Search Results (1,268)

To address the degradation of speed regulation performance in the permanent magnet synchronous motor (PMSM) transmission system caused by the gearbox broken tooth fault and disturbances, a fault model-assisted active disturbance rejection control (FMA-ADRC) algorithm is proposed in this paper. First, an electromechanical coupling model of the motor–gearbox transmission system is established based on the dynamic model of the tooth fault. Secondly, a fault model-assisted extended state observer (ESO) in the active disturbance rejection controller is designed, where the periodic torque disturbances caused by the fault are compensated to reduce the estimation burden on the observer. In addition, the observer is nonlinearized to improve the accuracy of tracking disturbances. The observer error of the nonlinear ESO (NESO) is proven to converge to a bounded region within finite time by using the Lyapunov stability proof theory. Finally, the speed regulation performance of the proposed FMA-ADRC controller is verified under different degrees of fault using an experimental platform based on DSP28335 and MATLAB/SIMULINK R2023b. The reliability and superiority of the proposed controller are verified by the experiment results. Full article

Focusing on the issue that false data injection (FDI) attacks on the secondary controllers of DC microgrids can affect the normal and stable operation of microgrids, a distributed resilient controller for DC microgrids is proposed to ensure that the two control objectives, voltage regulation and current sharing, can still be achieved under the action of time-varying bounded FDI attacks. First, the distributed secondary control problem of the microgrid is viewed as a leader–follower multi-agent consensus problem, and the impact of FDI attacks on the microgrid is analyzed. Second, a fully distributed resilient controller based on an adaptive compensation mechanism is designed to compensate for FDI attacks and mitigate their impact on the microgrid. Next, it is proven through Lyapunov stability theory that the microgrid can operate normally and stably under the designed distributed resilient controller, achieving the two control objectives. Finally, simulation analysis is used to verify the effectiveness of the proposed resilient control method. Full article

This paper proposes a hybrid SMC + ESO + RBF control architecture designed to evaluate trajectory tracking and liquid sloshing suppression in tanker robots navigating complex terrains within a simulated environment. A multi-variable dynamic model integrates the differential drive mobile platform with an equivalent mass-spring-damper sloshing system under terrain disturbances. To achieve robust stability, an Extended State Observer (ESO) neutralizes baseline generalized disturbances, while a Radial Basis Function (RBF) neural network adaptively compensates for residual nonlinear coupled sloshing errors. Practical stability and uniform ultimate boundedness (UUB) of the closed-loop system are proven via Lyapunov theory under bounded network approximation errors and observer uncertainties. Numerical simulations in MATLAB/Simulink demonstrate that the proposed controller achieves a baseline Root Mean Square Error (RMSE) of 0.0109 m, representing an 84.1% improvement over traditional Sliding Mode Control (SMC). Parametric sensitivity analysis under variable liquid filling ratios (30%, 50%, and 70%) and a circular steering topology indicates notable adaptability, with the tracking RMSE bounded between 0.0085 m and 0.0129 m under the considered virtual scenarios. Within the simulated environment, the system successfully smooths control profiles and dampens liquid oscillations, demonstrating a promising potential to support transport safety and mitigate actuator chattering under virtual constraints. However, these qualitative observations serve as preliminary hypotheses and must be formally verified through future hardware-in-the-loop (HIL) experiments to evaluate the impact of physical non-idealities, including sensor noise, actuator saturation, communication delays, and wheel slip. These findings confirm the competitive analytical robustness of the SMC + ESO + RBF framework in stabilizing tanker robots within highly uncertain simulated operational environments. Full article

This paper introduces a bias point transformation to deal with the nonholonomic constraints of multiple second-order underactuated mobile vehicles, and transforms such systems into equivalent holonomic systems. In complex environments, follower vehicles cannot directly acquire the leader’s position and velocity due to limited sensing ranges or communication constraints. To this end, a distributed fixed-time observer is developed, which can accurately estimate the leader’s state for all followers within a fixed settling time using only local neighboring information. Based on the estimated states, a distributed fixed-time controller is further proposed and it enables the system to achieve fixed-time rotating consensus without requiring velocity measurements. The fixed-time stability of the closed-loop system is rigorously analyzed via bilateral homogeneity theory and Lyapunov stability theory. Theoretical results confirm that the developed observer and controller ensure that all underactuated mobile vehicles achieve rotating consensus within a fixed time. Finally, numerical simulation results demonstrate the effectiveness of the presented control protocol. Full article

