Asymptotic Stability Research Articles

Synchronization Analysis of Coupled Fitzhugh Nagumo Dynamical Systems

Synchronization plays a pivotal role in understanding various natural events. Understanding this concept with reference to a biologically inspired dynamical model of a neuron is also essential. It is basically a rhythm adjustment phenomenon and a consequence of the coupling between the individual units. In the present work, we aim to derive sufficient conditions for the synchronization of coupled Fitzhugh Nagumo Dynamics using Lyapunov stability analysis. In particular, a non-smooth Lyapunov function based upon the geodesic distance between respective states of coupled systems has been chosen as the Lyapunov function, and the concept of upper Dini-derivative has been utilized to calculate the derivative of the Lyapunov function along the error dynamics. The negative definiteness of the derivative of the Lyapunov function gives sufficient coupling gain for synchronization. The findings are verified on the Matlab simulation platform. The results should help to enhance the knowledge of neural dynamics.

On the Global Existence of Solution and Lyapunov Asymptotic Practical Stability for Nonlinear Impulsive Caputo Fractional Derivative via Comparison Principle

This paper examines the existence of maximal solution of the comparison differential system and also establishes sufficient conditions for the asymptotic practical stability of the trivial solution of a nonlinear impulsive Caputo fractional differential equations with fixed moments of impulse using the vector Lyapunov functions. First, it was discovered that the vector form of the Lyapunov function was majorized by the maximal solution of the comparison system. From the results obtained, it was also established that the main system is asymptotically practically stable in the sense of Lyapunov.

Robust Distributed Load Frequency Control for Multi-Area Power Systems with Photovoltaic and Battery Energy Storage System

The intermittent power generation of renewable energy sources (RESs) interrupts the balance between power generation and demand load due to the increased frequency fluctuation, which challenges the frequency stability analysis and control synthesis of power generation systems. This paper proposes a robust distributed load frequency control (DLFC) scheme for multi-area power systems. Firstly, a multi-area power system is constructed by integrating photovoltaic (PV) and battery energy storage systems (BESSs). Then, by employing the linear matrix inequality (LMI) technique, the sufficient condition capable of ensuring that the proposed controller satisfies H∞ robust performance in the sense of asymptotic stability is derived. Finally, testing is conducted on a four-area renewable power system, and results verify the strong robustness of the proposed controller against load disturbance and intermittence of RESs.

The impact of obesity on chronic diseases: type 2 diabetes, heart disease, and high blood pressure

Obesity is a risk factor for several chronic diseases, including type 2 diabetes, heart disease, and high blood pressure. Developing models of obesity and its complications allows for close monitoring of these epidemics, informing the creation of effective control strategies. This research focuses on presenting an endemic model of obesity and its health complications, taking into account, social factors and relationships among people in society. The term epidemic is related to the influence of the health lifestyle of obese people on healthy individuals. The transmission of obesity and its complications is through peer pressure to consume fast food and acquire bad eating habits from relatives and friends. So, in our model, the effect of these factors is expressed with parameters β i . We demonstrate theoretically the asymptotic local stability of disease-free equilibrium and the asymptotic local stability of endemic equilibrium, proving the existence and uniqueness of the solution to the obesity model and its complications. To confirm the model's theoretical results, we conduct numerical simulations to study the impact of variation in social factor parameters on the diseases studied.

Reinforcement learning-adaptive fault-tolerant IGC method for a class of aircraft with non-affine characteristics and multiple uncertainties

Abstract In this paper, a brand-new adaptive fault-tolerant non-affine integrated guidance and control method based on reinforcement learning is proposed for a class of skid-to-turn (STT) missile. Firstly, considering the non-affine characteristics of the missile, a new non-affine integrated guidance and control (NAIGC) design model is constructed. For the NAIGC system, an adaptive expansion integral system is introduced to address the issue of challenging control brought on by the non-affine form of the control signal. Subsequently, the hyperbolic tangent function and adaptive boundary estimation are utilised to lessen the jitter due to disturbances in the control system and the deviation caused by actuator failures while taking into account the uncertainty in the NAIGC system. Importantly, actor-critic is introduced into the control framework, where the actor network aims to deal with the multiple uncertainties of the subsystem and generate the control input based on the critic results. Eventually, not only is the stability of the NAIGC closed-loop system demonstrated using Lyapunov theory, but also the validity and superiority of the method are verified by numerical simulations.

