Search Results (427)

This study addresses the practical stability analysis of Riemann-Liouville fractional-order nonlinear systems with time delays. We first establish a rigorous formulation of initial conditions that aligns with the properties of Riemann-Liouville fractional derivatives. Subsequently, a generalized definition of practical stability is introduced, specifically tailored to accommodate the hybrid dynamics of fractional calculus and time-delay phenomena. By constructing appropriate Lyapunov-Krasovskii functionals and employing an enhanced Razumikhin-type technique, we derive sufficient conditions ensuring practical stability in the $L_p$-norm sense. The theoretical findings are validated through illustrative example for fractional order nonlinear systems with time delays. Full article

This paper presents a flight control framework based on neural network Model Predictive Control (NN-MPC) to tackle the challenges of acceleration command tracking for supersonic vehicles (SVs) in complex flight environments, addressing the shortcomings of traditional methods in managing nonlinearity, random disturbances, and real-time performance requirements. Initially, a dynamic model is developed through a comprehensive analysis of the vehicle’s dynamic characteristics, incorporating strong cross-coupling effects and disturbance influences. Subsequently, a predictive mechanism is employed to forecast future states and generate virtual control commands, effectively resolving the issue of sluggish responses under rapidly changing commands. Furthermore, the approximation capability of neural networks is leveraged to optimize the control strategy in real time, ensuring that rudder deflection commands adapt to disturbance variations, thus overcoming the robustness limitations inherent in fixed-parameter control approaches. Within the proposed framework, the ultimate uniform bounded stability of the control system is rigorously established using the Lyapunov method. Simulation results demonstrate that the method exhibits exceptional performance under conditions of system state uncertainty and unknown external disturbances, confirming its effectiveness and reliability. Full article

This paper aims to investigate a Nash equilibrium (NE)-seeking approach for the aggregative game problem of second-order multi-agent systems (MAS) with uncontrollable malicious players, which may cause the decisions of global players to become uncontrollable, thereby hindering the ability of normal players to reach the NE. To mitigate the influence of malicious players on the system, a malicious player detection and disconnection (MPDD) algorithm is proposed, based on the fixed-time convergence method. Subsequently, a predefined-time distributed NE-seeking algorithm is presented, utilizing a time-varying, time-based generator (TBG) and state-feedback scheme, ensuring that all normal players complete the game problem within the predefined time. The convergence properties of the algorithms are analyzed using Lyapunov stability theory. Theoretically, the aggregative game problem with malicious players can be solved using the proposed algorithms within any user-defined time. Finally, a numerical simulation of electricity market bidding verifies the effectiveness of the proposed algorithm. Full article

In this paper, a robust optimized controller is implemented in the photovoltaic generator system (PVGS). The PVGS is composed of individual photovoltaic (PV) cells, which convert solar energy to electrical energy. To optimize the efficiency of the PVGS under variable solar irradiance and temperatures, a maximum power point tracking (MPPT) controller is necessary. Additionally, the PVGS output voltage is typically low for many applications. To achieve the MPPT and to gain the output voltage, an increasing boost converter (IBC) is employed. Then, two issues should be considered in MPPT. At first, a smooth control signal for adjusting the duty cycle of the IBC is important. Another critical issue is the PVGS and IBC unknown sections, i.e., the total system uncertainty. Therefore, to address the system uncertainties and to regulate the smooth duty cycle of the converter, a robust dynamic sliding mode control (DSMC) is proposed. In DSMC, a low-pass integrator is placed before the system to suppress chattering and to produce a smooth actuator signal. However, this integrator increases the system states, and hence, a sliding mode observer (SMO) is proposed to estimate this additional state. The stability of the proposed control scheme is demonstrated using the Lyapunov theory. Finally, to demonstrate the effectiveness of the proposed method and provide a reliable comparison, conventional sliding mode control (CSMC) with the same proposed SMO is also implemented. Full article