This paper presents a control framework that integrates adaptive sliding mode control (ASMC), time-delay control (TDC), and admittance filtering to achieve robust force and position tracking in robot manipulators. TDC is employed to estimate unmodeled dynamics using delayed measurements, while ASMC enhances robustness by compensating for time-delay estimation (TDE) errors and mitigating chattering effects. An adaptive law incorporating a decline-rate reduction factor is introduced to explicitly regulate the decay of the adaptive gain inside the boundary layer, thereby preserving compensation capability against time-delay estimation errors and external disturbances for a longer duration while improving position tracking performance. In addition, the admittance mechanism converts force-tracking errors into position correction signals, enabling force tracking without modifying the underlying position control structure. The stability of the closed-loop system is analyzed based on Lyapunov theory, ensuring bounded tracking performance in the presence of estimation errors and uncertainties. Simulation results demonstrate that the proposed method improves position tracking accuracy—reducing the root mean square error (RMSE) from 0.0522 mm to 0.019 mm—while maintaining reliable force tracking performance. Full article

We introduce the Hamiltonian pseudorandom function (HPRF), a new symmetric cryptographic primitive in which the function family $\left\{F_k\right\}$ is defined by $F_k\left(q\right)=\nabla S_k\left(q\right)$, the gradient of the generating function of a secret Lagrangian submanifold $L_k$ on the symplectic torus ${\mathbb{T}}^{2n}$. The key k specifies a composition of kicked-rotor maps in the strongly chaotic regime, whose classical Lyapunov exponents grow as $log(K/2)$ per kick. The HPRF is best understood as a seeded one-way function with high min-entropy output: $F_k$ is smooth ($C^{\infty }$), so its raw output is not directly usable as a uniform keystream, but it is computationally hard to invert. We construct three symmetric encryption modes—Mode A (key-dependent coordinate frame), Mode C (Lagrangian keystream), and Mode AC (hybrid)—in which the HPRF supplies the hardness and a key derivation function (HKDF) supplies bit-level uniformity. Standard symmetric composition then yields IND-CPA and IND-CCA2 security. Classical security reduces to the Lagrangian identification problem (LIP), shown as equivalent to the Hamiltonian inversion problem of recovering the kick parameters, which we state as an explicit hardness assumption supported by a precision/sample-complexity obstruction from the positive Lyapunov exponents, by the empirical failure of concrete attacks, and (more heuristically) by topological suggestiveness from the Arnold conjecture and Floer theory. We validate a gradient-fitting attack and an algebraic-structure attack and show that both fail. For quantum security, we propose what we believe is the right framing: that the composed Floquet operator ${\widehat{U}}_K^r$ is a candidate pseudorandom unitary (PRU) in the sense of Ji–Liu–Song. We provide three independent pillars of evidence—Wigner–Dyson spectral statistics, Lyapunov-rate scrambling, and conjectural approximate-design behaviour—and reduce the HPRF quantum security to the PRU conjecture for ${\widehat{U}}_K^r$. We then retire the dynamical-localisation argument of previous drafts as inapplicable at cryptographic parameters; the chaotic-pseudorandomness regime that the operator actually inhabits is, we argue, a stronger foundation than the one that localisation would have provided. A deterministic fixed-point arithmetic core ensures cross-platform bit-exact consistency. A reference implementation validates correctness across all modes, and an NIST SP 800-90B analysis of the output min-entropy fixes the parameter sets. As a foundational proposal, the HPRF is intended for settings that seek a symmetric hardness assumption structurally independent of the algebraic problems underlying current cryptography, for example, as a hedge primitive in defence-in-depth designs, or as a basis for further study of geometry- and chaos-based cryptography, rather than as a drop-in replacement for AES or lattice-based schemes at this stage. Full article

Understanding complex systems requires analytical tools capable of covering nonlinear dynamics, structural complexity, and informational uncertainty simultaneously. In this context, chaos theory, fractal analysis, and entropy measures provide complementary perspectives for examining any irregular behavior in natural and socio-economic systems. This paper examined the relation between the Geopolitical Risk Index and the World Uncertainty Index to the volatility of West Texas Intermediate crude oil, gold, and Bitcoin over the period October 2010–February 2026. The analysis was motivated by the recent intensification of geopolitical tensions, particularly conflicts involving Iran, the United States, and Israel, which have significantly heightened uncertainty in global energy and financial markets. The empirical analysis first investigated the underlying complexity of the variables using entropy, chaos, and fractionality measures. Results from the Shannon, R-T entropy, Kolmogorov–Sinai complexity, Hurst, H-M and Lo’s R/S statistics, Phillips, and GPH fractionality tests consistently indicate entropy, fractal persistence, and long-range dependence across the series. In addition, the largest Lyapunov exponents and Hurst coefficients confirmed the presence of chaotic dynamics. The results reveal strong regime heterogeneity with geopolitical shocks exerting significantly stronger effects during high-uncertainty periods. Forecast comparisons show that regime-switching models outperform linear specifications, highlighting the importance of fractal and nonlinear dynamics in understanding financial market responses to geopolitical risk. Full article