Improved adaptive robust control of direct-drive pump-valve cooperative brake-by-wire unit with disturbance compensation

Abstract Aiming at the needs of high-level autonomous driving, a direct-drive pump-valve coordinated brake-by-wire unit was designed. To improve the response speed, control accuracy, and robustness of the brake-by-wire unit, an improved adaptive integral robust control method (AIRC-AD) based on a novel adaptive law and disturbance compensation was proposed. By integrating pressure tracking error information and overall parameter estimation error information, a novel parameter adaptive law with fast convergence speed was designed. A finite-time disturbance observer was designed to observe the overall system disturbance, improving the system’s anti-disturbance performance. Finally, the stability of the control method was proven using the Lyapunov stability proof method. The results show that under step target signals, sinusoidal target signals and triangular wave target signals, AIRC-AD has better response speed and control accuracy. In conditions such as increased permanent magnet temperature, increased coil resistance, or reduced flow area due to hydraulic pipeline blockage, AIRC-AD has better adaptability. The unit and the method can meet the demand for precise braking force control in high-level autonomous driving.

Observer-based resilient cooperative output regulation for nonlinear multiagent systems with time-varying parameters and DoS attacks

This paper aims to address the cooperative output regulation (COR) problem of nonlinear multiagent systems (MASs) with time-varying parameters under denial-of-service (DoS) attacks. First, to address the challenges of unavailable leader signals and non-differentiability issue caused by the DoS attacks, a class of first-order low-pass filters is employed to develop a novel distributed resilient observer, which accurately estimate the exosystem state with the existence of high-order derivatives. Then, by viewing the output of observer as the reference signal, a distributed resilient controller is designed for each follower to address the reference-tracking problem. By introducing a smooth function with positive integrable time-varying function, novel adaptive laws are developed and incorporated with the controller design to effectively compensate for the unknown time-varying parameters. By utilising Lyapunov stability theory, the asymptotic convergence of output regulation error can be ensured. Finally, simulation results are conducted to verify the validity of the designed method.

Research on Voltage Prediction Using LSTM Neural Networks and Dynamic Voltage Restorers Based on Novel Sliding Mode Variable Structure Control

To address the issue of uncertainty in the occurrence time of voltage sags in power grids, which affects power quality, a voltage state prediction method based on LSTM neural networks is proposed for predicting voltage states. For the problem of quickly and accurately compensating for voltage sags, a DVR system based on a new approach law of sliding mode variable structure control is proposed, which significantly reduces chattering, improves response speed, and enhances the robustness of the system. The stability of the system is proven based on Lyapunov stability theory. Simulation experiments are conducted to analyze the voltage state prediction effect based on the LSTM neural network and the compensation effect of the novel reaching law of sliding mode variable structure control under different levels of voltage sag, validating the effectiveness and correctness of the proposed solution.

AQUILA OPTIMIZED NONLINEAR CONTROL FOR DC-DC BOOST CONVERTER WITH CONSTANT POWER LOAD

Constant power loads (CPL) can be operated by tight-controlled power electronic converters, which have negative impedance and absorb continuous power. Constant power load creates instability in an open-loop system because of its negative incremental impedance. To tackle this problem, a discrete sliding-mode (AQO-DSM) nonlinear control technique has been proposed for a DC-DC boost converter fed CPL based on Aquila optimization. In this paper, the proposed AQO-DSM controllers provide the system stability during a steady state and maintain output voltage regardless of input voltage or CPL variations. In this case, the DSM controller of a DC-DC boost converter's characteristics are adjusted using the Aquila optimization method (AQO). The Lyapunov stability concept is utilized to assess the system's overall stability. Under various system operating conditions, an experimental study and simulation are carried out to validate the proposed controller. The existing methods, such as sliding mode controller (SMC), fuzzy-based SMC (F-SMC), and super twisting algorithm (STA)-based SMC strategies, are compared with a proposed plan to demonstrate the superiority of the proposed AQO-DSMC. Simulated and experimental results have shown that the AQO-DSMC achieves the fastest convergence, the smallest steady-state, settling time under loaded conditions, and consistent chatter reduction compared with all contrasted control methods.

Adaptive Robust Control of Nonlinear Constrained Stirred‐Tank Reactors via Self‐Organizing Fuzzy Neural Network

ABSTRACTThis paper presents an adaptive robust constraint controller for a continuous stirred tank reactor (CSTR) system based on a self‐organizing fuzzy neural network (SOFNN). Due to the high complexity of the chemical reactions, the CSTR system contains many strong nonlinearities and uncertainties. This is the first time to introduce the SOFNN into the adaptive controller design of the CSTR system, which improves the adaptability to dynamic system changes through the adjustment of the fuzzy network structure. Meanwhile, the time‐varying integral barrier Lyapunov functions (TVIBLFs) are employed to ensure the dimensionless reactant concentration and mixture temperature within a reasonable scope, which can improve the stability and safety of the CSTR system. Based on Lyapunov stability analysis, all the signals in a closed‐loop system are ultimately bounded. Simulation results substantiate the efficacy of the proposed control scheme.

Analysis of stochastic epidemic model with awareness decay and heterogeneous individuals on multi-weighted networks.