This paper presents some of the most significant findings in the design of a hydraulic servomechanism for flight controls, which were primarily achieved by the first author during his activity in an aviation institute. These results are grouped into four main topics. The first one outlines a classical theory, from the 1950s–1970s, of the analysis of nonlinear automatic systems and namely the issue of absolute stability. The uninformed public may be misled by the adjective “absolute”. This is not a “maximalist” solution of stability but rather highlights in the system of equations a nonlinear function that describes, for the case of hydraulic servomechanisms, the flow-control dependence in the distributor spool. This function is odd, and it is therefore located in quadrants 1 and 3. The decision regarding stability is made within the so-called Lurie problem and is materialized by a matrix inequality, called the Lefschetz condition, which must be satisfied by the parameters of the electrohydraulic servomechanism and also by the components of the control feedback vector. Another approach starts from a classical theorem of V. M. Popov, extended in a stochastic framework by T. Morozan and I. Ursu, which ends with the description of the local and global spool valve flow-control characteristics that ensure stability in the large with respect to bounded perturbations for the mechano-hydraulic servomechanism. We add that a conjecture regarding the more pronounced flexibility of mathematical models in relation to mathematical instruments (theories) was used. Furthermore, the second topic concerns, the importance of the impedance characteristic of the mechano-hydraulic servomechanism in preventing flutter of the flight controls is emphasized. Impedance, also called dynamic stiffness, is defined as the ratio, in a dynamic regime, between the output exerted force (at the actuator rod of the servomechanism) and the displacement induced by this force under the assumption of a blocked input. It is demonstrated in the paper that there are two forms of the impedance function: one that favors the appearance of flutter and another that allows for flutter damping. It is interesting to note that these theoretical considerations were established in the institute’s reports some time before their introduction in the Aviation Regulation AvP.970. However, it was precisely the absence of the impedance criterion in the regulation at the appropriate time that ultimately led, by chance or not, to a disaster: the crash of a prototype due to tailplane flutter. A third topic shows how an important problem in the theory of automatic systems of the 1970s–1980s, namely the robust synthesis of the servomechanism, is formulated, applied and solved in the case of an electrohydraulic servomechanism. In general, the solution of a robust servomechanism problem consists of two distinct components: a servo-compensator, in fact an internal model of the exogenous dynamics, and a stabilizing compensator. These components are adapted in the case of an electrohydraulic servomechanism. In addition to the classical case mentioned above, a synthesis problem of an anti-windup (anti-saturation) compensator is formulated and solved. The fourth topic, and the last one presented in detail, is the synthesis of a fuzzy supervised neurocontrol (FSNC) for the position tracking of an electrohydraulic servomechanism, with experimental validation, in the laboratory, of this control law. The neurocontrol module is designed using a single-layered perceptron architecture. Neurocontrol is in principle optimal, but it is not free from saturation. To this end, in order to counteract saturation, a Mamdani-type fuzzy logic was developed, which takes control when neurocontrol has saturated. It returns to neurocontrol when it returns to normal, respectively, when saturation is eliminated. What distinguishes this FSNC law is its simplicity and efficiency and especially the fact that against quite a few opponents in the field, it still works very well on quite complicated physical systems. Finally, a brief section reviews some recent works by the authors, in which current approaches to hydraulic servomechanisms are presented: the backstepping control synthesis technique, input delay treated with Lyapunov–Krasovskii functionals, and critical stability treated with Lyapunov–Malkin theory. Full article

A well-known model of infectious diseases, described by a nonlinear system of delay differential equations, is investigated under the influence of stochastic perturbations. Using the general method of Lyapunov functional construction combined with the linear matrix inequality (LMI) approach, we derive sufficient conditions for the stability of the equilibria of the considered system. Numerical simulations illustrating the system’s behavior under stochastic perturbations are provided to support the thoretical findings. The proposed method for stability analysis is broadly applicable to other systems of nonlinear stochastic differential equations across various fields. Full article

The authors investigate an epidemic model described by a differential equation, which includes a piecewise constant argument of the generalized type (DEPCAG). In this work, the main goal is to find an invariant region for the system and prove the existence and uniqueness of solutions with the defined conditions using integral equations. On top of that, an auxiliary result is established, outlining the relationship between the unknown function values in the deviation argument and the time parameter. The stability analysis is conducted using the Lyapunov–Razumikhin method, adapted for differential equations with a piecewise constant argument of the generalized type. The trivial equilibrium’s stability is examined, and the stability of the positive equilibrium is assessed by transforming it into a trivial form. Finally, sufficient conditions for the uniform asymptotic stability of both the trivial and positive equilibria are established. Full article

