Asymptotic Stability Research Articles

Transmission Power Control in Multi-Hop Communications of THz Communication Using a Potential Game Approach

Terahertz (THz)-band communications are a possible candidate for fast communication. Transmission power needs to be optimised in order to satisfy the requirements of such a network of nodes. Multi-hop communication can be used in THz communications to add relays when obstacles or other interference is evident. This paper investigates the domain of multi-hop THz communications, acknowledging the possibility of interference from other devices affecting the communication process and utilises interference cancellation. It formulates the Transmission Power Control (TPC) problem within a game-theoretic framework, specifically as a potential game, with the assurance of convergence to a Nash equilibrium in the majority of scenarios. Bounds of the Price of Anarchy (PoA) and the Price of Stability (PoS) are provided, given assumed factors. Also, asymptotic Lyapunov stability is shown. The findings from simulations conducted to assess the effectiveness of this approach are then discussed. In particular, the final utilities when utilising interference cancellation show an improvement compared to without-interference cancellation between 19.30 and 67.30% for five simulated players.

Collaborative Design of Observer and Controller for Singular Systems With Transmission Delay Based on Dynamic Event‐Triggered

ABSTRACTThis article investigates the dynamic event‐triggered with communication delay fault estimation and fault‐tolerant control problem of singular systems in network environments under system faults and external disturbances. By considering both the current time and transmission delay output error, a fault diagnosis observer is constructed to estimate the system state and faults simultaneously based on dynamic event‐triggered sampling. On the basis of estimating the system state and fault signals, a fault‐tolerant controller is proposed to compensate for the impact of faults on the system and maintain its performance. Through the collaborative design of observers, controllers, and event‐triggering schemes, the required performance of the faulty system is ensured while reducing the consumption of communication resources. In addition by constructing a new enhanced Lyapunov functional and utilizing linear matrix inequalities and Lyapunov stability theory, the conditions for asymptotic stability of the system are less conservative and easily obtained. Finally, the effectiveness of the proposed method was verified through simulation results of two examples.

Learning and Uncertainty Compensation in Robotic Motion Systems using Li-Slotine Adaptive Tracking and Intelligent Adaptive Control

This paper examines adaptive control strategies for stabilizing robots, focusing on Li-Slotine adaptive control and Iterative Learning Control (ILC). Both methods handle uncertainties through learning and compensation, ensuring stability and precision. Li-Slotine control, based on Lyapunov theory, dynamically adjusts parameters for asymptotic stability in uncertain systems. ILC improves performance in repetitive tasks by refining control inputs using tracking errors, making it suitable for robotics and manufacturing. While Li-Slotine excels in real-time adaptation and robustness to disturbances, its computational demands challenge high-degree-of-freedom systems. ILC enhances accuracy through iterative learning but is sensitive to noise and requires careful tuning. MATLAB simulations and experimental results demonstrate the effectiveness of both approaches. Future work will explore hybrid frameworks that combine the adaptability of Li-Slotine with the data-driven refinement of ILC to provide robust solutions for complex, dynamic robotic systems.

Observer‐Based Preview Sliding Mode Tracking Control of Discrete‐Time T‐S Fuzzy System With Input Saturation

ABSTRACTThis paper investigates the observer‐based sliding mode tracking problem of the discrete‐time fuzzy system with input saturation via a previewable information approach. Firstly, an augmented system (AS) containing discrete‐time integrators and previewable reference signals is established for the discrete‐time T‐S fuzzy system based on a previewable length. Secondly, a sliding surface and a sliding preview controller are given, which can guarantee the asymptotic stability of the quasi‐sliding motion and the reachability of the sliding region. Finally, a simulation example is given to demonstrate the effectiveness of the proposed control law.

Robust adaptive motion control for cable-driven aerial manipulators with input saturation

This article explores robust adaptive motion control for a cable-driven aerial manipulator in the presence of input saturation. The investigation begins by considering the physical attributes of the aerial manipulator and establishing a kinematic and dynamic model of the system with lumped disturbances. Following this, a new control law is formulated using the parameter adaptive technique, where the adaptive law offers continuous estimation of the virtual parameters. Moreover, a Gaussian error function is utilized to tackle the challenge of input saturation. The stability of the controller proposed is confirmed using Lyapunov theory. Ultimately, numerical simulations and experimental comparisons are conducted to validate the accuracy and effectiveness of the proposed control strategy.

