Search Results (298)

This paper addresses the stabilization and drive–response synchronization of the four-dimensional hyperchaotic finance model using active backstepping (ABS) and active control (AC). The contribution is not the introduction of a new control paradigm but a unified implementation of AC and ABS for the Yu finance model, together with explicit Lyapunov convergence estimates, reproducible numerical benchmarking, and robustness-oriented performance assessment. For the ideal full-state-feedback setting, Lyapunov arguments establish exponential stabilization for the ABS-controlled system and exponential synchronization for both AC and ABS. The numerical protocol quantifies settling time, norm-relative overshoot, envelope-based decay rate, integrated control energy, CPU time, and actuator peak/RMS values. The results show that AC provides smooth and energy-efficient synchronization, whereas ABS gives fast convergence and a nonlinear Lyapunov-based stabilization framework but requires higher actuation effort. Robustness tests under parameter mismatch and additive measurement noise indicate bounded trajectories and decaying synchronization errors under the tested perturbation levels. The results also clarify the trade-off between convergence speed, control energy, implementation complexity, and actuator feasibility. Full article

This paper addresses the real-time trajectory tracking problem for the Twin Rotor MIMO System (TRMS), a nonlinear, strongly coupled, open-loop unstable aerodynamic laboratory benchmark whose six-dimensional state space is only partially observable through pitch and yaw angle encoders. A High-Gain Observer (HGO) is designed to reconstruct the four unmeasured states, comprising angular velocities and rotor torques, from encoder measurements alone. Three observer-based backstepping control architectures are proposed and experimentally validated on the physical TRMS platform at a 1 kHz embedded sampling rate: (i) adaptive backstepping with tuning functions, which eliminates the over-parametrization inherent in conventional adaptive formulations through a single unified parameter update law; (ii) backstepping with online Brain Storm Optimization (BSO) of the design gains; and (iii) backstepping with online Artificial Bee Colony (ABC) gain optimization. All three architectures achieve stable 100 s trajectory tracking, whereas the conventional non-adaptive backstepping baseline diverges after 42 s due to progressive yaw-channel instability exceeding 4 rad. The BSO- and ABC-optimized controllers achieve the highest pitch-axis tracking precision (reducing pitch root-mean-square errors by 68% relative to the baseline), while the adaptive tuning functions architecture yields the best yaw-axis stability (0.2244 rad RMSE, a 91% reduction). The tuning functions architecture primarily resolves the yaw-channel instability caused by parametric over-parametrization, while the metaheuristic optimizers primarily improve pitch tracking precision through online gain refinement. Closed-loop stability is rigorously established via Lyapunov analysis and the nonlinear separation principle. The High-Gain Observer is directly validated on the two measured states through comparison of its pitch and yaw angle estimates against the incremental encoder signals over the full 100 s trial; the angular velocity and rotor torque estimates are only indirectly supported by the sustained stability of the closed loop, since no velocity or torque sensor is available on the rig. Comprehensive simulation and real-time experimental comparisons quantify the performance, robustness, and computational feasibility of each architecture under identical operating conditions. Full article

Quadrotor unmanned aerial vehicles (QUAVs) exhibit strongly coupled nonlinear dynamics and are highly sensitive to disturbances and measurement noise, which can significantly degrade trajectory tracking performance and induce chattering in sliding mode-based controllers. In this work, a fractional-order backstepping sliding mode control (FO-BSMC) strategy is proposed for QUAV trajectory tracking. In contrast to existing fractional-order sliding mode approaches, where the fractional operator is typically introduced into the sliding surface or control law, the proposed methodology incorporates fractional-order behavior directly into the QUAV dynamic model through the Caputo definition, while the Grünwald–Letnikov approximation is adopted for numerical implementation. A conventional integer-order BSMC scheme is also developed, and Lyapunov-based stability analyses are presented for both the conventional BSMC and the proposed FO-BSMC formulations. The fractional order is selected using the PSO algorithm. The performance of both controllers is evaluated under external disturbances, perturbed initial conditions, and measurement noise. Monte Carlo simulations are further conducted to assess the sensitivity of the closed-loop system to initialization uncertainties. The simulation results demonstrate that the proposed FO-BSMC achieves lower tracking errors, faster convergence, improved robustness against external disturbances and measurement noise, and smoother control actions with reduced chattering than the conventional BSMC. Full article