In this paper, a fixed-time control strategy based on neural networks is proposed for a space robot with an input dead zone. First, a model-based control method is proposed based on the fixed-time convergence framework. Due to internal errors and external environmental disturbances, the inertial parameters of dynamic models generally exhibit uncertainties, and model-based control methods may exhibit deviations in trajectory tracking. In order to counteract the adverse effects of uncertain inertial parameters on the system and ensure the stability of the control system, an adaptive learning control method based on neural networks is further proposed. To enhance the learning rate of neural networks and achieve the convergence of neural weights within a fixed time, a neural network update rate combined with virtual control rate is proposed. In addition, considering the issue of the joint input dead zone affecting the precision and stability of the space robot, a novel adaptive law is proposed in conjunction with system error signal feedback to mitigate adverse effects. According to the Lyapunov stability theory, the stability of the closed-loop system is proven, with the trajectory tracking error converging to a small neighborhood around zero. Finally, numerical simulation results demonstrate the effectiveness of the control algorithm. Full article

This paper proposes a super-twisting sliding-mode control (STSMC) strategy to enhance the efficiency and stability of a heaving point absorber wave energy converter (PAWEC) system equipped with a permanent magnet synchronous generator (PMSG). In particular, the STSMC is designed to address both generator-side and grid-side control challenges by ensuring precise regulation under varying wave conditions. A dynamical model of the PAWEC is developed to describe system responses, while the power take-off (PTO) mechanism is tailored to maintain consistent generator speed and efficient energy conversion. Lyapunov stability theory is employed to verify the stability of the proposed controller. Simulation studies and tests on a small-scale experimental setup with a 500 W PAWEC model under regular and irregular waves demonstrate that STSMC improves generator speed regulation and power output by more than 30% compared to field-oriented control (FOC), nonlinear adaptive backstepping (NAB), and first-order sliding-mode control (FOSMC). The proposed approach also manages grid-side total harmonic distortion (THD) effectively, keeping it below 5%. These results indicate that STSMC can substantially improve the dynamic performance and energy efficiency of wave energy systems. Full article

General aviation trajectory prediction plays a crucial role in enhancing safety and operational efficiency at non-towered airports. However, current research faces multiple challenges including variable weather conditions, complex aircraft interactions, and flight pattern constraints specified by general aviation regulations. This paper proposes a deep learning method based on stochastic processes aimed at addressing uncertainty issues in general aviation trajectory prediction. First, we design a probabilistic encoder–decoder structure enabling the model to output trajectory distributions rather than single paths, with regularization terms based on Lyapunov stability theory to ensure predicted trajectories maintain stable convergence while satisfying flight patterns. Second, we develop a multi-layer attention mechanism that accounts for weather factors, enhancing the model’s responsiveness to environmental changes. Validation using the TrajAir dataset from Pittsburgh-Butler Regional Airport (KBTP) not only advances deep learning applications in general aviation but also provides new insights for solving trajectory prediction problems. Full article

The issue of multi-switch generalized projective anti-synchronization of fractional-order chaotic systems is investigated in this work. The model is constructed using Caputo–Fabrizio derivatives, which have been rarely addressed in previous research. In order to expand the symmetric and asymmetric synchronization modes of chaotic systems, we consider modeling chaotic systems under such fractional calculus definitions. Firstly, a new fractional-order differential inequality is proven, which facilitates the rapid confirmation of a suitable Lyapunov function. Secondly, an effective multi-switching controller is designed to confirm the convergence of the error system within a short moment to achieve synchronization asymptotically. Simultaneously, a multi-switching parameter adaptive principle is developed to appraise the uncertain parameters in the system. Finally, two simulation examples are presented to affirm the correctness and superiority of the introduced approach. It can be said that the symmetric properties of Caputo–Fabrizio fractional derivative are making outstanding contributions to the research on chaos synchronization. Full article

