Exponential Stability Research Articles

Sufficient and necessary conditions of exponential stabilisation for a class of distributed second-order semilinear systems with time delay

In this paper, we investigate the problem of exponential stabilisation for a class of retarded distributed second-order semilinear systems by means of a bounded feedback control. The existence and uniqueness of mild solution for the considered systems are proved in Hilbert space framework. Sufficient and necessary conditions for exponential stabilisation are given. Some illustrating applications are provided.

Pth Moment Exponential Stability of Impulsive Stochastic Differential Equations with Unbounded Delays

Stochastic impulsive differential equations with Markovian switching have been applied extensively in various areas including ecology systems, neural networks, and control systems, and stability analysis is one fundamental premise of their applications. For two categories of Markovian switched impulsive stochastic differential functional equations with unbounded delays, this paper investigates the pth moment exponential stability by adopting stochastic Lyapunov stability theory and stochastic analysis approach. Several criteria on pth moment exponential stability have been acquired. In the proposed model, the time-varying coefficients and the hybrid impulsive effects are considered simultaneously. It can be seen that the criteria derived in this paper are more concise and the conditions are easier to verify compared with those existing results based on Razumikhin theory. Finally, two examples are illustrated to show the effectiveness of the theoretical findings.

Stabilization by discrete‐time feedback control for highly nonlinear hybrid neutral stochastic functional differential equations with infinite delay

The problem of stabilizing an unstable highly nonlinear hybrid neutral stochastic functional differential equation with infinite delay (HNSFDEwID) is addressed in this article. The objective of this study is to propose a discrete‐time feedback control (DTFC) approach for stabilizing the original system. Sufficient conditions are derived for the existence and uniqueness of the system's solution, as well as its boundedness, prerequisites for studying the system's dynamic behavior. Four distinct criteria for stabilizing the controlled system are provided, including stabilization, asymptotic stabilization, exponential stabilization, and almost surely exponentially stabilization. Additionally, the upper limit of the time interval for discrete observations is calculated based on these criteria. Finally, the proposed theory is validated through an illustrative example.

Pth Moment exponential stability of stochastic delayed differential systems with impulsive control involving delays

pth Moment exponential stability of stochastic delayed differential systems with impulsive control involving delays

Pinning Event-Triggered Scheme for Synchronization of Delayed Uncertain Memristive Neural Networks

To reduce the communication and computation overhead of neural networks, a novel pinning event-triggered scheme (PETS) is developed in this paper, which enables pinning synchronization of uncertain coupled memristive neural networks (CMNNs) under limited resources. Time-varying delays, uncertainties, and mismatched parameters are all considered, which makes the system more interpretable. In addition, from the low energy cost point of view, an algorithm for pinned node selection is designed to further investigate the newly event-triggered function under limited communication resources. Meanwhile, based on the PETS and following the Lyapunov functional method, sufficient conditions for the pinning exponential stability of the proposed coupled error system are formulated, and the analysis of the self-triggered method shows that our method can efficiently avoid Zeno behavior under the newly determined triggered conditions, which contribute to better PETS performance. Extensive experiments demonstrate that the PETS significantly outperforms the existing schemes in terms of solution quality.

Supervisory adaptive control revisited: Linear‐like convolution bounds and tolerance of slow time‐variations

SummarySupervisory control has been shown to be a very effective approach to adaptive control which ensures step‐tracking, exponential stability, and a degree of robustness to unmodeled dynamics. Here we apply the technique to the classical ‐step‐ahead adaptive control problem: we not only prove exponential stability and tracking of a general bounded reference signal, but also a never‐before‐seen linear‐like convolution bound on the effect of the noise/disturbance. This latter property is then leveraged to not only prove robustness to a degree of unmodeled dynamics, but also to a never‐before‐seen tolerance to a degree of nonlinearities and to slow (on average) plant parameter variations.

