Search Results (62)

This paper presents a rigid–flexible coupling dynamic modeling framework and a fixed-time control strategy for a flexible space-tethered satellite (STS) system. A high-fidelity rigid–flexible coupling dynamic model of STS is developed using the finite element method, accurately capturing the coupled attitude dynamics of the satellite platform and flexible tether. Leveraging a simplified representation of the STS model, a nonsingular terminal sliding-mode controller (NTSMC) is synthesized via fixed-time stability theory. Uncertainties and disturbances within the system are compensated for by a radial basis function neural network (RBFNN), ensuring strong robustness. The controller’s fixed-time convergence property—with convergence time independent of initial conditions—is established using Lyapunov stability theory, enabling reliable operation in complex space environments. Numerical simulations implemented on the STS rigid–flexible coupling model validate the controller’s efficacy. Comparative analyses demonstrate superior tracking performance and enhanced practicality over conventional sliding-mode controllers, especially in the aspect of chattering suppression for the satellite thrusters. Full article

Chaotic systems appear in a wide range of natural and engineering contexts, making the design of reliable and flexible control strategies a crucial challenge. This work proposes a robust control scheme based on the Fractional-Order Backstepping Control (FOBC) method for the stabilization of non-commensurate fractional-order chaotic systems subject to bounded uncertainties and external disturbances. The method is developed through a rigorous stability analysis grounded in the Mittag–Leffler function, enabling the step-by-step stabilization of each subsystem. By incorporating fractional-order derivatives into carefully selected Lyapunov candidate functions, the proposed controller ensures global system stability. The performance of the FOBC approach is validated on fractional-order versions of the Duffing–Holmes system and the Rayleigh oscillator, with the results compared against those of a fractional-order PID (FOPID) controller. Numerical evaluations demonstrate the superior performance of the proposed strategy: the error dynamics converge rapidly to zero, the system exhibits strong robustness by restoring state variables to equilibrium quickly after disturbances, and the method achieves low energy dissipation with a high error convergence speed. These quantitative indices confirm the efficiency of FOBC over existing methods. The integration of fractional-order dynamics within the backstepping framework offers a powerful, robust, and resilient approach to stabilizing complex chaotic systems in the presence of uncertainties and external perturbations. Full article

We investigate the solvability and stability properties of a class of nonlinear stochastic delay differential equations (SDDEs) driven by Wiener noise and incorporating discrete time delays. The equations are formulated within a Banach space of continuous, adapted sample paths. Under standard Lipschitz and linear growth conditions, we construct a solution operator and prove the existence and uniqueness of strong solutions using a fixed-point argument. Furthermore, we derive exponential mean-square stability via Lyapunov-type techniques and delay-dependent inequalities. This framework provides a unified and flexible approach to SDDE analysis that departs from traditional Hilbert space or semigroup-based methods. We explore a Banach space fixed-point approach to SDDEs with multiplicative noise and discrete delays, providing a novel functional-analytic framework for examining solvability and stability. Full article

In this paper, an adaptive sliding mode fault-tolerant control (FTC) scheme is proposed for small Quadrotor Unmanned Aerial Vehicles (QUAVs) used in education and teaching formation in the presence of systematic unknown external disturbances with actuator failures. A radial basis function neural network (RBFNN) is employed to handle the nonlinear interaction function, and a fault-tolerant-based NN extended state observer (NNESO) is designed to estimate the unknown external disturbance. Meanwhile, an adaptive fault observer is developed to estimate and compensate for the fault parameters of the system. To achieve satisfactory trajectory tracking performance for the QUAV, an adaptive sliding mode control (SMC) strategy is designed. This strategy mitigates the strong coupling effects among the design parameters within the QUAV formation. The stability of the closed-loop system is rigorously demonstrated by Lyapunov analysis, and the controlled QUAV formation can achieve the desired tracking position. Simulation results verify the effectiveness of the proposed control method. Full article

A tethered Unmanned Aerial Vehicle (UAV) is a special type of UAV that is powered continuously through a cable, ensuring long-duration flight. However, the pulling interference of the cable significantly affects the UAV’s stability control, limiting its application and development. This paper addresses this issue by first analyzing the effect of cable tension on the UAV’s wind resistance capability and demonstrates the possibility of using cable tension to assist in wind resistance control. Building on this, a robust time-delay compensator is designed to address the problem of unknown external disturbance and unknown time delay in the cable control input. Sufficient conditions for system boundedness are provided using the Lyapunov–Krasovskii functional. Subsequently, to deal with the strong nonlinearity and strong coupling issues of the sufficient conditions, the Harris Hawks Optimization (HHO) algorithm is employed for intelligent optimization of the controller parameters. Simulation results indicate that the HHO-based robust time-delay compensator exhibits excellent robustness and fast response. Full article

