Distributed secondary control (DSC) is essential for frequency restoration in islanded microgrids, but its reliance on communication networks makes it vulnerable to false data injection (FDI) attacks and leads to slow convergence in conventional schemes. This paper proposes a finite-time FDI-attack-resilient distributed secondary frequency control strategy based on a hidden-layer architecture. By introducing a finite-time nonlinear term into the hidden-layer framework, the proposed controller, compared with conventional hidden-layer control, ensures robustness against bounded actuator and communication-link attacks while accelerating frequency restoration. Lyapunov-based analysis establishes sufficient conditions for finite-time convergence. Simulation studies on an islanded AC microgrid verify that the proposed method achieves faster frequency recovery and improved resilience compared with existing distributed secondary-control approaches under various FDI attack scenarios.
This paper investigates the synchronization and control of a reduced-order representation of the two-dimensional (2D) Kolmogorov flow, a canonical fluid-flow model governed by the incompressible Navier–Stokes equations under periodic boundary conditions and sinusoidal external forcing. Using a spectral Fourier–Galerkin expansion, a nine-mode dynamical system is obtained that captures the principal dynamical transitions and nonlinear interactions observed across a wide range of Reynolds numbers. Within this framework, the study develops static and dynamic sliding-mode synchronization schemes designed to drive the trajectories of a slave (controlled) system toward those of a master (reference) system, thereby achieving synchronization of the reduced-order dynamics. Synchronization strategies are examined under two scenarios: when the Reynolds number is precisely known and when it is not known. In the latter case, an adaptive control law is introduced to estimate the unknown Reynolds number online. Numerical simulations are performed to evaluate the proposed synchronization strategies under various dynamical regimes. The results demonstrate that all four controllers achieve effective synchronization of the reduced-order systems under both known and unknown Reynolds numbers. Furthermore, the dynamic sliding mode controllers significantly reduce the chattering associated with conventional sliding mode control while preserving the synchronization accuracy.
Recently, pinning control of fractional-order dynamical networks with or without time delay has been extensively studied. Nevertheless, the delay inherently introduced by the pinning control mechanism itself has received limited attention. This paper addresses the delayed pinning control scheme designed to achieve lag synchronization and lag quasi-synchronization in fractional-order dynamical networks. First, two generalized fractional-order inequalities are developed. Subsequently, we propose two pinning control schemes with uniform and nonuniform delays, which exhibit greater practical relevance compared to the widely adopted delay-free counterpart. For these schemes, we derive criteria for lag synchronization and lag quasi-synchronization in fractional-order dynamical networks by constructing a system of functional differential inequalities. Additionally, an upper bound on the tolerable delays ensuring synchronization is obtained. Particularly, the ultimate bound of the synchronization error is derived for lag quasi-synchronization. Finally, two numerical examples are provided to show the validity of derived theoretical results.
Topological phases in phononic systems enable robust and unconventional control of wave propagation. However, realistic acoustic, elastic, and mechanical platforms are open, while loss or gain, active feedback, and spatiotemporal modulation provide tunable routes to non-hermiticity and nonreciprocity. Non-hermiticity reshapes complex-frequency spectra, eigenstates, and bulk-boundary correspondence beyond conventional Hermitian band theory, thereby giving rise to a wide range of unconventional wave phenomena. In this review, we provide a unified overview of topological non-Hermitian phononic crystals (PCs) and metamaterials from one to three dimensions, emphasizing physical mechanisms. In one-dimensional (1D) systems, non-Hermitian extensions of the Su–Schrieffer–Heeger (SSH) model reveal the emergence of the non-Hermitian skin effect (NHSE) and the breakdown of conventional Bloch band theory, necessitating the generalized Brillouin zone (GBZ) formalism and non-Bloch topological invariants. In two-dimensional (2D) systems, the interplay of non-hermiticity with lattice symmetry gives rise to exceptional degeneracies, anisotropic and higher order skin localization, and valley- and pseudospin-dependent transport. In three-dimensional (3D) systems, non-Hermitian Weyl phases support exceptional rings, complex Fermi arcs, and surface states governed by biorthogonal topology. Finally, we discuss non-hermiticity in space–time-modulated systems, non-Abelian exceptional-point braiding, and synthetic Landau-level physics as emerging directions. This review aims to offer a unified perspective on non-Hermitian topology in PCs and to stimulate further developments toward next-generation intelligent elastic metamaterials and topological wave devices.