A Simple Linear Controller Design to Ensure Global Exponential Stability for a Class of Uncertain Fifth-Order Nonlinear Systems

This paper intends to explore the controller design problem for a class of uncertain fifth-order nonlinear control systems. Combining the theory of differential and integral inequalities, a linear controller will be proposed to promote a class of nonlinear control systems with multiple uncertainties to achieve the goal of global exponential stability. In addition, the guaranteed exponential convergence rate of such uncertain nonlinear systems will also be precisely calculated. Finally, some numerical simulation results will also be presented to verify and illustrate the correctness of this main theorem and the design process of the controller

Event-triggered H∞ control for switched systems based on interval observer

The paper studies the design of interval observer–based event-triggered [Formula: see text] controller for switched systems with frequent asynchronism. We first propose an interval observer–based event-triggered mechanism, which is used to transmit the observer states and the activated mode information for controller updating. Then, we design an interval observer–based event-triggered [Formula: see text] controller for the considered systems. By using the controller mode–dependent Lyapunov function method, sufficient conditions for the globally exponential stability of the closed-loop switched systems are obtained under average dwell time switching law. Moreover, we prove that the interevent interval length is a positive constant, which can exclude the Zeno behavior. Compared with the literature, the paper removes the strict requirement of at most one switch between two event-triggered instants, that is, frequent switches within an interevent interval are allowed. Finally, a numerical example is given to verify the effectiveness of the proposed method.

Dynamic output feedback control of switched systems: A dynamic event-triggered sampling control scheme

A dynamic event-triggered sampling scheme for dynamic output feedback control for a class of switched systems is proposed, where the triggering mechanism can exclude the Zeno phenomenon even if the state of the switched systems is within the output kernel space, and subsystems of the resulting closed-loop switched systems are not necessarily required to be stable. The proposed method can guarantee the Zeno-freeness property and global uniform exponential stability of the origin simultaneously under the impacts of triggering asynchronism and sampling errors. Moreover, sufficient conditions on the globally exponential stability are also given. Finally, the effectiveness of the proposed scheme is illustrated by a numerical example.

Intermittent boundary control for fixed-time stability of reaction–diffusion systems

This work is a pilot effort to investigate the fixed-time stability (FxTS) of reaction–diffusion systems under aperiodically intermittent boundary control (AIBC). The average control rate and a new Lyapunov function are proposed to overcome the challenges of handling the FxTS of reaction–diffusion systems with AIBC. Moreover, the proposed method is applicable to the study of finite-time stability and exponential stability of reaction–diffusion systems under AIBC. Based on the Wirtinger’s inequality and the Lyapunov method, a FxTS criterion for a reaction–diffusion system with AIBC is given. Finally, two examples are discussed along with the simulated results to verify the effectiveness of the proposed method.

Non-fragile control associated with exponential stability for unmanned surface vessels with the rudder failure and dynamic event-trigger

In this paper, non-fragile control associated with exponential stability for unmanned surface vessels(USVs) with the rudder failure and dynamic event-trigger is presented. To begin with, the event trigger and switch system are introduced, taking into account the distribution characteristics of faults and resource efficiency, and a class of independence-distributed random failure models are built. Furthermore, acknowledging the practical challenges associated with parameter uncertainties, USVs are used as uncertain Nomoto model(NM) and the rudder system is described with uncertain second-order underdamped system(UDS). Then, in the presence of dynamic disturbances, an appropriate non-fragile controller is proposed to demonstrate that the closed-loop system states can be exponentially stabilized through the application of the Lyapunov–Krasovskii functions(LKF) and Linear Matrix Inequalities (LMIs). Lastly, the simulation results confirmed that control design methods proposed are effective.

Uniform Turnpike Property and Singular Limits

Motivated by singular limits for long-time optimal control problems, we investigate a class of parameter-dependent parabolic equations. First, we prove a turnpike result, uniform with respect to the parameters within a suitable regularity class and under appropriate bounds. The main ingredient of our proof is the justification of the uniform exponential stabilization of the corresponding Riccati equations, which is derived from the uniform null control properties of the model.Then, we focus on a heat equation with rapidly oscillating coefficients. In the one-dimensional setting, we obtain a uniform turnpike property with respect to the highly oscillatory heterogeneous medium. Afterward, we establish the homogenization of the turnpike property. Finally, our results are validated by numerical experiments.