In the current study, we present a stochastic SAIS (unaware susceptible-aware susceptible-infectious-unaware susceptible) epidemic dynamic model on complex networks with multi-weights. The disease dynamic is influenced by random perturbations to the force of the infection rates, as well as awareness rates. To analyze the problem of extinction, we discuss both the stochastic asymptotic stability in the large and almost surely exponential stability of the trivial solution. Then, we get some sufficient conditions, which guarantee the stochastic persistence of infectious disease. Based on the Erdös-Réyni random graph, the numerical simulations are given. These not only validate our conclusions but also obtain else significative results. Both theoretical results and numerical simulations further reflect that improvement of risk awareness and reduction of decay in awareness are highly effective in preventing disease spread. And then, environmental noises play a significant role in disease transmission.

Intelligent sliding mode fault-tolerant control for aircraft engines with actuator dynamics and faults based on adaptive dynamic programming

Abstract The fault-tolerant control issue of aircraft engines with actuator dynamics and faults is investigated in this paper. By proposing a novel intelligent sliding mode fault-tolerant control (ISMFTC) method, which combines an adaptive dynamic programming (ADP) sliding surface with Grey Wolf Optimizer (GWO) for controller parameter optimisation, the goal is to achieve quality steady-state and dynamic performance in aircraft engines while maintaining strong fault-tolerance properties. Firstly, by considering not only actuator dynamics but also actuator faults, an uncertain nonlinear cascaded model of aircraft engines is developed according to characteristic of aircraft engines and their actuators. Secondly, an ADP-based sliding surface is proposed for considered aircraft engine uncertain nonlinear cascaded system. It can obtain a certain sense of optimised performance, and could be solved by ADP strategy off-line as well. Thirdly, fault-tolerant controller is obtained on the basis of sliding mode theory and adaptive fault estimation law, namely, ADP-based ISMFTC controller. Meanwhile, GWO is integrated into the investigation of ADP-based ISMFTC controller, optimised designable control parameters are obtained subsequently. Besides, robustness analysis is elaborated according to Lyapunov theory, fault estimation error is bounded and states of closed-loop system are uniformly ultimately bounded. Simulation on a twin-shaft turbofan aircraft engine, indicates the effect of proposed ADP-based ISMFTC method.

Comparative analysis of two novel chaotic systems, and validation of hybrid function projective and complete synchronization using active-adaptive control

Abstract This study investigates the nonlinear characteristics of two novel 3D-chaotic models using phase portraits, bifurcation diagrams, Lyapunov exponents, time series analysis, and Poincaré maps. Here, we have examined hybrid-function projective and complete synchronization schemes via adaptive and active control methods. Moreover, the performance of hybrid-function projective synchronization, utilizing sine, cosine, and exponential terms, is compared to complete synchronization through two control strategies. Our designed controllers ensure asymptotic global chaotic synchronization based on Lyapunov stability principles. We have also compared our results with other competitive schemes and validated the theoretical findings through simulations on the MATLAB platform.

Motion controller for multi-joint robotic arm with deep cascade gated Bayesian broad learning system

Intelligent controllers based on the broad learning system can simplify the process of model parameter adjustment, finding wide applications in the motion control of multi-joint robotic arms. However, motion controllers for multi-joint robotic arms based on broad learning system exhibit insufficient precision and overlook the impact of joint motion commonalities on controller design. Therefore, this paper proposes a novel motion control strategy for a multi-joint robotic arm based on a deep cascade feature-enhancement gated Bayesian broad learning system. Firstly, the motion controller of the deep cascade feature-enhancement Bayesian broad learning system is constructed to enhance the robotic arm motion control precision. Secondly, an incremental node generation module with an attention-gated mechanism is constructed to capture the unique motion characteristics of the target joints, which is further combined with model generalization to simplify the motion control process of the multi-joint robotic arm. Finally, controller convergence is enhanced by combining it with the Lyapunov theory to constrain the learning parameters. Simulations and physical experiments are designed to verify the feasibility and superiority of the proposed motion control strategy. The results demonstrated that the strategy improved the accuracy of robotic arm motion control, with the root mean square error in position tracking reduced to 0.0019 rad. This represents a 93.39% reduction in error compared to existing techniques.