To address the issue of broadband vibration transmission from road surface excitations to vehicle occupants that compromises riding comfort and safety, this paper proposes a synergistic vibration reduction strategy by coupling a nonlinear energy sink (NES) with a full-vehicle body-seat dynamic system. By integrating Newton's second law with multi-degree-of-freedom vehicle kinematics, a vehicle-seat coupled dynamic model with NES is established, and the system response is analyzed using the Runge–Kutta (RK) method. To circumvent the local optima trapping and excessive computational cost of traditional parameter tuning, a random-mutation particle swarm optimization (RM-PSO) algorithm is introduced to globally optimize key NES parameters, with the objective of minimizing the seat vibration amplitude at resonance. The results indicate that the optimized NES exhibits robust broadband vibration absorption with adaptive characteristics: under seat-road resonance conditions, the vibration reduction rate reaches 33.7
This work explores the finite-time synchronization (FTS) problem of fractional-order fuzzy cellular neural networks (FOFCNNs) that comprise mixed time-varying delays (TVDs) and interaction terms. To more accurately characterize the complex dynamics encountered in practical neural networks, the master–slave systems incorporate nonlinear activation functions along with fuzzy AND and OR operators. To achieve FTS, a novel quantized memory-based sampled-data controller (QMSDC) is proposed. The proposed controller combines sampled-data implementation, logarithmic quantization, and a memory mechanism to reduce communication burden while maintaining synchronization performance. A Lyapunov-Krasovskii functional (LKF) is devised, incorporating additional information about the fractional derivatives, mixed TVDs, and sampling instants. By utilizing the Lyapunov stability theory with the QMSDC technique and finite time (FT) stability theory, sufficient conditions are derived to guarantee the synchronization of FOFCNNs. Furthermore, a precise formula is derived to calculate the settling time, which provides a competent way to evaluate synchronization performance. Finally, numerical simulations are carried out to assure the practicality and effectiveness of the presented results.
To address the performance degradation of brushless DC (BLDC) motors operating under complex and uncertain conditions such as parameter perturbations, external load disturbances, and execution delays inherent in embedded systems, a collaborative control strategy is proposed that integrates an adaptive sliding mode observer (ASMO) with a fuzzy self-tuning PID controller on an FPGA-MCU heterogeneous platform, where first a comprehensive mathematical model of the BLDC motor is established incorporating interphase coupling effects, nonlinear back electromotive force (EMF), and varying load disturbances to accurately represent real operating environments, then an adaptive sliding mode observer is designed to estimate rotor speed and lumped disturbances in real time while boundary layer functions and adaptive gain mechanisms are introduced to suppress chattering and improve robustness, further a fuzzy self-tuning PID controller is constructed using the speed error and its rate of change as inputs to dynamically adjust proportional, integral, and derivative gains online through fuzzy inference rules enabling adaptive control under varying conditions, and finally a hardware-software co-design is implemented on an FPGA-MCU heterogeneous architecture where time-critical tasks such as observer iteration and PWM generation are executed on the FPGA to reduce latency and timing jitter while the MCU manages supervisory functions, with experimental results demonstrating that the proposed method outperforms traditional PID, fuzzy PID, and sliding mode control approaches by achieving superior speed tracking, enhanced disturbance rejection, greater parameter robustness, reduced overshoot, faster settling time, and lower steady-state error.
This paper investigates the torsional vibration behavior of non-circular nanobeams using Rao’s refined torsion theory, which incorporates the warping function into all components of the displacement field. In the torsional vibration of non-circular nanobeams, the warping of the cross section leads to the appearance of in-plane strains. Classical torsion theories do not account for all in-plane strain components. To overcome this limitation, Rao’s refined torsion theory considers the Poisson effect in the displacement field, thereby ensuring that all in-plane strains are fully incorporated. The warping function explicitly accounts for these Poisson-induced in-plane deformations, enabling a more accurate and physically consistent description of torsional behavior in non-circular cross sections, such as elliptical and rectangular shapes. For the first time, Rao’s refined theory is used with the nonlocal strain gradient (NSG) framework to capture size-dependent phenomena in the torsional vibration of non-circular nanobeams. The nanobeam is assumed to be subjected to a longitudinal magnetic field and supported by an elastic foundation. Hamilton’s principle is used to derive the governing equations for free and forced torsional vibrations. Natural frequencies are analyzed with respect to key parameters, including length-scale parameters, aspect ratio, magnetic field permeability, and elastic foundation stiffness. The forced vibration response under a harmonic moving torque is also investigated, and the results are compared with those of the classical theory, highlighting the significant roles of warping, size effects, and magnetic fields. The findings provide valuable physical insights for the design of nanoscale torsional devices.