This paper investigates the synchronization control problem for delayed fractional-order neural networks (DFONNs) with mismatched parameters. A novel synchronization behavior termed quasi-Mittag-Leffler projective synchronization (QMLPS) is studied. The core contribution of this work lies in the following: (1) The time delay and mismatched parameters between driven and response systems are considered, which is more general. Both static controllers and adaptive controllers are designed to synchronize the DFONNs. (2) The synchronization errors are estimated, and the rate of convergence is clarified description. By using the Lyapunov stability theory and some significant fractional-order differential inequalities, some sufficient conditions for DFONNs are derived under two kinds of control methods; furthermore, the bound of synchronization errors is estimated by the Mittag-Leffler function. Quantitative numerical simulations have demonstrated the superiority of our controller. Compared to existing results, the QMLPS introduced in this paper is more general, incorporating many existing synchronization concepts. The numerical simulation section verifies the effectiveness of the theoretical results, providing several types of synchronization behaviors of the controlled system under both mismatched and matched parameter conditions, and it also demonstrates the accuracy of the theoretical estimation of synchronization error bounds. Full article

This study proposes a novel fuzzy disturbance observer (FDO)-augmented adaptive nonsingular terminal sliding mode control (NTSMC) framework for multi-joint robotic manipulators, addressing critical challenges in trajectory tracking precision and disturbance rejection. Unlike conventional disturbance observers requiring prior knowledge of disturbance bounds, the proposed FDO leverages fuzzy logic principles to dynamically estimate composite disturbances—including unmodeled dynamics, parameter perturbations, and external torque variations—without restrictive assumptions about disturbance derivatives. The control architecture achieves rapid finite-time convergence by integrating the FDO with a singularity-free terminal sliding manifold and an adaptive exponential reaching law while significantly suppressing chattering effects. Rigorous Lyapunov stability analysis confirms the uniform ultimate boundedness of tracking errors and disturbance estimation residuals. Comparative simulations on a 2-DOF robotic arm demonstrate a 97.28% reduction in root mean square tracking errors compared to PD-based alternatives and a 73.73% improvement over a nonlinear disturbance observer-enhanced NTSMC. Experimental validation on a physical three-joint manipulator platform reveals that the proposed method reduces torque oscillations by 58% under step-type disturbances while maintaining sub-millimeter tracking accuracy. The framework eliminates reliance on exact system models, offering a generalized solution for industrial manipulators operating under complex dynamic uncertainties. Full article

Neural network (NN)-based controllers have emerged as a paradigm-shifting approach in modern control systems, demonstrating unparalleled capabilities in governing nonlinear dynamical systems with inherent uncertainties. This comprehensive review systematically investigates the theoretical foundations and practical implementations of NN controllers through the prism of Lyapunov stability theory, NN controller frameworks, and robustness analysis. The review establishes that recurrent neural architectures inherently address time-delayed state compensation and disturbance rejection, achieving superior trajectory tracking performance compared to classical control strategies. By integrating imitation learning with barrier certificate constraints, the proposed methodology ensures provable closed-loop stability while maintaining safety-critical operation bounds. Experimental evaluations using chaotic system benchmarks confirm the exceptional modeling capacity of NN controllers in capturing complex dynamical behaviors, complemented by formal verification advances through reachability analysis techniques. Practical demonstrations in aerial robotics and intelligent transportation systems highlight the efficacy of controllers in real-world scenarios involving environmental uncertainties and multi-agent interactions. The theoretical framework synergizes data-driven learning with nonlinear control principles, introducing hybrid automata formulations for transient response analysis and adjoint sensitivity methods for network optimization. These innovations position NN controllers as a transformative technology in control engineering, offering fundamental advances in stability-guaranteed learning and topology optimization. Future research directions will emphasize the integration of physics-informed neural operators for distributed control systems and event-triggered implementations for resource-constrained applications, paving the way for next-generation intelligent control architectures. Full article

This paper presents a vector control (VC) scheme with a position sensor designed for hybrid stepper motors (HSMs). The proposed scheme consists of three main components: a current tracking controller, a position controller, and a phase reference current generation algorithm. Based on the principle of optimal current control, the algorithm calculates the minimum target phase current required to generate the desired torque under transient conditions by evaluating the stator flux. This approach eliminates the need for coordinate transformations typically used in conventional vector control methods, as the current tracking is performed directly in the stator reference frame. A current controller in the stator reference frame is designed using the Lyapunov stability theory, featuring a simple structure with only one adjustable control parameter. Additionally, a nonlinear torque modulation algorithm is employed for position control. Closed-loop stability analysis demonstrates that the proposed scheme is robustly stable. Both simulation and experimental results confirm that the position tracking performance of the HSM is significantly improved under the proposed control scheme. Full article