Search Results (125)

This study focuses on the stability of time-delay load frequency control (LFC) systems. Based on the Lyapunov–Krasovskii (L–K) functional method, a stability criterion with less conservatism and lower computational complexity is proposed. Unlike recent methods that decrease conservatism through enhancing the complexity of L–K functional, only the double integral is augmented in this paper. To estimate the L–K functional derivatives more precisely, an improved matrix-separation-based inequality is proposed, which introduces some delay-derivative-dependent matrices rather than the high-dimensional free matrices. By applying the augmented L–K functional and the improved matrix-separation-based inequality, the stability criterion is established. Case analysis demonstrates that the new stability criterion has less conservatism and lower computational complexity, thereby validating the correctness of the method presented. Full article

Coordinated cyber attacks tamper with measurement data to disrupt the situational awareness of active distribution systems. Various sensors report measurements asynchronously at different rates, which introduces challenges during state estimation. In addition, this forces cyber intruders to exert greater effort to compromise multiple communication channels and launch coordinated attacks. Therefore, multi-channel and asynchronous measurements could be harnessed to develop more secure cyber defense strategies. In this paper, a prediction-correction-based multi-rate observer is designed to exploit the value of asynchronous measurements for the detection of coordinated false data injection (FDI) attacks. First, a time-function-dependent prediction-correction strategy is proposed to adjust the sampling interval for each sensor’s measurement. Then, an observer is designed based on the trade-off between estimation error and the optimal period of the most recent sampling instant, with the convergence of estimation error with the maximum permitted sampling interval. Moreover, the conditions for exponential stability are developed using the Lyapunov–Krasovskii functional technique. Next, a coordinated FDI attack detection strategy is developed based on the dual nonlinear minimization problem. The proposed attack detection and secure state estimation strategies are tested on the IEEE 13-node system. Simulation results show that these schemes are effective in enhancing attack detection based on asynchronous measurements or compromised data. Full article

Fixed-time coordination is critical for networked unmanned aerial vehicle (UAV) systems to accomplish time-sensitive missions such as rapid target encirclement, cooperative search, and emergency response. However, dynamic topology variations, caused by mission reassignment, obstacle avoidance, or communication disruptions, along with model uncertainties and external disturbances, present significant challenges to robust and timely coordination. To address these issues, this paper investigates the fixed-time bipartite containment tracking control problem of uncertain multi-UAV systems under switching communication topologies. A neuroadaptive robust containment tracking controller is developed to guarantee that all follower UAVs converge within a fixed time to the region spanned by multiple dynamic leaders, regardless of initial conditions. To handle unknown nonlinear dynamics, a neuroadaptive estimator is constructed using online parameter adaptation. A topology-dependent multiple Lyapunov function framework is employed to rigorously establish fixed-time convergence under switching topologies. Moreover, an explicit upper bound on the convergence time is analytically derived as a function of system parameters and dwell time constraints. Comparative analysis demonstrates that the proposed method reduces conservativeness in convergence time estimation and enhances robustness against frequent topology changes. Simulation results are provided to validate the effectiveness and advantages of the proposed control scheme. Full article

This paper proposes a finite-time adaptive observer with online disturbance learning for time-varying disturbed systems. By integrating parameter-dependent Lyapunov functions and slack matrix techniques, the method eliminates conservative static disturbance bounds required in prior work while guaranteeing fixed-time convergence. The proposed approach features a non-diagonal gain structure that provides superior noise rejection capabilities, demonstrating 41% better performance under measurement noise compared to conventional methods. A power systems case study demonstrates significantly improved performance, including 62% faster convergence and 63% lower steady-state error. These results are validated through LMI-based synthesis and adaptive disturbance estimation. Implementation analysis confirms the method’s feasibility for real-time systems with practical computational requirements. Full article

This paper addresses the problem of observer-based control (OBC) for nonlinear systems with time delay (TD). A novel hybrid modeling framework for nonlinear TD systems is first introduced by synergistically combining TD Takagi–Sugeno (TDTS) fuzzy and Lipschitz approaches. The proposed methodology broadens the range of representable systems by enabling Lipschitz nonlinearities to fulfill dual functions: they may describe essential dynamic behaviors of the system or represent aggregated uncertainties, depending on the specific application. The proposed TDTS–Lipschitz (TDTSL) model class features measurable premise variables while accommodating Lipschitz nonlinearities that may depend on unmeasurable system states. Then, through the construction of an appropriate Lyapunov–Krasovskii (L-K) functional, we derive sufficient conditions to ensure exponential stability of the augmented closed-loop model. Subsequently, through a decoupling methodology, these stability conditions are reformulated as a set of linear matrix inequalities (LMIs). Finally, the proposed OBC design is validated through application to a continuous stirred tank reactor (CSTR) with lumped uncertainties. Full article

This paper investigates the synchronization problem of singularly perturbed complex networks with time delays, in which a novel event-triggered delayed impulsive control strategy is developed. To conserve limited communication bandwidth, a dynamic event-triggered mechanism is proposed based on a Lyapunov function construction, while incorporating both delay and singular perturbation parameter $\mathit{\epsilon }$ information to avoid ill conditioning. Unlike conventional triggering approaches, the proposed mechanism only requires the Lyapunov function to decrease at impulsive instants, thereby relaxing the constraint on the energy function. Moreover, an impulse-assisted variable $\mathit{\theta }$ is introduced to adjust the event-triggered threshold according to the intensity of impulsive control, which reduces the triggering frequency while ensuring synchronization. By employing stability theory and the singular perturbation method, a singular perturbation parameter $\mathit{\epsilon }$-dependent Lyapunov function is constructed to derive sufficient synchronization conditions and provide the design of the impulsive gain matrix. Finally, a numerical example is presented to demonstrate the effectiveness of the proposed approach. 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