This paper provides a comprehensive analysis of the global dynamics and an exact mechanical application for a class of time-reversal symmetric quadratic differential systems in ℝ^3 having an elliptic cylinder as an invariant algebraic surface. A normal form for this family is first derived. When the polynomial defining the cylinder is a first integral, the phase space is foliated by a continuum of invariant cylinders. For fixed coefficients of the differential system, the initial condition selects a level of this first integral, and the vector fields restricted to the corresponding cylinders undergo pitchfork-type and degenerate topological transitions as the level crosses critical values. In the broader terminology used for systems with first integrals, these phenomena may be interpreted as initial-condition-induced bifurcations without parameters. The critical equilibrium collision is analyzed in regular coordinates and the resulting nilpotent singularities are classified. We also prove that every periodic orbit of the restricted flow on a nondegenerate invariant cylinder belongs to a local period annulus. Consequently, there are no limit cycles on the invariant cylinders, neither when they foliate the phase space nor when there is a single cylinder. Furthermore, we characterize all possible invariant parallels and meridians and describe the compactified flow at infinity, including the precise conditions under which invariant meridians form direct heteroclinic connections between the antipodal directions of the cylinder. Finally, we give an exact embedding into the classical problem of a bead sliding on a rotating hoop, showing that the same equilibrium-collision geometry is realized on the unit cylinder as the classical Hamiltonian pitchfork bifurcation when the angular velocity is varied.
This paper proposes an event-triggered, observer-based adaptive output-feedback control scheme for a class of nonlinear systems with partially unavailable states, formulated using a General Type-2 Takagi–Sugeno Fuzzy Neural Network (GT2-TS-FNN). The proposed framework comprises two components: an intelligent event-triggered full-state observer that estimates the unmeasurable states and a fuzzy output-feedback controller, both constructed based on the GT2-TS-FNN. To decompose a General Type-2 Fuzzy Set into several Interval Type-2 Fuzzy Sets, an efficient α-cut strategy is employed. In addition, a direct defuzzification method is adopted to reduce the computational burden associated with type reduction, thereby avoiding the iterative Karnik–Mendel algorithm. Based on Lyapunov stability theory, an adaptive updating law is derived to ensure fast convergence and guarantees the stability of the overall closed-loop system. The proposed scheme is further implemented on a microcontroller for the real-time speed control of an induction-motor drive operating over a networked communication protocol, where the event-triggered mechanism significantly reduces both the communication frequency and the computational load. Both simulation and experimental results confirm improved tracking performance under random disturbances, external load variations, and sensor-dropout conditions.
This paper develops a fractal–fractional fixed-time synchronization controller for a two-degree-of-freedom robotic manipulator driven by hyperchaotic reference trajectories. A four-dimensional hyperjerk-type generator with nonlinear state-dependent damping and inversion symmetry is used to produce demanding reference signals, and its dissipativity, Lyapunov exponents, bifurcation behavior, basins of attraction, and symmetric coexisting attractors are examined. The main contribution is the control framework: A fractal–fractional sliding surface incorporates memory and fractal time-scaling effects, while a fixed-time reaching law guarantees bounded convergence independently of the initial conditions. The mapping between the hyperchaotic states and the robot joint references is explicitly defined. Simulations with bounded external disturbances show fast tracking, small residual errors, and smoother control behavior than a conventional sign-based sliding mode structure.
In this paper, we propose a robust precision altitude control method for a six-axis agricultural unmanned air vehicle (UAV) based on nonsingular fast terminal supertwist-optimal robust Active Disturbance Rejection Control (ADRC). The novelty of this paper is to propose a nonsingular fast terminal supertwist-robust ADRC and optimize it by an improved Particle Swarm Optimization-Difference Evolution hybrid intelligent optimization algorithm to realize robust precision altitude control of a six-axis agricultural UAV. Uncertainties due to external disturbances such as wind and air flow on agricultural six-axis UAV, non-uniformity of mass distribution, mass loss due to pesticides and petrol consumption, etc. are considered as total disturbances in nonsingular fast terminal supertwist-robust ADRC. Simulation results show that the proposed control method is much improved in disturbance rejection performance and robust performance. The results of flight tests show that the proposed method is improved by an average of 11.7 times compared to the previous methods. As a result, the practical effectiveness of the proposed method has been verified and the promising potential for full application in precision control applications is well demonstrated.
