynamics of OEW-TP-IM machine and offers potential for broad industrial applications requiring precise and reliable motor control. Full article

This paper investigates the distributed time-varying (TV) resource management problem (RMP) for microgrids (MGs) within a multi-agent system (MAS) framework. A novel fixed-time (FXT) distributed optimization algorithm is proposed, capable of operating over switching communication graphs and handling both local inequality and global equality constraints. By incorporating a time-decaying penalty function, the algorithm achieves an FXT consensus on marginal costs and ensures asymptotic convergence to the optimal TV solution of the original RMP. Unlike the prior methods with centralized coordination, the proposed algorithm is fully distributed, scalable, and privacy-preserving, making it suitable for real-time deployment in dynamic MG environments. Rigorous theoretical analysis establishes FXT convergence under both identical and nonidentical Hessian conditions. Simulations on the IEEE 14-bus system validate the algorithm’s superior performance in convergence speed, plug-and-play adaptability, and robustness to switching topologies. Full article

This paper conducts an in-depth investigation into the fundamental relationship between the fractal dimensions and convergence properties of mathematical sequences. By concentrating on three representative classes of sequences, namely, the factorial-decay, logarithmic-decay, and factorial–exponential types, a comprehensive framework is established to link their geometric characteristics with asymptotic behavior. This study makes two significant contributions to the field of fractal analysis. Firstly, a unified methodology is developed for the calculation of multiple fractal dimensions, including the Box, Hausdorff, Packing, and Assouad dimensions, of discrete sequences. This methodology reveals how these dimensional quantities jointly describe the structures of sequences, providing a more comprehensive understanding of their geometric properties. Secondly, it is demonstrated that different fractal dimensions play distinct yet complementary roles in regulating convergence rates. Specifically, the Box dimension determines the global convergence properties of sequences, while the Assouad dimension characterizes the local constraints on the speed of convergence. The theoretical results presented herein offer novel insights into the inherent connection between geometric complexity and analytical behavior within sequence spaces. These findings have immediate and far-reaching implications for various applications that demand precise control over convergence properties, such as numerical algorithm design and signal processing. Notably, the identification of dimension-based convergence criteria provides practical and effective tools for the analysis of sequence behavior in both pure mathematical research and applied fields. Full article

The identification of the orders of time series models plays a crucial role in their accurate specification and forecasting. The Autocorrelation Function (ACF) is commonly used to identify the order q of Moving Average (MA(q)) models, as it theoretically vanishes for lags beyond q. This property is widely used in model selection, assuming the sample ACF follows an asymptotic normal distribution for robustness. However, our examination of the sum of the sample ACF reveals inconsistencies with these theoretical properties, highlighting a deviation from normality in the sample ACF for MA(q) processes. As a natural extension of the ACF, the Extended Autocorrelation Function (EACF) provides additional insights by facilitating the simultaneous identification of both autoregressive and moving average components. Using simulations, we evaluate the performance of q-order identification in MA(q) models, which is based on the properties of ACF. Similarly, for ARMA($p,q$) models, we assess the ($p,q$)-order identification relying on EACF. Our findings indicate that both methods are effective for sufficiently long time series but may incorrectly favor an ARMA($p,q-1$) model when the $a_q$ coefficient approaches zero. Additionally, if the cumulative sums of ACF (SACF) behave consistently and the Ljung–Box test validates the proposed model, it can serve as a strong candidate. The proposed models should then be compared based on their predictive performance. We illustrate our methodology with an application to wind speed data and sea surface temperature anomalies, providing practical insights into the relevance of our findings. Full article

In this paper, we propose a smoothing estimation method for censored quantile regression models. The method associates the convolutional smoothing estimation with the loss function, which is quadratically derivable and globally convex by using a non-negative kernel function. Thus, the parameters of the regression model can be computed by using the gradient-based iterative algorithm. We demonstrate the convergence speed and asymptotic properties of the smoothing estimation for large samples in high dimensions. Numerical simulations show that the smoothing estimation method for censored quantile regression models improves the estimation accuracy, computational speed, and robustness over the classical parameter estimation method. The simulation results also show that the parametric methods perform better than the KM method in estimating the distribution function of the censored variables. Even if there is an error setting in the distribution estimation, the smoothing estimation does not fluctuate too much. Full article