Four-wheel independent steering (4WIS) vehicles can improve low-speed maneuverability and high-speed stability by independently regulating the steering angles of all four wheels. However, under large-curvature trajectories, parameter perturbations, and external disturbances, inconsistent coordination among the four-wheel steering angles may increase tire lateral slip, yaw response deviation, and trajectory tracking errors. To address the difficulty of conventional trajectory tracking methods in simultaneously ensuring geometric consistency, tracking accuracy, and robustness, this paper proposes an adaptive sliding mode trajectory tracking control method based on instantaneous center of rotation (ICR) constraints. First, the tire instantaneous turning center (TTC) of each wheel is derived using rigid-body spatial kinematics, and the TTCs are mapped onto a unified vehicle-body reference plane based on the SAE J670 coordinate system to obtain a real-time vehicle-level ICR estimation. Second, a lateral–yaw dynamic model and a trajectory tracking error model are established. The yaw rate and sideslip angle are corrected using ICR geometric information, and an adaptive sliding mode controller is designed with an equivalent control term, adaptive switching gain, adaptive boundary layer, and sideslip suppression term. The uniform ultimate boundedness of the sliding variable and closed-loop tracking errors is proven using Lyapunov theory. Finally, MATLAB (2023a)2024/CarSim (2019) co-simulations are conducted under small-curvature sinusoidal, double-lane-change, large-curvature sinusoidal, low-adhesion, and mass-perturbation conditions. The results show that the proposed ICR-SMC method significantly reduces lateral and heading errors compared with U-LQR and U-SMC, especially under large-curvature and low-adhesion conditions, demonstrating improved tracking accuracy and robustness for 4WIS vehicles. Full article

While minimalist kinetic models effectively capture the acute inverse coupling between Hepatitis B (HBV) and Hepatitis Delta (HDV), they often fail to account for the asymptotic stability and long-term viral plateaus observed during clinical therapy. In this work, we present an expanded compartmental framework integrating the non-linear dynamics of susceptible (S) and infected (I) hepatocyte populations, explicitly incorporating the satellite nature of HDV. Using the next-generation matrix method and Lyapunov stability theory, we analytically derive R₀ and prove the global attractivity of the endemic equilibrium. We demonstrate that “Target Cell Limitation” serves as the fundamental homeostatic governor. A transcritical bifurcation at threshold drug efficacy ε ≈ 0.9 marks the mathematical boundary between chronic persistence and viral extinction. Full article

To address the problems of communication delay and waste of communication resources in the formation process of UAVs, a dynamic event-triggered formation control method for second-order multi-leader UAV systems with communication delay is studied. On the basis of considering the communication delay, a dynamic triggering mechanism is designed. By adjusting the triggering time in real time, the system can be more effectively controlled based on its current state. According to the control method, the mathematical models for the extended state observer, controller, and dynamic event-triggering function of the system have been established. Its stability is demonstrated by Lyapunov stability theory and linear matrix inequality theory, and Zeno behavior is excluded. The simulation results show that compared with the existing methods, the proposed method can avoid the dependence on the global information of the network topology, reduce the communication frequency, and effectively save communication resources. Full article

This paper introduces an adaptive fixed-time position controller (AFxTPC) designed for the lifting axis servo mechanism of a computer numerical control (CNC) plasma machine. It integrates a permanent magnet synchronous motor, gearbox, and ball screw into a unified electromechanical model. The proposed AFxTPC combines a fixed-time terminal sliding surface function with adaptive fixed-time sliding mode control to achieve fixed-time convergence, precise tracking, and robustness in the presence of parameter uncertainties. A specially designed reaching law guarantees accurate trajectory tracking, while the fixed-time terminal sliding surface function effectively minimizes chattering near the sliding manifold. Importantly, a novel fixed-time nonlinear disturbance observer is developed to simultaneously estimate the unmeasured system states and lumped disturbances in real time within a guaranteed initial-state-independent settling time. These estimated values are explicitly fed back into controller for active disturbance compensation. The stability of the overall closed-loop system is rigorously established using Lyapunov stability theory. Simulation results demonstrate that the proposed observer-based controller achieves superior performance compared with conventional proportional–integral–derivative (PID) and standard sliding mode controllers. It exhibits zero steady-state error, reduced overshoot, minimal chattering, and strong robustness over a wide range of operating conditions. Full article