Adaptive Integral Sliding Mode Control with Chattering Elimination Considering the Actuator Faults and External Disturbances for Trajectory Tracking of 4Y Octocopter Aircraft

This paper presents a control strategy for a 4Y octocopter aircraft that is influenced by multiple actuator faults and external disturbances. The approach relies on a disturbance observer, adaptive type-2 fuzzy sliding mode control scheme, and type-1 fuzzy inference system. The proposed control approach is distinct from other tactics for controlling unmanned aerial vehicles because it can simultaneously compensate for actuator faults and external disturbances. The suggested control technique incorporates adaptive control parameters in both continuous and discontinuous control components. This enables the production of appropriate control signals to manage actuator faults and parametric uncertainties without relying only on the robust discontinuous control approach of sliding mode control. Additionally, a type-1 fuzzy logic system is used to build a fuzzy hitting control law to eliminate the occurrence of chattering phenomena on the integral sliding mode control. In addition, in order to keep the discontinuous control gain in sliding mode control at a small value, a nonlinear disturbance observer is constructed and integrated to mitigate the influence of external disturbances. Moreover, stability analysis of the proposed control method using Lyapunov theory showcases its potential to uphold system tracking performance and minimize tracking errors under specified conditions. The simulation results demonstrate that the proposed control strategy can significantly reduce the chattering effect and provide accurate trajectory tracking in the presence of actuator faults. Furthermore, the efficacy of the recommended control strategy is shown by comparative simulation results of 4Y octocopter under different failing and uncertain settings.

Consensus analysis for heterogeneous multiagent systems subject to input saturation

AbstractThis paper investigates the consensus problem of heterogeneous multiagent systems (HMASs) consisting of first‐order and second‐order agents, where second‐order linear and second‐order nonlinear agents are included in the second‐order agents. Firstly, the consensus problem of HMASs without input saturation is studied in the first part. However, in practical applications, due to the physical limitations of actuators, saturation often occurs. Therefore, we focus on the consensus problem of HMASs with input saturation in the second part. Then based on the knowledge of Lyapunov stability theory and graph theory, it gives sufficient conditions for these HMASs to reach consensus, which ensures that each agent eventually reaches consensus. Eventually, the effectiveness of the theory is verified by performing simulations.

Partial state-constrained integrated guidance and control for an STT missile with self-adjusting prescribed performance via non-barrier Lyapunov function method

A state-constrained guidance and control law is vital to the flight safety of an aerial interceptor against a maneuvering target. Taking the flight angle limitations, manipulation saturation, and terminal constraints into consideration, a novel integrated guidance and control (IGC) schema with a self-adjusting prescribed performance is proposed. To avoid the feasibility condition via the conventional barrier Lyapunov function-based method, a new state-dependent nonlinear mapping function is designed, based on which the state-constrained IGC system is converted into a constrained-free model. A novel prescribed performance with a self-tuning mechanism is proposed to guarantee satisfied transit and steady guidance performances. The backstepping technique combined with super-twisting integral sliding modes and newly defined predefined-time disturbance observers is implemented to generate state-constrained virtual command signals. All the signals in the closed-loop system are strictly proven to be bounded by Lyapunov stability theory. The simulation results show the effectiveness of the proposed IGC schema.

Assessing Stability in Discrete-Time Systems Impacted by Interference and State Delays: An Approach Using ISS

In this study, we introduce a criterion for addressing the input to state stability (ISS) problem inherent in nonlinear discrete systems featuring state delay, saturation overflow (SO), and external interference (EI). This paper proposes three novel theorems by employing the Lyapunov function to assure the stability of the targeted discrete time systems (DTS) under complex conditions such as state delay, SO, EI and the first theorem utilizes system information more effectively by considering EI, state delay and SO, the second theorem focuses on asymptotic stability (AS) analysis of the system when EIs are zero, the third theorem proposes the system is AS when state delays are zero. These theorems impose fewer constrains additionally these conditions are demonstrated to be more relaxed and computationally less intensive to existing criteria. The advantage of the suggested technique is proven through three numerical examples and comparison research.

Fractional pseudo-parabolic equation with memory term and logarithmic nonlinearity: Well-posedness, blow up and asymptotic stability

Fractional pseudo-parabolic equation with memory term and logarithmic nonlinearity: Well-posedness, blow up and asymptotic stability

Adaptive fault-tolerant containment control for heterogeneous uncertain nonlinear multi-agent systems under actuator faults

As modern control systems involve a growing number of actuators, the consequent number of faults occurrence, which may deteriorate the closed-loop system performance, is increasing. Focusing on the containment control problem of generic nonlinear high-order heterogeneous uncertain Multi-Agent Systems, this study proposes a novel distributed adaptive fault-tolerant Proportional-Integral-Derivative control protocol to improve the reliability and the resilience of the whole networked systems against actuator failures. The Lyapunov theory, combined with the Barbalat lemma, provides the design of suitable adaptive mechanisms that adjust the PID control actions to ensure the asymptotic convergence of the closed-loop containment errors for the overall network, hence implying the convergence of each agent state toward the convex region shaped by the multiple leaders, despite the occurrence of actuators faults. The fulfillment of the fault-tolerant containment objective is ensured by requiring a lower computational burden with respect to alternative solutions, hence resulting in more attractive for wider practical engineering applications. Numerical simulation results, also including a comparison analysis with a state-of-the-art controller, corroborate the efficiency and the advantages of the proposed distributed PID controller.