An adaptive sliding mode controller (SMC) design with a reinforcement-learning parameter optimization method is proposed for variable-speed trajectory tracking control of underactuated vessels under scenarios involving model uncertainties and external environmental disturbances. First, considering the flexible control requirements of the vessel’s propulsion system, the desired navigation speed is designed to satisfy an S-curve acceleration and deceleration process. The rate of change of the trajectory parameters is derived. Second, to address the model uncertainties and external disturbances, an extended state observer (ESO) is designed to estimate the unknown bounded disturbances and to provide feedforward compensation. Moreover, an adaptive law is designed to estimate the upper bound of the unknown disturbances, ensuring system stability even in the presence of asymptotic observation errors. Finally, the Twin-Delayed Deep Deterministic Policy Gradient (TD3) algorithm is employed for real-time controller parameter tuning. Numerical simulation results demonstrate that the proposed method significantly improves the trajectory tracking accuracy and dynamic response speed of the underactuated vessel. Specifically, for a sinusoidal trajectory with an amplitude of 200 m and a frequency of 0.01, numerical results show that the proposed method achieves convergence of the longitudinal tracking error to zero, while the lateral tracking error remains stable within 1 m. For the circular trajectory with a radius of 300 m, the numerical results indicate that both the longitudinal and lateral tracking errors are stabilized within 1 m. Compared with the fixed-value sliding mode controller, the proposed method demonstrates superior trajectory tracking accuracy and smoother control performance. Full article

Symmetry is widely present in science and daily life. And the internal structure of surface-mounted permanent magnet synchronous motors (PMSMs) has good symmetry. This article is dedicated to studying the tracking problem of PMSMs with adaptive and backstepping control methods. The research objective of this study is to design new adaptive controllers $U_q$ and $U_d$, which enable the state of the motor position servo system to asymptotically and stably track the given signals of the system. They can suppress the impact of changes in B, J, and $T_L$ and can also enhance the robustness of the system. (i) The strongly coupled current and speed, variation of parameters over time, and nonlinearity of motor torque objectively pose significant challenges in the design of adaptive tracking controllers for PMSMs. (ii) Adaptive control technology and backstepping control methods are used for designing controllers for the PMSMs. (iii) After rigorous reasoning, an intelligent adaptive tracking control strategy for the PMSMs has been derived, which is for the direct axis current and the angle. (iv) The new adaptive tracking controllers are superior to existing controllers in that they can strongly suppress the disturbance of system parameters J, $T_L$, and B, make the system state asymptotically stable, and achieve good tracking performance for the given signals. The results of the simulation indicate the validity of the designed control strategy. Full article

In this paper, two ultra-wideband monopoles in a colinear structure are presented for application in remote terrestrial communication systems. The antennas consist of a loaded monopole with a hat and an elevated loaded monopole located in the upper position. All lumped loads are modeled as linear frequency-dependent components to approximate the practical component property for achieving ultra-wideband characteristics, since the constant value property of a component is only present in a relatively narrow band. The antennas are simulated by the method of moments (MoM) with asymptotic waveform evaluation (AWE) to speed up frequency sweep across a wide bandwidth. For proper simulation with the AWE process, the parallel RLC load with linear frequency-dependent components is modeled in a corresponding impedance function. With the optimized load parameters, one antenna covers 30–750 MHz with a VSWR < 3.5 and the other one covers 800 MHz–3000 MHz with a VSWR < 2.5, which are promising results for terrestrial omnidirectional applications. Full article

The conventional approach to intensity-modulated radiation therapy treatment planning involves two distinct strategies: optimizing an evaluation function while accounting for dose constraints, and solving feasibility problems using feasibility-seeking projection methods that incorporate inequality constraints. This paper introduces a novel iterative scheme within the framework of continuous dynamical systems, wherein constraint conditions dynamically evolve to enhance the optimization process. The validity of dynamically varying dose constraints is theoretically established through the foundation of continuous-time dynamical systems theory. In particular, we formalize a system of differential equations, with both beam coefficients and dose constraints modeled as state variables. The asymptotic stability of the system’s equilibrium is rigorously proven, ensuring convergence to a solution. In practical terms, we leverage a discretized iteration formula derived from the continuous-time system to achieve rapid computational speed. The mathematical structure of the proposed approach, which directly incorporates dose-volume constraints into the objective function, facilitates significant computational efficiency and solution refinement. The proposed method has an inherent dynamics that approaches more desirable solutions within the set of solutions when the solution to the optimization problem is not an isolated point. This property guarantees the identification of optimal solutions that respect the prescribed dose-volume constraints while enhancing accuracy when such constraints are feasible. By treating dose constraints as variables and concurrently solving the optimization problem with beam coefficients, we can achieve more accurate results when compared with using fixed values for prescribed dose conditions. Full article

In recent decades, there have been many studies on Hopf bifurcation and population stability with time delay. However, the stability and Hopf bifurcation of fractional-order population systems with time delay are lower. In this paper, we discuss the dynamic behavior of a fractional-order three-population model with pregnancy delay using Laplace transform of fractional differential equations, stability and bifurcation theory, and MATLAB software. The specific conditions of local asymptotic stability and Hopf bifurcation for fractional-order time-delay systems are determined. A fractional-order proportional–integral–derivative (PID) controller is applied to the three-population food chain system for the first time. The convergent speed and vibration amplitude of the system can be changed by PID control. For example, after fixing the values of the integral control gain $k_i$ and the differential control gain $k_d$, the amplitude of the system decreases and the convergence speed changes as the proportional control gain $k_p$ decreases. The effectiveness of the PID control strategy in complex ecosystem is proved. The numerical simulation results are in good agreement with the theoretical analysis. The research in this paper has potential application values concerning the management of complex population systems. The bifurcation theory of fractional-order time-delay systems is also enriched. Full article