The increasing demand for clean, reliable, and sustainable energy has intensified the need for advanced control strategies in modern wind energy conversion systems. Although conventional backstepping control (BC) offers strong stability and robustness, its performance may deteriorate under parameter uncertainties and dynamic operating conditions, leading to power fluctuations and reduced energy quality. To overcome these challenges, this study proposes an intelligent fuzzy fractional-order BC (FFOBC) strategy for multi-machine wind energy systems. By integrating fuzzy logic with fractional-order calculus into the classical BC framework, the proposed approach enhances adaptability, dynamic response, and robustness against system disturbances and nonlinearities. The controller is implemented at the machine-side inverter and validated in MATLAB/Simulink under varying wind and load conditions. Comparative results demonstrate that the proposed FFOBC significantly outperforms conventional sliding mode control in terms of overshoot reduction, steady-state accuracy, response smoothness, and total harmonic distortion minimization. Furthermore, the proposed strategy improves energy conversion efficiency, reduces mechanical and electrical stress, and ensures stable power injection into the grid. These findings highlight the potential of the proposed intelligent control framework to support sustainable, resilient, and high-quality wind energy integration in future smart power systems. Full article

The underground caverns of pumped-storage power stations generally feature large inclination angles. During the bottom-up oblique excavation by hard-rock Tunnel Boring Machines (TBMs), the Anti-Back-Slip (ABS) support system is the core device ensuring safe operations. Specifically, the synchronization of the multiple hydraulic cylinders within the ABS system is a critical factor determining the stability and safety of the TBM. Therefore, this paper designs a hydraulic control system for the ABS device and proposes an adjacent cross-coupling synergistic control strategy based on adaptive backstepping. This strategy innovatively integrates an adaptive backstepping control law into the adjacent cross-coupling topology to achieve high-precision multi-cylinder control. Utilizing the AMESim-Simulink platform, high-fidelity co-simulations are conducted under both uniform and eccentric load conditions. The results demonstrate that under nominal conditions, the proposed algorithm exhibits asymptotic convergence at the mathematical level. The system maintains robust stability under dynamic excitations. When subjected to sudden asymmetric eccentric loads of 1.0–2.0 times, the system prevents tracking divergence and limits the maximum multi-cylinder synchronization error to within 1.82 mm. This research satisfies the requirements for synchronous control and provides a theoretical and engineering reference for the disturbance-rejection synergy of inclined shaft TBM support systems. Full article

This paper presents a robust dual-loop control strategy for the lateral motion and heading-angle regulation of an autonomous vehicle equipped with a Steer-By-Wire (SBW) system under unknown time-varying disturbances. The proposed framework comprises a fuzzy PID controller in the inner loop to generate the motor torque and track the front-wheel steering angle, and an optimal backstepping controller in the outer loop—integrated with a finite-time disturbance observer—to ensure lateral trajectory tracking and wind-disturbance rejection. The PID gains are tuned online by a Mamdani-type fuzzy inference system, while the backstepping parameters are optimized offline via a genetic algorithm. Beyond the bicycle-model-based design, the controller is evaluated through supplementary simulations using a 6-degree-of-freedom (6-DOF) vehicle model, as well as through a detailed robustness analysis that includes measurement noise and increasing lateral disturbance forces. The results demonstrate that the closed-loop system achieves precise path tracking, finite-time convergence of both tracking and estimation errors, and effective compensation of road vibrations and wind disturbances. Furthermore, the controller maintains stable performance under significant measurement noise and tolerates lateral disturbance forces up to at least 10,000 N without violating safety constraints. The effectiveness of the proposed method is consistently confirmed across both the reduced-order bicycle model and the higher-fidelity 6-DOF validation environment. Full article

This paper proposes a finite-time adaptive backstepping active suspension control strategy, integrating command filtering and composite learning, to address the degradation of ride comfort and attitude stability in heavy-duty vehicles caused by shifting loads and harsh roads. First, a nonlinear dynamic vehicle model is established, treating multi-source complex disturbances as a single lumped disturbance and accounting for suspension stiffness and damping nonlinearities. To stabilize the body attitude, a tri-axis controller governing the vertical, pitch, and roll motions is developed, incorporating the practical physical constraints of actuators. By employing a composite learning Radial Basis Function neural network, the controller achieves smooth approximation and precise compensation of lumped disturbances, significantly enhancing the system’s active disturbance rejection performance under complex excitations. Furthermore, the finite-time stability of the closed-loop system is rigorously proven using Lyapunov stability theory. Finally, the strategy is evaluated under a 40% load mass mismatch and continuous random road excitations. Results indicate that the proposed strategy effectively curbs the deterioration of suspension nonlinearities during overloads, ensuring smoother dynamic transitions across all three axes. Compared to conventional backstepping control, the proposed approach reduces the root mean square values of vertical, pitch, and roll accelerations by 19%, 13%, and 35%, respectively. Ultimately, this framework effectively improves vehicle stability and disturbance rejection, providing a robust reference for heavy-duty vehicle chassis control. Full article