Feedback stability analysis via dissipativity with dynamic supply rates

We propose a general notion of dissipativity with dynamic supply rates for nonlinear systems. This extends classical dissipativity with static supply rates and dynamic supply rates of miscellaneous quadratic forms. The main results of this paper concern Lyapunov and asymptotic stability analysis for nonlinear feedback dissipative systems that are characterised by dissipation inequalities with respect to compatible dynamic supply rates but involving possibly different and independent auxiliary systems. Importantly, dissipativity conditions guaranteeing stability of the state of the feedback systems, without concerns on the stability of the state of the auxiliary systems, are provided. The key results also specialise to a simple coupling test for the interconnection of two nonlinear systems described by dynamic (Ψ,Π,Υ,Ω)-dissipativity, and are shown to recover several existing results in the literature, including small-gain, passivity indices, static (Q,S,R)-dissipativity, dissipativity with terminal costs, etc. Comparison with the input–output approach to feedback stability analysis based on integral quadratic constraints is also made.

The Existence and Stability of a Periodic Solution of a Nonautonomous Delayed Reaction–Diffusion Predator–Prey Model

In this study, we research a nonautonomous, three-species, delayed reaction–diffusion predator–prey model (RDPPM). Firstly, we derive sufficient conditions to guarantee the existence of a strictly positive, spatially homogeneous periodic solution (SHPS) for the delayed, nonautonomous RDPPM. These conditions are obtained using the comparison theorem for delayed differential equations and the fixed point theorem. Secondly, we present sufficient conditions to ensure the global asymptotic stability of the SHPS for the delayed, nonautonomous RDPPM. These conditions are established through the application of the upper and lower solution method (UALSM) for delayed parabolic partial differential equations (PDEs), along with Lyapunov stability theory. Finally, to demonstrate the practical application of our results, we numerically validate the proposed conditions using a 2-periodic, delayed, nonautonomous RDPPM.

Robust adaptive integral sliding mode control of a half-bridge bidirectional DC-DC converter

A novel approach to improving the dynamic response of a half-bridge bidirectional DC-DC converter is presented in this paper, particularly in the face of disturbances from internal or external sources. These converters, which are integral to the operation of DC microgrids, are responsible for stepping up or stepping down voltage as required. To optimize the converter's performance under varying conditions, we propose an adaptive integral sliding mode controller (AISMC) enhanced by particle swarm optimization (PSO). The proposed controller leverages the strengths of both super-twisting sliding mode control (STSMC) and adaptive control, providing a robust and responsive solution to the challenges posed by the converter's nonlinear dynamics. The system's stability is rigorously ensured through the application of Lyapunov stability criteria, which underpin the enhanced performance of the controller. Simulations conducted in the MATLAB/Simulink environment demonstrate that the AISMC-PSO outperforms conventional control strategies, offering superior stability, robustness, and precision. The results clearly indicate that the proposed approach minimizes errors and enhances the overall efficiency and reliability of the bidirectional half-bridge DC-DC converter, making it a highly effective solution for DC microgrid applications.

Stabilization of a coupled bridge system with past history and gurtin-pipkin’s heat conduction

The asymptotic stability of the vertical vibrations of a suspension bridge and the main cables from which the bridge is suspended by the cables is investigated. The history of the materials of the bridge and the effect of heat governed by Gurtin-Pipkin’s thermal law on main cables are taking into consideration. We show that the damping induced by the infinite memory of the bridge and the heat on the main cables are strong enough to stabilize the system.

Consensus of second-order multi-agent systems based on PIDD-like control protocol with time delay

This paper concentrates on investigating the consensus for general second-order linear multiagent systems subjected to time-varying delay. Initially, a novel PIDD-like consensus control protocol with time-varying delay is designed, which includes information on position and its integration, as well as velocity and its differentiation. Subsequently, based upon model transformation, the consensus problem is transformed into the asymptotic stability of the error system. Through constructing of a novel augmented vector Lyapunov-Krasovskii functional, including delay-product terms and multiple integral terms, and then by adopting auxiliary-function-based integral inequalities and the delay-dependent-matrix-based reciprocally convex inequality to address the derivative of the constructed functional, the less conservative consensus conditions for multi-agent systems are obtained. Additionally, numerical simulations are given to demonstrate that the presented consensus conditions not only ensure the consensus of position and velocity states but also exhibit better dynamic performance.

