Search Results (145)

This paper addresses the controller design problem for linear systems with time-varying delays. By constructing a novel Lyapunov–Krasovskii functional incorporating delay-partitioning techniques, we establish delay-dependent stability criteria for the solvability of the robust stabilization problem. The derived conditions are formulated as linear matrix inequalities (LMIs) that become affine upon fixing a single scalar parameter, thereby facilitating efficient numerical computation. Furthermore, these criteria guarantee that the reachable set of the closed-loop system remains bounded within a prescribed ellipsoid under zero initial conditions. The effectiveness and superiority of the proposed approach are demonstrated through two comparative numerical examples, including a benchmark problem with varying delay. Full article

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 study examines the extended dissipativity analysis for newly designed mixed traffic systems (MTSs) utilizing the coupling memory sampled-data control (CMSDC) approach. The traffic flow creates a platoon, and the behavior of human-driven vehicles (HDVs) is presumed to adhere to the optimal velocity model, with the acceleration of a single-linked automated vehicle regulated directly by a suggested CMSDC. The ultimate objective of this work is to present a CMSDC approach for optimizing traffic flow amidst disruptions. The primary emphasis is on the proper design of the CMSDC to ensure that the closed-loop MTS is extended dissipative and quadratically stable. A more generalized CMSDC methodology incorporating a time delay effect is created using a Bernoulli-distributed sequence. The existing Lyapunov–Krasovskii functional (LKF) and enhanced integral inequality methods offer sufficient conditions for the suggested system to achieve an extended dissipative performance index. The suggested criteria provide a comprehensive dissipative study, evaluating $L_2-L_{\infty }$, $H_{\infty }$, passivity, and dissipativity performance. A simulation example illustrates the accuracy and superiority of the proposed controller architecture for the MTS. Full article

In unmanned systems, especially in large-scale and complex ones, sensor and communication failures occur from time to time and are hard to avoid. Therefore, this paper studies the fault detection problem of a class of unknown nonlinear singular uncertain time-varying delay Markov jump systems (UNSUTVDMJSs). Firstly, the corresponding sliding mode controller (SMC) is designed by using the equivalent control principle, and the unknown nonlinearity is equivalently replaced by changing the system input. Then, a fault detection filter adapted to this system is designed, thereby obtaining the unknown nonlinear stochastic singular uncertain Augmented filter residual system (UNSSUAFRS) model. To obtain the sufficient conditions for the random admissibility of this augmented system, a weak infinitesimal generator was used to design the required Lyapunov-Krasovskii functional. With the help of the Lyapunov principle and $H_{\infty }$ performance analysis method, the sufficient conditions for the random admissibility of UNSSUAFRS under the $H_{\infty }$ performance index $\gamma$ were derived. Finally, with the aid of the designed residual evaluation function and threshold, simulation analysis was conducted on the examples of DC servo motors and numerical calculation examples to verify the effectiveness and practicability of this fault detection filter. 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

The formation control technology of the multi-ASV (autonomous surface vehicle) system is one of the key technologies required for performing maritime missions. In this paper, a leaderless formation controller is proposed, where the issues of sampled communication and data transmission delays in formation are taken into consideration. By introducing the desired displacements and the implicit formation center (IFC), the control goal of the leaderless formation is explicitly defined. Through the application of a state-space transformation, the achievement of the leaderless formation is shown to be equivalent to the stabilization of the transformed subsystem. The implicit formation center of the leaderless framework is derived, which facilitates the description and analysis of formation movements. The stability of the system is rigorously analyzed by using the Lyapunov–Krasovskii functional. Furthermore, an $H_{\infty }$ performance controller is designed to evaluate the tolerance of the leaderless formation against marine environmental disturbances. Numerical simulations with 10 ASVs under sampled communication and transmission delay demonstrate the effectiveness of the proposed controller, achieving an $H_{\infty }$ performance bound $\gamma$ of 10. Full article

This paper presents a novel control design methodology for a magnetorheological (MR) damper-based semi-active suspension system operating under communication-induced time delays, which introduce nonlinear sampled-data dynamics. To address these challenges, a linear matrix inequality (LMI) framework is developed for synthesizing the current controller, with the dual goals of enhancing ride comfort and safety while ensuring system stability and robustness against road disturbances. The proposed approach deliberately avoids the use of Lyapunov-Krasovskii functionals, offering a more practical and computationally efficient alternative. Experimental results confirm that the proposed MR damper model outperforms traditional Lyapunov-Krasovskii-based methods. Additionally, two simulated road profiles are used to evaluate the suspension system’s behavior, further demonstrating the effectiveness of the proposed control strategy. Full article

With the rapid development of smart grid technologies, communication networks have become the core infrastructure supporting control and energy optimization in microgrids. However, the excessive reliance of microgrid control on communication networks faces dual challenges: On one hand, the high-frequency information exchange under traditional periodic communication patterns causes severe waste of network resources; on the other hand, cyberattacks may cause information loss, abnormal delays, or data tampering, which can ultimately lead to system instability. To address these challenges, this paper investigates the secure dynamic integral event-triggered stabilization of photovoltaic microgrids under multimodal deception attacks. To address the communication resource constraints in photovoltaic (PV) microgrid systems, a dynamic integral-event-triggered scheme (DIETS) is proposed. This scheme employs average processing of historical state data to filter out redundant triggering events caused by noise or disturbances. Simultaneously, a time-varying triggering threshold function is designed by integrating real-time system states and historical information trends, enabling adaptive adjustment of dynamic triggering thresholds. In terms of cybersecurity, a secure control strategy against multi-modal deception attacks is incorporated to enhance system resilience. Subsequently, through the Lyapunov–Krasovskii functional and Bessel–Legendre inequality, collaborative design conditions for the controller gain and triggering matrix are formed as symmetric linear matrix inequalities to ensure system stability. The simulation results demonstrate that DIETS recorded only 99 triggering events, achieving a 55.2% reduction compared to the normal event-triggered scheme (ETS) and a 52.6% decrease relative to dynamic ETS, verifying the outstanding communication effectiveness of DIETS. Full article