This paper investigates a class of electro-hydraulic servo systems with unknown nonlinear functions and parameters. To address the issues of modeling uncertainties and unmodeled dynamics, an adaptive robust nonlinear controller integrating neural networks and predefined-time prescribed performance is proposed. First, an exponential-type predefined-time prescribed performance function is designed to ensure that the system tracking error converges to a prescribed region within a predefined time. An adaptive law based on the discontinuous projection method is developed to estimate unknown parameters and compensate for them in the controller. The dynamic surface technique is introduced to overcome the “explosion of complexity” problem inherent in the traditional backstepping method. Meanwhile, neural networks are employed to approximate system nonlinearities, thereby reducing modeling errors. Finally, the stability of the closed-loop system is rigorously proved using Lyapunov theory, and numerical simulations validate the superiority of the designed controller over conventional control strategies. Full article

This paper addresses the tracking control problem of robotic manipulators under a universal symmetry constraint framework in the presence of lumped uncertainties and external disturbances. Unlike conventional constrained control schemes that treat tracking error bounds and state bounds separately, the proposed method explicitly exploits the symmetric structure of the prescribed constraints and formulates both tracking error constraints and full-state constraints in a unified manner. Based on the Euler–Lagrange dynamics of robotic manipulators, a universal symmetry constraint transformation is introduced to convert the original constrained system into an equivalent unconstrained form while preserving the intrinsic symmetry of the admissible sets. To enhance robustness against uncertainties and disturbances, a sliding-mode extended state observer is designed to estimate the total disturbance online. Meanwhile, a tracking differentiator is incorporated into the recursive design to avoid repeated differentiation of virtual control signals. On this basis, a disturbance-compensated backstepping controller is developed for the transformed manipulator system. It is shown that all closed-loop signals remain bounded, the prescribed symmetric tracking error and state constraints are never violated, and the tracking error converges asymptotically when the observer and differentiator errors vanish asymptotically. Simulation results obtained from a robotic manipulator verify the effectiveness of the proposed control strategy. Full article

This paper investigates the formation tracking problem for a group of autonomous underwater vehicles (AUVs) operating under quantized communication and actuation. A novel adaptive learning framework is proposed, capable of extracting cooperative control policies directly from quantized relative measurements and quantized input signals. Unlike conventional approaches that rely on continuous signal assumptions, the developed method enables each AUV to learn and adapt its behavior in real time from coarsely quantized data, thereby enhancing robustness in digital and bandwidth-limited environments. Within a backstepping control structure, an improved quantized consensus mechanism and a hysteresis quantizer compensation strategy are integrated to mitigate quantization effects. Using Lyapunov stability theory, it is proven that all closed-loop signals remain bounded and the formation tracking errors converge to an adjustable neighborhood of zero. Simulation results demonstrate that the proposed learning-based controller achieves accurate formation tracking and exhibits strong adaptability under dual quantization constraints. Full article

Due to their superior harmonic profiles and minimal switching energy losses, modular multilevel converters (MMCs) have emerged as the primary topology for high voltage direct current (HVDC) applications. However, traditional Proportional–Integral (PI) control exhibits inferior dynamic performance using MMC-HVDC supplying power in the passive networks. This study proposes a backstepping super-twisting sliding mode control strategy, which significantly improves the dynamic performance of the MMC-HVDC system and mitigates fluctuations in the DC side voltage. First, a mathematical model is established based on the topology of the modular multilevel HVDC transmission system. Then, utilizing the backstepping method, a virtual control law for the current inner loop is designed according to the mathematical model. Subsequently, the super-twisting sliding mode algorithm is introduced based on the backstepping method to form the backstepping super-twisting sliding mode control law. Finally, a comprehensive model is established within the Matlab/Simulink environment, and extensive simulation studies are carried out to evaluate the effectiveness the effectiveness and advantages of the proposed backstepping super-twisting sliding mode control under stable operation, grid voltage sag, and single-phase grounding fault conditions. Comparative evaluations verify that the introduced strategy effectively lowers the total harmonic distortion (THD) of the current and suppresses DC voltage ripples. Moreover, compared to the conventional PI method, the new approach provides enhanced transient robustness with noticeably reduced overshoot with considerably lower overshoot compared to traditional PI control, thereby providing a highly reliable and stable solution for MMC-HVDC systems supplying passive networks. Full article