Accurate trajectory control during atmospheric entry is critical for the success of Mars landing missions, where strong non-linearities and uncertain dynamics pose significant challenges to conventional control strategies. This study develops a computational framework that integrates fuzzy parameter-varying models with Lyapunov-based analysis to achieve robust trajectory stabilization of Mars entry vehicles. The non-linear longitudinal dynamics are reformulated via sector-bounded approximation into a Takagi–Sugeno fuzzy parameter-varying model, enabling systematic gain-scheduled controller synthesis. To reduce the conservatism typically associated with quadratic Lyapunov functions, a fuzzy Lyapunov function approach is adopted, in conjunction with the Full-Block S-procedure, to derive less restrictive stability conditions expressed as linear matrix inequalities. Based on this formulation, several controllers are designed to accommodate the variations in atmospheric density and flight conditions. The proposed methodology is validated through numerical simulations, including Monte Carlo dispersion and parametric sensitivity analyses. The results demonstrate improved stability, faster convergence, and enhanced robustness compared to existing fuzzy control schemes. Overall, this work contributes a systematic and less conservative control design methodology for aerospace applications operating under severe non-linearities and uncertainties. Full article

This paper presents a resilient observer-based and event-triggered control scheme for discrete-time Cyber–Physical Systems (CPS) under Markovian Cyber-Attacks (MCA). The proposed framework integrates a Luenberger observer for cyberattack detection with a state-feedback controller designed to preserve system stability in the presence of Denial-of-Service (DoS) and False Data Injection (FDI) attacks. Attack detection is achieved through residual signal generation combined with Markovian modeling of the attack dynamics. System stability is guaranteed by formulating relaxed Linear Matrix Inequality (LMI) conditions that incorporate relaxation variables, a diagonal Lyapunov function, the S-procedure, and congruence transformations. Moreover, the Event-Triggered Mechanism (ETM) efficiently reduces communication load without degrading control performance. Numerical simulations conducted on a three-tank system benchmark confirm enhanced detection accuracy, faster recovery, and strong robustness against uncertainties. Full article

Unmanned surface vehicles (USVs) course control research constitutes a vital branch of ship motion control studies and serves as a key technology for the development of marine critical equipment. Aiming at the problems of model uncertainties, external marine disturbances, performance optimization, and actuator constraints encountered by the autopilot system, this paper proposes a composite disturbance cancellation optimized control method based on fuzzy reinforcement learning. Firstly, a coupling design of the finite-time disturbance observer and fuzzy logic system is conducted to estimate and reject the composite disturbance composed of internal model uncertainty and ocean disturbances. Secondly, a modified backstepping control technique is employed to design the autopilot controller and construct the error system. Based on the designed performance index function, the fuzzy reinforcement learning is utilized to propose an optimized compensation term for the error system. Meanwhile, to address the actuator saturation issue, an auxiliary system is introduced to modify the error surface, reducing the impact of saturation on the system. Finally, the stability of the autopilot system is proved using the Lyapunov stability theory. Simulation studies conducted on the ocean-going training ship “Yulong” demonstrate the effectiveness of the proposed algorithm. Under the strong and weak ocean conditions designed, this algorithm can ensure that the tracking error converges within 7 s. 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

Altitude test facilities for aero-engines employ multi-chamber, multi-valve intake systems that require effective decoupling and strong disturbance rejection during transient tests. This paper proposes a coordinated active disturbance rejection control (ADRC) scheme based on external penalty functions. The chamber pressure safety limit is formulated as an inequality-constrained optimization problem, and an exponential penalty together with a gradient based algorithm is designed for dynamic constraint relaxation, with guaranteed global convergence. A coordination term is then integrated into a distributed ADRC framework to yield a multi-valve coordinated ADRC controller, whose asymptotic stability is established via Lyapunov theory. Hardware-in-the-loop simulations using MATLAB/Simulink and a PLC demonstrate that, under ±3 kPa pressure constraints, the maximum engine inlet pressure error is 1.782 kPa (77.1% lower than PID control), and under an 80 kg/s² flow-rate disturbance, valve oscillations decrease from ±27% to ±5%. These results confirm the superior disturbance rejection and decoupling performance of the proposed method. Full article

The dynamic vibration absorber (DVA) based on delayed fractional PID (DFOPID) can achieve a more superior vibration suppression effect. However, the strong nonlinear characteristics of the system and the computational burden resulting from its high dimensionality make solving and optimizing more challenging. This paper presents a coupled model of DFOPID and DVA, exploring its parameter tuning mechanism and optimization problem. First, using the averaging method and Lyapunov stability theory, the amplitude-frequency equation and the stability condition of the steady-state solution of the primary system are derived. Numerical simulations validate the accuracy of the analytical result. Next, based on the mechanics of vibration, the approximate expressions of the controller under different differential conditions are calculated, and their equivalent action mechanisms are analyzed. Finally, by minimizing the maximum amplitude of the primary system as the objective function, the Particle Swarm Optimization (PSO) algorithm is applied to optimize the parameters of the passive DVA and the DVA models controlled by PID, FOPID, and DFOPID, successfully addressing the parameter optimization challenges posed by traditional fixed-point theory. The vibration reduction performance is compared across different loading environments. The results demonstrate that the model presented in this paper performs the best, exhibiting excellent vibration suppression and robustness. Full article