This study investigates the global asymptotic stability of hybrid bidirectional associative memory (BAM) complex-valued neural networks (CVNNs) with time-varying delays and uncertain parameters, where the system matrices are assumed to be symmetric. By constructing an appropriate Lyapunov–Krasovskii functional (LKF), new sufficient conditions are derived to guarantee the existence and uniqueness of equilibrium points, as well as to establish the global asymptotic stability of the proposed symmetric hybrid BAM CVNNs. The validity and effectiveness of the theoretical results are further demonstrated through detailed numerical examples. Full article

In this paper, the fixed-time control for high-order nonlinear multi-agent systems under unknown stochastic time delay is investigated via an event-triggered approach. First of all, RBF neural networks are utilized to approximate the system’s uncertain nonlinearities. After that, an event-triggered scheme, which is designed with a relative threshold for more flexible control, is proposed to alleviate the communication burden. In consideration of the unknown stochastic time delay in the inter-communication among high-order nonlinear multi-agent systems, the Lyapunov–Krasovskii functional (LKF) is used to construct the system’s Lyapunov function, specifically targeting the adverse effects caused by time delay. Further, the fixed-time stability theory is employed to ensure that the convergence time remains independent of the initial values. Finally, the proposed control strategy is validated through numerical simulations. Full article

This paper addresses fault estimation in discrete-time semi-Markov jump neural networks (s-MJNNs) under the Round-Robin protocol and proposes an innovative extended state observer-based approach. Unlike studies considering only constant transition rates, this work investigates s-MJNNs with time-varying transition probabilities, which more closely reflect practical situations. By incorporating actuator and sensor faults as augmented state variables, an extended state observer is proposed to estimate system states and faults simultaneously. To alleviate network congestion and optimize communication resources, the Round-Robin protocol is adopted to schedule data transmission efficiently. By constructing a Lyapunov–Krasovskii functional and applying the discrete Wirtinger inequality, sufficient conditions are derived to ensure the mean square exponential stability and dissipative performance of the system. The observer gain parameters are computed using the linear matrix inequality (LMI) method. Numerical simulations validate the effectiveness and performance of the proposed fault estimation method. Full article

This paper takes as its starting point the distributed parameter models for both torsional and axial vibrations of the oilwell drillstring. While integrating several accepted features, the considered models are deduced following the Hamilton variational principle in the distributed parameter case. Then, these models are completed in order to take into account the elastic strain in driving signal transmission to the drillstring motions—rotational and axial (vertical). Stability and stabilization are tackled within the framework of the energy type Lyapunov functionals. From such “weak” Lyapunov functionals, only non-asymptotic Lyapunov stability can be obtained; therefore, asymptotic stability follows from the application of the Barbashin–Krasovskii–LaSalle invariance principle. This use of the invariance principle is carried out by associating a system of coupled delay differential and difference equations, recognized to be of neutral type. For this system of neutral type, the corresponding difference operator is strongly stable; hence, the Barbashin–Krasovskii–LaSalle principle can be applied. Note that this strong stability of the difference operator has been ensured by the aforementioned model completion with the elastic strain induced by the driving signals. Full article

This paper presents a novel Proportional Damping Injection (P + d) control scheme that incorporates a damping regulation strategy and an adaptive method for networked telerobotic systems. Unlike the traditional P + d controller with a fixed damping coefficient, the proposed approach includes a dynamic damping adjuster, designed based on position error, to enhance the position tracking speed and improve the system robustness. To address uncertainties in dynamic models and external forces, Radial Basis Function (RBF) neural networks and an adaptive strategy are employed for dynamic estimation. The closed-loop stability of the teleoperation system was rigorously established using the Lyapunov–Krasovskii method, and the relationship between the controller gains and communication delay boundaries was explicitly derived. Finally, simulations and experimental results validated the system’s stability and effectiveness, demonstrating the advantages of the proposed controller. Full article

The present research investigates the global asymptotic stability of bidirectional associative memory (BAM) neural networks using distinct sufficient conditions. The primary objective of this study is to establish new generalized criteria for the global asymptotic robust stability of time-delayed BAM neural networks at the equilibrium point, utilizing the Frobenius norm and the positive symmetrical approach. The new sufficient conditions are derived with the help of the Lyapunov–Krasovskii functional and the Frobenius norm, which are important in deep learning for a variety of reasons. The derived conditions are not influenced by the system parameter delays of the BAM neural network. Finally, a numerical example is provided to demonstrate the effectiveness of the proposed conclusions regarding network parameters. Full article

This paper focuses on a class of fractional-order systems with state delays and studies the design problem of the finite-time bounded tracking controller. The error system method in preview control theory is first used. By taking fractional-order derivatives of the state equations and error signals, a fractional-order error system is constructed. This transforms the tracking problem of the original system into an input–output finite=time stability problem of the error system. Based on the output equation of the original system and the error signal, an output equation for the error system is constructed, and a memory-based output feedback controller is designed by means of this equation. Using the input–output finite-time stability theory and linear matrix inequality (LMI) techniques, the output feedback gain matrix of the error system is derived by constructing a fractional-order Lyapunov–Krasovskii function. Then, a fractional-order integral of the input to the error system is performed to derive a finite-time bounded tracking controller for the original system. Finally, numerical simulations demonstrate the effectiveness of the proposed method. Full article