This research examines how false data injection attacks (FDIAs) impact the trajectory tracking control of underactuated surface vessels (USVs). The internal uncertain dynamics of the system are reconstructed using radial basis function neural networks (RBFNNs). In order to avoid the computational pressure of the RBFNNs on the system, the neural network weights, external disturbances, and FDIAs are converted into a single parameter learning form using the minimum learning parameters (MLPs). Next, a nonlinear feedback function is constructed and introduced into the controller design process, thereby avoiding the controller accuracy loss caused by MLPs. Within the backstepping method framework, the adaptive laws leverage deep information robust adaptive technology to estimate the upper limits of the uncertainty term. The closed-loop system is provided with a rigorous theoretical analysis by combining the Lyapunov stability theory. Finally, the effectiveness of the control scheme is verified by simulation. The results show that the proposed controller guarantees boundedness of all closed-loop signals and drives the tracking errors into a small neighborhood of the reference trajectory even under the attack of FDIAs and the influence of internal and external uncertainties. Full article

This paper introduces the Quantum-Inspired Impulsive Continuous Hopfield Network (Q-ICHN), a novel hybrid control framework designed to handle non-smooth, high-energy perturbations in nonlinear dynamical systems. Standard Continuous Hopfield Networks (CHNs) rely on sigmoidal activation functions that are prone to gradient saturation, which leads to an insufficient corrective response when the system undergoes large deviations from equilibrium. To overcome this shortcoming, the proposed Q-ICHN adopts a wave-packet-based activation function grounded in the stationary Schrödinger equation, yielding a non-monotonic and oscillatory activation profile that sustains effective compensatory dynamics across a broad range of states. Furthermore, the proposed framework incorporates Madelung’s quantum potential into the control architecture, thereby enabling a fundamental reshaping of the system’s energy landscape. Specifically, this induces a tunneling-like mechanism that allows the system to circumvent local minima and rapidly recover from impulsive disturbances, manifested as a sharpened attractor structure in the phase-space domain. Together, these properties yield enhanced convergence behavior and improved robustness over traditional neural control approaches. To rigorously assess its merits, the performance of the Q-ICHN is evaluated through a large-scale benchmark involving 20 established control methods, including Sliding Mode Control (SMC), Model Predictive Control (MPC), and Backstepping. The experimental results obtained across 20 heterogeneous scenarios demonstrate that the proposed model achieves a 48% reduction in Mean Squared Error (MSE) relative to the classical ICHN. In addition, the Q-ICHN exhibits improved smoothness, reflected in a 30% reduction in jerk with respect to high-gain robust controllers, and enhanced reliability, validated by superior spectral purity and a 34% reduction in integrated variance under stochastic perturbations. Collectively, these results underscore the potential of quantum-inspired activation mechanisms to favorably balance control responsiveness and harmonic stability, providing a robust framework for handling both continuous dynamics and impulsive effects. Full article

Quadrotor UAVs present a significant control challenge due to their underactuated nature; strong coupling effects; nonlinear dynamics; and high sensitivity to unknown effect parameters, external disturbances, and uncertainties. To address this issue, this study proposes a Lyapunov-based backstepping (LYP) controller that ensures robust stability and precise trajectory tracking. The controller employs an inner- and outer-loop architecture for coupled position and attitude control. Its performance is compared with Proportional–Integral–Derivative (PID) and Fractional-Order PID (FOPID) controllers under three scenarios: nominal conditions, external disturbances, and model parameter uncertainties. All controller gains are optimized using Particle Swarm Optimization (PSO). Simulation results, which are evaluated using time-domain metrics and root mean square error (RMSE), demonstrate that the proposed LYP controller achieves superior robustness, faster disturbance rejection, and improved tracking accuracy compared to both PID and FOPID controllers. Full article

This paper investigates the cooperative formation control problem in unmanned surface vehicles (USVs) with prescribed performance constraints under complex marine conditions including external disturbances, model uncertainties, actuator faults, and input saturation. A novel fault-tolerant control (FTC) algorithm is developed by integrating cooperative learning neural networks (NNs), distributed disturbance observers, and the backstepping technique. Specifically, the learning NNs adaptively approximate system uncertainties, and the learned weight information is shared among vehicles to enhance cooperative cognition. Additionally, an auxiliary dynamic system and an actuator configuration matrix are designed to compensate for input saturation and propeller failures. Theoretical analysis based on the Lyapunov method proves that all signals in the closed-loop system are bounded, and the formation tracking errors strictly remain within the predefined transient and steady-state performance bounds. Finally, simulation experiments involving a group of four USVs validate the proposed algorithm. The results demonstrate that the USVs can rapidly converge to and maintain the desired quadrilateral formation shape despite time-varying disturbances and actuator efficiency loss. Furthermore, comparative simulation results indicate that the proposed cooperative learning FTC scheme significantly reduces velocity tracking error oscillations compared to traditional non-learning methods, explicitly verifying its superior robustness and fault-tolerant capabilities. Full article