Dynamic Models of the Infection of Lassa Fever Epidemics Incorporating Detected and Undetected Class

In the scope of this research endeavor, we embarked on the development of a dynamic model, intricately designed to scrutinize the intricate dynamics of Lassa fever transmission, encompassing both detected and undetected cases. Our central objective revolved around the meticulous examination of how a vaccine could exert its influence on the transmission dynamics of Lassa disease. The study encompassed an exhaustive exploration of the model's equilibrium states, diligently scrutinizing both disease-free and endemic equilibria. To shed light on the potential for disease spread, we calculated the pivotal epidemiological parameter, the basic reproduction number, employing the rigorous next-generation matrix methodology. Subsequently, we delved into a comprehensive stability analysis, encompassing both local and global stability assessments. The Routh-Hurwitz conditions were harnessed for local stability analysis, while the Castillo-Chavez criterion was leveraged for global stability analysis. In our quest for a profound understanding, we ventured into analytical techniques to derive exact solutions for the model, coupled with numerical computations facilitated by the versatile MATHEMATICA software. The culmination of our endeavors unveiled a compelling insight: the disease-free equilibrium attains local asymptotic stability if and only if the basic reproduction number assumes a value below unity; conversely, it stands as unstable when this threshold is exceeded. In essence, this implies that the complete eradication of Lassa fever is within reach when the secondary infection rate remains constrained below a critical threshold.

Global Asymptotic Stabilization of the Double Integrator System With Output Saturation

Global Asymptotic Stabilization of the Double Integrator System With Output Saturation

Reinforcement learning-based near-optimal control for discrete time-delay singularly perturbed systems with unmeasurable states

This brief proposes a novel reinforcement learning-based composite near-optimal output feedback (OPFB) control method for discrete time-delay singularly perturbed systems (SPSs) with unknown dynamics and unmeasured system states. Firstly, an optimal control problem of the full-order time-delay SPS is formulated. The singular perturbation techniques are used to obtain the reduced-order subsystems and equivalent subproblems. Then, a state reconstruction method is presented to represent the state in terms of available input and output data. In addition, a reinforcement learning (RL) algorithm based on input and output data is developed. Theoretical analyses are discussed on the convergence of the proposed algorithm and the asymptotical stability of the system under the composite controller. Finally, numerical simulation results illustrate the effectiveness of the proposed approach.

Asymptotic Stability of the Magnetohydrodynamic Flows with Temperature-Dependent Transport Coefficients

The objective of this paper is to analyze the asymptotic stability of global strong solutions to the boundary value problem of the compressible magnetohydrodynamic (MHD) equations for the ideal polytropic gas in which the viscosity λ and heat conductivity κ depend on temperature, i.e., λ=θα and κ=θβ with α,β∈[0,+∞). Both the global-in-time existence and uniqueness of strong solutions are obtained under certain assumptions on the parameter α and initial data. Moreover, based on accurate uniform-in-time estimates, we show that the global large solutions decay exponentially in time to the equilibrium states. Compared with the existing results, the initial data could be large if α is small and the growth exponent β can be arbitrarily large.

Adaptive nonsingular fast terminal sliding mode control based finite-time disturbance observer for a quadrotor system

The present paper introduces an adaptive non-singular fast terminal sliding mode control (ANFTSMC) combined with a finite-time disturbance observer (FTDO), designed to address the trajectory tracking problem of a quadrotor system under the influence of external perturbations, model uncertainties, and mass variations. First, the nonlinear simplified dynamic model of the quadrotor is derived using the Newton-Euler approach. Then, an ANFTSMC method is employed to formulate control strategies for both the inner and outer loops of the quadrotor system. Backpropagation laws are used to tune the gains of the discontinuous reaching law. In addition, the paper integrates a finite-time disturbance observer with the proposed approach to estimate and counteract external disturbances. The closed-loop control stability is verified using Lyapunov theory. To assess the effectiveness of the suggested method, multiple flight tests are proposed using numerical simulations carried out in MATLAB/SIMULINK software. Simulation results are compared with an adaptive nonsingular fast terminal sliding mode controller (ANFTSMC). Numerical simulations demonstrate the superior performance of the suggested approach in terms of convergence time, tracking precision, and ability to reject external disturbances and uncertainties.

Quaternion-Based Robust Sliding-Mode Controller for Quadrotor Operation Under Wind Disturbance

This paper presents a quaternion-based robust sliding-mode controller for quadrotors operating under significant wind disturbances. The proposed control method improves the reliability and efficiency of quadrotor control by eliminating the singularity problem inherent in the Euler angle method. The quadrotor dynamics and wind environment are modeled, and dynamic analysis is performed via numerical simulation. A realistic wind model is used, similar to a combination of deterministic and statistical models. The Lyapunov stability theory is utilized to prove the convergence and stability of the proposed control system. The simulation results demonstrate that the quaternion-based controller enables the quadrotor to follow the desired path and remain stable, even under external wind disturbances. Specifically, both position and attitude converge to the desired values within 10 s, demonstrating stable performance despite the challenging wind disturbances in both scenarios. Scenario 1 features turbulence with an average wind speed of 12 m/s and changing wind directions, while Scenario 2 models an environment with wind speeds that change abruptly and discretely over time, coupled with temporal variations in wind direction. Additionally, a comparative analysis with the conventional PD controller highlights the superior performance of the proposed RSMC controller in terms of trajectory tracking, stability, and energy efficiency. The rotor speeds remain within a reasonable and hardware-feasible range, ensuring practical applicability.