Multiscale systems are expensive to simulate because fast dynamics require small time-steps, while slow dynamics require long prediction horizons. We propose latent hierarchical time-stepping (L-HiTS), which combines nonlinear coordinate discovery with multiscale flow-map learning. A deep autoencoder first compresses the high-dimensional PDE state into a validated low-dimensional latent space. Residual neural network time-steppers are then trained and coupled directly in this reduced space using validation-based hierarchy selection and vectorized prediction. Unlike multiscale HiTS, L-HiTS performs recursive forecasting in latent coordinates and reconstructs the full state only after prediction. The method is validated on the FitzHugh–Nagumo model, the chaotic Kuramoto–Sivashinsky equation, and a two-dimensional Burgers’ system. L-HiTS achieves comparable prediction accuracy to multiscale HiTS while substantially reducing training and prediction costs, with near order-of-magnitude prediction-time savings in the reported cases.
This manuscript investigates the existence, uniqueness, and approximate controllability of second-order abstract differential systems featuring state-dependent delay. The study first establishes local and global existence as well as uniqueness of mild solutions under appropriate assumptions. The controllability analysis is carried out through the introduction of an intercept system, which allows us to transfer controllability properties from the associated linear control system to the nonlinear delayed system. It is shown that the approximate controllability of the linear control system ensures the approximate controllability of both the intercept system and, ultimately, the original semilinear system on the interval [0,β ] . Furthermore, illustrative examples are presented to highlight the applicability of the theoretical findings.
Accurate dynamic models can significantly enhance the performance of feedforward control, trajectory planning and disturbance compensation, thereby reducing tracking errors and vibration levels and improving the stability and reliability of robotic manipulators operating under high-speed, high-precision, and complex working conditions. A major challenge in dynamic parameter identification lies in the accurate estimation of nonlinear parameters (NP) in the friction model. This difficulty arises from the fact that NP do not satisfy the parameter-function separability principle in the same manner as linear parameters. To address this issue, this paper proposes a Taylor-series-based linearization approach for NP, which enables the separation of NP from their corresponding functional expression. As a result, unified identification of linear and nonlinear parameters is achieved, while eliminating the need to decouple friction torque from the total torque during NP identification. The selection of the Taylor expansion order and expansion points is also theoretically analyzed. Experimental results validate the effectiveness of the proposed identification approach, and the identified dynamic parameters satisfy the physically consistent constraints. Compared with the iterative methods, the proposed approach achieves faster computational speed and demonstrates superior overall performance in terms of root-mean-square error, relative error ratio, and correlation coefficient.
Speed variations, current-speed coupling, and load disturbances challenge nominal optimal controllers in achieving fast tracking and effective disturbance rejection for permanent magnet synchronous motor (PMSM) drives. To address this problem, this paper proposes a predictive error-dynamics optimal control strategy with disturbance-augmented Kalman filtering. A discrete current speed model with channel-wise lumped disturbances is first established. Different from conventional error-difference optimal control or observer-based feedforward compensation, the proposed method incorporates the one-step disturbance estimates into the prediction of the next-step tracking error. Based on this disturbance-informed prediction, a predictive error-dynamics residual is constructed to describe the deviation between the predicted tracking error and the desired error evolution. By embedding this residual into a quadratic performance index, the voltage increment generation is formulated as a generalized quadratic optimal control problem with a state-input cross term, and the optimal voltage increment is obtained through a Riccati-based solution. Comparative simulations and RT-LAB-based real-time experiments on an actual PMSM drive platform, covering loaded start-up, speed-step, load-change, and forward-reverse conditions, show that the proposed method reduces overshoot, tracking error, load-induced speed fluctuation, and q-axis current oscillation compared with PI and standard optimal controllers. These results indicate improved coordination between predictive error regulation and disturbance-aware voltage increment generation.