This study aims to develop an event-triggered control strategy of grid-connected inverters, based on the linear parameter-varying (LPV) modeling approach. Regarding the changes in grid voltage, filter capacitance and inductance, and random electromagnetic interference, a stochastic LPV model for three-phase two-level inverters is established. To reduce computation burden, an event trigger with a continuous-time form is adopted to derive the state feedback controller for the LPV plant. Unlike the existing common approach to dealing with event-triggered mechanisms, a predesignated event-triggering threshold is used to determine the triggering instant of the event condition. Using parameter-dependent Lyapunov functions, sufficient conditions reliant on parameters are introduced. Based on the derived conditions, the corresponding event-triggered controllers are engineered to ensure uniform ultimate bounded stability for the resulting event-triggered LPV inverter system subject to exogenous disturbance. The simulation results are presented to confirm the efficacy of the proposed methods. Full article

This paper establishes the global existence of solutions to a chemotaxis system with indirect signal production in the whole two-dimensional space. This system exhibits a mass threshold phenomenon governed by a critical mass $m_c=8\pi \delta$, where $\delta$ represents the decay rate of the static individuals. When the total initial mass $m={\int }_{R^2}{u}_{0}dx<m_c$, all solutions exist globally and remain bounded. In the critical case of $m=m_c$, the global existence or finite-time blow-up may occur depending on the initial conditions. The critical mass obtained in the whole space coincides with that previously derived in radially symmetric bounded domains. A key novelty lies in extending the analysis to the full plane, where the absence of compactness is overcome by constructing a suitable Lyapunov functional and employing refined Trudinger–Moser-type inequalities. Full article

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 paper addresses the trajectory tracking control problem of underactuated ships in ocean engineering, which faces the dual challenges of tracking error time–performance regulation and robustness design due to the system’s underactuated characteristics, model uncertainties, and external disturbances. Aiming to address the issues of traditional finite-time control (convergence time dependent on initial states) and fixed-time control (control chattering and parameter conservativeness), this paper proposes a predefined-time adaptive control framework that integrates an event-triggered mechanism and neural networks. By constructing a Lyapunov function with time-varying weights and designing non-periodic dynamically updated dual triggering conditions, the convergence process of tracking errors is strictly constrained within a user-prespecified time window without relying on initial states or introducing non-smooth terms. An adaptive approximator based on radial basis function neural networks (RBF-NNs) is employed to compensate for unknown nonlinear dynamics and external disturbances in real-time. Combined with the event-triggered mechanism, it dynamically adjusts the update instances of control inputs, ensuring prespecified tracking accuracy while significantly reducing computational resource consumption. Theoretical analysis shows that all signals in the closed-loop system are uniformly ultimately bounded, tracking errors converge to a neighborhood of the origin within the predefined-time, and the update frequency of control inputs exhibits a linear relationship with the predefined-time, avoiding Zeno behavior. Simulation results verify the effectiveness of the proposed method in complex marine environments. Compared with traditional control strategies, it achieves more accurate trajectory tracking, faster response, and a substantial reduction in control input update frequency, providing an efficient solution for the engineering implementation of embedded control systems in unmanned ships. 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 aim of this paper is to study a nonlinear system of impulsive fractional differential equations and Caputo fractional derivatives with respect to another function (CFF). The main characteristics of these fractional derivatives are two-fold: first, the lower limit of CFF equals the impulsive time of the considered interval; second, the applied function in CFF is changeable at each interval without impulses. An auxiliary system of two linear scalar impulsive fractional differential equations with CFF is considered, and strict stability in a couple is defined. The behavior of its solutions is illustrated with several examples. Also, we use appropriate Lyapunov functions to obtain sufficient conditions for the strict stability of the studied system. These sufficient conditions depend significantly on the type of impulsive function. Full article

This paper is concerned with the event-based synchronization control for chaotic neural networks by using a refined discontinuous trigger scheme. To get rid of the Zeno phenomenon and decrease the triggering times, a refined discontinuous event-trigger (RDET) scheme is employed by designing a new threshold function. The proposed threshold function consists of two parts, i.e., quadratic term and exponential decay term, which makes the derivative of the Lyapunov function possibly not less than zero. On this basis, an important lemma is derived, which contributes to performing a stability analysis. Then, the corresponding closed-loop system model is established in the presence of a trigger scheme. Then, a time-dependent Lyapunov function (TLF) method is established based on the features of an RDET. In view of inequality estimation techniques and stability theory, some synchronization criteria are developed to guarantee that the synchronization of chaotic neural networks can be realized by using the novel discontinuous event-trigger schemes. Finally, a Hopfield neural network is displayed to demonstrate the advantages and effectiveness of the derived results. Full article

The conventional model predictive control (MPC) for dual active bridge (DAB) converters relies heavily on the accuracy of system parameters. To address this issue, this paper proposes a model predictive voltage control strategy for DAB based on a super-twisting integral sliding mode observer (STISMO). By reducing the system parameter sensitivity and incorporating a disturbance compensation mechanism, the proposed strategy enhances robustness while preserving the dynamic response advantages of MPC. Firstly, an ultra-local model of the DAB converter is constructed to reduce dependence on system parameters. Secondly, a STISMO with an integral sliding surface is designed to achieve rapid and accurate estimation of unmodeled dynamics and disturbances in the ultra-local model, along with real-time compensation. The finite-time convergence of observation errors is rigorously proven via Lyapunov stability theory. Subsequently, a two-step prediction model combined with rolling optimization of the cost function is employed to solve for the optimal phase-shift angle, which is then applied in the next control cycle. Finally, experimental validation was conducted through a DAB converter test platform, demonstrating the effectiveness of the proposed method in enhancing system robustness and dynamic performance. Full article