Stability of Second‐Order Discrete Linear Switching Systems: The Case of All Subsystems With Eigenvalue Modulus >1$$ >1 $$ Under State‐Dependent Switching

ABSTRACTThis article investigates the asymptotic stability of discrete‐time switching systems in which the modulus of all subsystem eigenvalues are greater than one. The study begins by constructing an energy function with practical physical meaning for each discrete‐time subsystem. Specifically, a standard linear discrete system is derived by discretizing a single‐degree‐of‐freedom vibratory model, with its energy function defined as the sum of the model's kinetic and potential energies. An invertible transform is then applied to convert a general linear discrete system into standard form, enabling the construction of a general energy function based on that of a standard one. Since the construction of subsystem energy functions depends on the choice of invertible transform, which is not unique, the resulting energy functions for different subsystems under distinct transforms cannot be directly compared. To address this issue, an intermediate subsystem is introduced to define a relative energy ratio function between two subsystems. Using this relative energy ratio function, a state‐dependent switching rule is developed to maximize energy loss within a switch circuit, thereby achieving rapid asymptotic stability of the discrete switching system. Finally, numerical examples are provided to validate the effectiveness of the proposed method.

Global dynamics on a delayed double-strain influenza model with vaccination and cross-immunity

In this paper, a delayed double-strain influenza model with vaccination and cross-immunity is proposed to explore the effect of coinfection of double-strain on disease spread. First, the nonnegativity and ultimate boundedness of solution are proved. Second, the basic reproduction numbers of strains 1, 2, and the whole model are defined respectively, by which criteria on the local and global asymptotic stability of (disease-free, dominant) equilibria are established. The uniform persistence of (strains 1, 2 coexistent) disease is obtained as well. Finally, the validity of the theoretical results is demonstrated by numerical simulations. We find that neglecting cross-immunity and vaccination would misestimate the size of influenza outbreaks. Cross-type multivalent vaccines will be the main direction for effective control measure for influenza.

Secure Control of Networked Control Systems Under Replay Attacks: A Switching‐Like Approach

ABSTRACTThis paper focuses on the secure control design of networked control systems (NCSs) under replay attacks. Mitigating replay attacks is a challenging task since the statistical similarity between replayed signals and real observations makes them difficult to distinguish. Given the persistence of potential attackers and the probability of individual attack failures, a novel switching‐based replay attack model is introduced. By employing this replay attack model, NCSs vulnerable to replay attacks can be transformed into a class of switching‐like systems. Within the framework of the average dwell time switching strategy and multiple Lyapunov stability theory, sufficient conditions for the mean‐square exponential stability of the underlying system are presented. Compared with the existing control schemes using the delay‐based replay attack model, the proposed secure control method effectively reduces the impact of replay attacks on the control performance. The effectiveness of the proposed approach is validated through simulation experiments carried out on two practical systems.

Synchronization control of complex networks with bit-rate constraint via dynamic event-triggered strategy

A sampling-based dynamic event-triggered strategy is proposed for the synchronization control of continuous complex networks with uncertainties and delayed coupling, taking into account a bit-rate constraint in node communication. First, a synchronization error system is established by integrating the dynamics of complex networks with those of an isolated node. To conserve limited network bandwidth resources, a sampling-based dynamic event-triggered strategy is designed. By introducing bit-rate constraints to characterize the communication limitations of the system, the available bit rate for each node is allocated using an average allocation protocol. Subsequently, a binary encoding–decoding method is developed to transmit the triggered data, and the decoded signals are utilized to design the controller. Then, a closed-loop synchronization error system is derived. Given that coding errors are inevitable, an exponentially ultimately bounded definition of synchronization error is introduced. The coupling and transmission delays within the system are addressed by constructing Lyapunov-Krasovskii (L-K) functions. Utilizing Lyapunov stability theory and other technical theorems, the exponentially ultimately bounded condition for the closed-loop system is obtained. Based on this condition, the co-design of the controller gain and triggering parameters is achieved. In addition, the explicit relationship between synchronization error and bit rate is presented. Finally, the effectiveness of the proposed method is validated through three numerical examples.