This work examines the state estimation of fuzzy control systems subject to disturbances, particularly perturbations bounded by a Hölderian continuous function. Under these constraints, the observer design problem is solved using the Takagi–Sugeno (T–S) fuzzy approach with specific restrictions on the nonlinearities. Several sufficient conditions are provided to demonstrate the exponential convergence of the error equation solutions to a bounded neighborhood of the origin. The main theoretical contribution lies in establishing explicit bounds for the convergence region while relaxing the classical Lipschitz assumption to Hölderian nonlinearities. A numerical simulation example and an application to battery management systems are provided to demonstrate the efficacy of the main result. The proposed approach is compared with existing fuzzy observer design methods, highlighting its advantages in handling broader classes of nonlinearities.
Commercial integrated robotic joints encapsulate their inner servo loops and expose only a position command interface to the external controller. Consequently, continuous trajectory tracking is constrained by interface residuals, recorded sampling intervals, and command bounds. This paper develops a prescribed performance command-shaping controller termed RL-PALS. In this work, reinforcement learning assistance refers only to an offline CEM-based elite candidate search for selecting fixed controller settings before hardware testing; no policy search is conducted during hardware operation. During operation, external position corrections are generated by a continuous performance transformation with a recovery extension and a radial basis function (RBF) residual compensator. Velocity filtering based on recorded sampling intervals, command smoothing, feasible command handling, and weight holding during constraint activation are incorporated to keep the total command, correction magnitude, and correction rate within implementable bounds. The analysis establishes recursive nonemptiness of the feasible correction set. The residual compensation output is bounded by explicit saturation, and conditional practical boundedness of the external shaping state is derived under a local dissipation condition. Hardware identification, sensitivity assessment based on the nominal model, and three repeated hardware trials show that, relative to an auto-tuned proportional integral derivative baseline (AT-PID), RL-PALS reduces the 99th-percentile absolute tracking error ( E_99 ) from 1.229^∘ to 1.017^∘ . Moreover, the external command remains within the prescribed bounds throughout the recorded hardware trials.
Mechanical ventilation is routinely used to assist patients who require respiratory support. The control system of such devices must be effective and reliable because patient-specific respiratory mechanics, including lung compliance and airway resistance, vary considerably. Moreover, the controller should maintain satisfactory performance in the presence of modelling errors, disturbances, and parametric uncertainties. In this work, a Fuzzy-PID controller is proposed, in which a fuzzy logic controller (FLC) is employed to adaptively tune the PID gains according to the airway-pressure tracking error and its rate of change. The performance of the underlying fuzzy inference system (FIS) depends largely on the selection of the membership-function (MF) families, operating ranges, and scaling factors. However, no systematic procedure exists for determining these parameters, and they are commonly selected empirically. To address this limitation, four widely used MF families, namely triangular, trapezoidal, sigmoidal, and Gaussian, are considered as candidate structures. An Ensemble Class Topper Optimization (EnCTO) algorithm is proposed to automatically determine the optimal MF family together with the corresponding operating ranges and scaling factors for the input and output variables of the FIS. The optimized FIS is then incorporated into the proposed Fuzzy-PID controller to enhance the airway-pressure tracking performance of a blower-driven mechanical ventilation system. Finally, the proposed controller is evaluated through comprehensive simulation studies involving comparative airway-pressure tracking, control effort, tracking error, disturbance rejection, measurement noise, respiratory parameter variations, and variable breathing patterns. The simulation results demonstrate that the proposed EnCTO-based Fuzzy-PID controller provides improved tracking accuracy, smoother control action, and enhanced robustness compared with existing optimization-based ventilator controllers.
We develop a seven-dimensional ordinary differential equation model for brain-tumor dynamics coupling therapy-sensitive, therapy-resistant, and aggressive tumor phenotypes with immune activity, myeloid suppression, vascular support, and pharmacokinetic drug exposure. The formulation includes vascular-dependent growth limitation, immune-mediated killing, phenotype transfer, suppressive feedbacks, and saturating Emax-type pharmacodynamics. Positivity, boundedness, and global well-posedness are proved. The tumor-free equilibrium is characterized, and a local invasion threshold is derived by the next-generation formulation. A bounded four-control problem is formulated for drug infusion, immunotherapy, myeloid targeting, and vascular targeting. Existence of an optimal control is established and the normal Pontryagin optimality system is derived. A Latin-hypercube/partial-rank-correlation analysis is performed over all threshold-defining parameters and a finite-horizon response output. Numerical simulations use one fully specified normalized parameter regime and a common RK4/FBS protocol. In this regime, drug treatment is the strongest individual intervention, vascular targeting is the strongest isolated microenvironmental intervention, and the combined computed strategy gives the lowest cumulative and terminal tumor burdens for the stated weights.