To achieve precise trajectory tracking for surface vessels subject to unknown dynamics, strict physical limitations, and external disturbances, this paper proposes an Adaptive Fixed-Time Control Framework that ensures a deterministic response under full constraints. First, navigation safety is guaranteed by employing a Barrier Lyapunov Function (BLF) to strictly confine vessel position states, enabling constrained position tracking without requiring prior knowledge of the desired trajectory. Second, addressing the input constraint aspect of the “full constraints” problem, a fixed-time auxiliary system is introduced to compensate for nonlinearities induced by actuator saturation, thereby maintaining control feasibility. Central to this framework is the realization of a deterministic response; by incorporating fixed-time convergence theory, the controller guarantees that velocity tracking errors converge within a predefined time bound independent of initial conditions. Furthermore, an RBF neural network combined with adaptive techniques is utilized to estimate unknown dynamics and external disturbance bounds online, enhancing robustness and safety in realistic marine environments. Full article

To address the trajectory tracking problem of networked unmanned surface vessels (USVs) under false data injection (FDI) attacks, an adaptive neural network-based prescribed performance control scheme is proposed. First, considering the adverse effects of network attacks, system uncertainties, and time-varying disturbances, an adaptive neural network observer is designed to estimate and compensate for the lumped disturbances. Building on this, a dynamic event-triggered mechanism is separately developed for the sensor-to-controller and controller-to-actuator channels, forming a novel dual-channel dynamic event-triggered mechanism (DDETM). This mechanism reduces unnecessary communication overhead and actuator wear caused by frequent data exchanges while enabling thrust allocation for a quantitative analysis of actuator degradation. Furthermore, a control algorithm based on a second-order prescribed performance function (SOPPF) and dynamic surface control (DSC) is proposed to ensure transient and steady-state performance of the tracking error while mitigating the computational complexity associated with the traditional backstepping method. Using Lyapunov theory, it is demonstrated that all signals in the closed-loop system are uniformly ultimately bounded and that Zeno behavior is avoided. Simulation results further validate the effectiveness of the proposed control approach in solving the trajectory tracking problem of USV. Full article

The transition toward renewable-dominated power systems introduces significant complexity and nonlinearity, rendering traditional mechanism-based modeling computationally prohibitive for real-time security assessment. While data-driven approaches offer computational efficiency, they fundamentally lack physical interpretability and often exhibit generalization failures under rare, large-signal disturbances due to the absence of intrinsic physical constraints. To bridge this gap, this paper proposes a Physics-Guided Symbolic Regression (PGSR) framework for constructing interpretable and robust dynamic equivalent models. The methodology embeds domain knowledge via topological masks and dimensional consistency rules to restrict the evolutionary search space to physically admissible manifolds. A multi-resolution extraction strategy based on the Pareto frontier is developed to autonomously identify both linear small-signal models and nonlinear large-signal formulations adaptable to varying analytical requirements. Furthermore, a post hoc verification stage based on Lyapunov stability theory ensures the dynamic validity and energy dissipation properties of the generated equations. A case study on the WSCC 9-bus system demonstrates that the proposed method accurately recovers the underlying Taylor-series structure of swing equations and significantly outperforms four data-driven baselines—including polynomial, kernel, and neural network models—in out-of-distribution generalization, achieving 12–42× lower trajectory error under unseen large perturbations. Full article

To address the parameter coordination and system integration issues in nonlinear discrete-time cascade control systems, this paper proposes, for the first time, a novel collaborative PI-P controller design method. First, an augmented state-space model for the PI-P controller is introduced, where the integral term is embedded into the state variables. Then, stability conditions are derived using Lyapunov stability theory, which are formulated as linear matrix inequality (LMI) constraints, enabling the simultaneous design of both primary and secondary controllers. The method is validated through simulations on a steam temperature control system. The results demonstrate that the proposed method outperforms conventional methods, achieving a faster response, reduced overshoot, and enhanced robustness. Moreover, the proposed method shows strong disturbance rejection capability and improved overall dynamic performance, further confirming its effectiveness and potential for application in nonlinear discrete-time cascade control systems. Full article