The 1-day fast-sampling orbit phase of the Surface Water Ocean Topography (SWOT) satellite mission provides a unique opportunity to analyze high-frequency sea-state variability and its implications for altimeter sea state bias (SSB) model development. Time series with 1-day repeat sampling of sea-level anomaly (SLA) and SSB input parameters—comprising the significant wave height (SWH), wind speed (WS), and mean wave period (MWP)—are constructed using SWOT’s nadir altimeter data. The analyses corroborate the following key SSB modelling assumption central to empirical developments: the SLA noise due to all factors, aside from sea state change, is zero-mean. Global variance reduction tests on the SSB model’s performance using corrected SLA differences show that correction skill estimation using a specific (1D, 2D, or 3D) SSB model is unstable when using short time difference intervals ranging from 1 to 5 days, reaching a stable asymptotic limit after 5 days. It is proposed that this result is related to the temporal auto- and cross-correlations associated with the SSB model’s input parameters; the present study shows that SSB wind-wave input measurements take time (typically 1–4 days) to decorrelate in any given region. The latter finding, obtained using unprecedented high-frequency satellite data from multiple ocean basins, is shown to be consistent with estimates from an ocean wave model. The results also imply that optimal time-differencing (i.e., >4 days) should be considered when building SSB model data training sets. The SWOT altimeter data analysis of the temporal cross-correlations also permits an evaluation of the relationships between the SSB input parameters (SWH, WS, and MWP), where distinct behaviors are found in the swell- and wind-sea-dominated areas, and associated time scales are less than or on the order of 1 day. Finally, it is demonstrated that computing cross-correlations between the SLA (with and without SSB correction) and the SSB input parameters offers an additional tool for evaluating the relevance of candidate SSB input parameters, as well as for assessing the performance of SSB correction models, which, so far, mainly rely on the reduction in the variance of the differences in the SLA at crossover points. Full article

The propagation speeds of excitations are a crucial input in the modeling of interacting systems of particles. In this paper, we assume the microscopic physics is described by a kinetic theory for massless particles, which is approximated by a generalized relaxation time approximation (RTA) where the relaxation time depends on the energy of the particles involved. We seek a solution of the kinetic equation by assuming a parameterized one-particle distribution function (1-pdf) which generalizes the Chapman–Enskog (Ch-En) solution to the RTA. If developed to all orders, this would yield an asymptotic solution to the kinetic equation; we restrict ourselves to an approximate solution by truncating the Ch-En series to the second order. Our generalized Ch-En solution contains undetermined space-time-dependent parameters, and we derive a set of dynamical equations for them by applying the moments method. We check that these dynamical equations lead to energy–momentum conservation and positive entropy production. Finally, we compute the propagation speeds for fluctuations away from equilibrium from the linearized form of the dynamical equations. Considering relaxation times of the form $\tau ={\tau }_0{(-{\beta }_{\mu }{p}^{\mu })}^{-a}$, with $-\infty <a<2$, where ${\beta }_{\mu }=u_{\mu }/T$ is the temperature vector in the Landau frame, we show that the Anderson–Witting prescription $a=1$ yields the fastest speed in all scalar, vector and tensor sectors. This fact ought to be taken into consideration when choosing the best macroscopic description for a given physical system. Full article

This paper studies aeroelastic control for a two-dimensional airfoil–flap system with unknown gust disturbances and model uncertainties. Open loop limit cycle oscillation (LCO) happens at the post-flutter speed. The structural stiffness and quasi-steady and unsteady aerodynamic loads of the aeroelastic system are represented by nonlinear models. To robustly suppress aeroelastic vibration within a finite time, a backstepping terminal sliding-mode control (BTSMC) is proposed. In addition, a learning rate (LR) is incorporated into the BTSMC to adjust how fast the aeroelastic response converges to zero. In order to overcome the fact that the BTSMC design is dependent on prior knowledge, a nonlinear disturbance observer (DO) is designed to estimate the variable observable disturbances. The closed-loop aeroelastic control system has proven to be globally asymptotically stable and converges within a finite time using Lyapunov theory. Simulation results of an aeroelastic two-dimensional airfoil with both trailing-edge (TE) and leading-edge (LE) control surfaces show that the proposed DO-BTSMC is effective for flutter suppression, even when subjected to gusts and parameter uncertainties. Full article