This study presents a novel two-dimensional hyperchaotic map, referred to as the 2D exponent-logarithm-sine chaotic map (2D-ELSCM), which is intricately designed through the interplay of exponential, logarithmic, and sine functions. To comprehensively evaluate the chaotic performance of the 2D-ELSCM, several critical metrics are employed, including the largest Lyapunov exponent (LLE), permutation entropy (PE), sample entropy (SE), Kolmogorov entropy (KE), and the results of the 0–1 test, which yield values of 8.3175, 0.9998, 1.9826, 2.1117, and 0.9970, respectively. Furthermore, the 2D-ELSCM successfully passes the NIST randomness tests, collectively confirming its exceptional randomness and complexity. Building upon this robust chaotic map, we develop a distinctive chaotic image encryption scheme that employs an improved Knuth-Durstenfeld shuffle (IKDS) to rearrange pixel positions, effectively disrupting the correlation between adjacent pixels. Complementing this, we introduce a dynamic diffusion mechanism that integrates DNA encoding with the Zigzag transform, thereby promoting global pixel diffusion and enhancing encryption security. The initial conditions of the chaotic map are generated from the SHA-512 hash of the plaintext image in conjunction with an external key, which not only expands the key space but also significantly improves key sensitivity. Simulation results demonstrate that the proposed encryption scheme achieves correlation coefficients approaching 0 in the encrypted test images, with an average NPCR of 99.6090% and UACI of 33.4707%. These findings indicate a strong resistance to various attacks and showcase excellent encryption quality, thereby underscoring the scheme’s potential for secure image transmission and storage. Full article

The trajectory tracking the control of autonomous underwater vehicle (AUV) systems faces considerable challenges due to strong inter-axis coupling and complex time-varying external disturbances. This paper proposes a novel fixed-time control scheme incorporating a switching threshold-based event-driven strategy to address critical issues in multi-AUV formation control, including full-state constraints, unmeasurable states, model uncertainties, limited communication resources, and unknown time-varying disturbances. A rapid and stable dimensional augmented state observer (RSDASO) was first developed to achieve fixed-time convergence in estimating aggregated disturbances and unmeasurable states. Subsequently, a logarithmic barrier Lyapunov function was constructed to derive a fixed-time control law that guarantees bounded system errors within a predefined interval while strictly confining all states to specified constraints. The introduction of a switching threshold event-triggering mechanism (ETM) significantly reduced communication resource consumption. The simulation results demonstrate the effectiveness of the proposed method in improving control accuracy while substantially lowering communication overhead. Full article

In this paper, we develop new necessary and sufficient Lyapunov conditions for fixed-time stability that refine the classical fixed-time stability results presented in the literature by providing an optimized estimate of the settling time bound that is less conservative than the existing results. Then, building on our new fixed-time stability results, we introduce the notion of uniformly strongly dissipative dynamical systems and show that for a closed dynamical system (i.e., a system with the inputs and outputs set to zero) this notion implies fixed-time stability. Specifically, we construct a stronger version of the dissipation inequality that implies system dissipativity and generalizes the notions of strict dissipativity and strong dissipativity while ensuring that the closed system is fixed-time stable. The results are then used to derive new Kalman–Yakubovich–Popov conditions for characterizing necessary and sufficient conditions for uniform strong dissipativity in terms of the system drift, input, and output functions using continuously differentiable storage functions and quadratic supply rates. Furthermore, using uniform strong dissipativity concepts, we present several stability results for nonlinear feedback systems that guarantee finite-time and fixed-time stability. For specific supply rates, these results provide generalizations of the feedback passivity and nonexpansivity theorems that additionally guarantee finite-time and fixed-time stability. Finally, several illustrative numerical examples are provided to demonstrate the proposed fixed-time stability and uniform strong dissipativity frameworks. Full article

This study presents a novel finite-time robust control framework for quadrotor systems subjected to model uncertainties and unknown external disturbances. A fast terminal sliding mode (FTSM) manifold is first constructed to achieve finite-time convergence of tracking errors. To address the challenges posed by uncertain system dynamics, a radial basis function neural network (RBFNN) is integrated for real-time approximation of unknown nonlinearities. In addition, an adaptive gain regulation mechanism based on a barrier Lyapunov function (BLF) is developed to ensure boundedness of system trajectories while enhancing robustness without requiring prior knowledge of disturbance bounds. The proposed control scheme guarantees finite-time stability, strong robustness, and precise trajectory tracking. Numerical simulations substantiate the efficacy and superiority of the proposed method in comparison with existing control approaches. Full article