Adaptive Cartesian space control of robotic manipulators: A concurrent learning based approach

This work introduces a concurrent learning-based adaptive control design for end-effector tracking and the corresponding stability analysis for robotic manipulators. The presented controller is developed directly in Cartesian space, thereby removing the necessity for inverse kinematics calculations at the position level. The designed adaptive controller ensures global exponential tracking of the end-effector in Cartesian space. Moreover, the developed controller assures globally exponential convergence of uncertain dynamical parameters to their actual values without demanding persistence excitation conditions via a combination of a standard gradient-based adaptation with a novel integral concurrent learning component. The developed integral concurrent learning part operates both real-time output data and the most informative historical data gathered by employing the singular-value maximization algorithm (SVMA) to reduce the size of memory allocation. Lyapunov-based arguments are applied to ensure the exponential stability of the closed-loop system. Numerical studies are performed to depict the feasibility and performance of the proposed design.

Non‐fragile observer‐based security control for networked systems via event‐triggered WTOD protocol

AbstractThis paper investigates the security control issue for fuzzy networked systems with uncertainty under false data injection (FDI) and aperiodic denial‐of‐service (ADoS) attacks via sliding mode approach. To mitigate the communication burden, a novel mechanism compromising the advantages of the adaptive event‐triggered (AET) scheme and weighted try‐once‐discard (WTOD) protocol is proposed. In particular, the triggered threshold with real‐time characteristics varies with the measurement outputs. To be specific, the shared insecure communication network can be subjected to hybrid attacks including the stochastic FDI attacks and ADoS attacks limited by duration and frequency. Moreover, the token‐dependent fuzzy non‐fragile observer (NFO) with norm‐bounded uncertainty and corresponding fuzzy control law are constructed by virtue of the Zero‐Order‐Hold (ZOH) strategy. Then, several sufficient criteria that guarantee the exponential stability of the system and the reachability of the specified sliding surface are given. Eventually, a numerical example is presented to verify the applicability of the proposed security control strategy.

Exponential stability and relative controllability of first‐order delayed integro‐differential systems with impulses

We establish sufficient conditions for the exponential stability of nonsingular impulsive delayed integro‐differential systems. Our approach to addressing nonsingular differential problems involves the application of permutable matrices and their associated delayed exponential. Furthermore, we investigate the controllability of a nonlinear impulsive and delayed problem by employing the corresponding Gramian matrix. Finally, to illustrate the theoretical outcomes, we provide examples and graphical representations for each situation.

Robust attitude tracking control for a variable‐pitch quadrotor with uncertainties

SummaryVariable‐pitch quadrotors have demonstrated their capability to enhance control performance and overcome limitations compared to conventional fixed‐pitch quadrotors, while still facing challenges such as nonlinearity, couplings, uncertainties and so on. This article aims to address the robust attitude control problem of variable‐pitch quadrotors afflicted with parametric uncertainties and unpredictable external disturbances. Initially, a practical actuator allocation strategy for the motor‐propeller is proposed, followed by the development of a nonlinear robust attitude tracking controller capable of addressing all uncertainties. The effectiveness of the proposed controller in ensuring exponential stability of the closed‐loop system, thereby driving the attitude tracking error to a small range within a finite time, has been substantiated. To evaluate the control performance, a hardware‐in‐the‐loop testbed is constructed to conduct real‐time experiments. The experimental results from attitude control case, comparative case, and position control case demonstrate that the designed motor‐propeller allocation method and robust controller are effective in achieving a fast response and excellent control performance.

Optimal stability for laminated beams with Kelvin–Voigt damping and Fourier’s law

This article deals with the asymptotic behavior of a mathematical model for laminated beams with Kelvin–Voigt dissipation acting on the equations of transverse displacement and dimensionless slip. We prove that the evolution semigroup is exponentially stable if the damping is effective in the two equations of the model. Otherwise, we prove that the semigroup is polynomially stable and find the optimal decay rate when damping is effective only in the slip equation. Our stability approach is based on the Gearhart–Prüss–Huang Theorem, which characterizes exponential stability, while the polynomial decay rate is obtained using the Borichev and Tomilov Theorem.

Observer‐based dual event‐triggered control for non‐weighted L2$$ {\mathcal{L}}_2 $$‐gain of switched linear systems

AbstractAs everyone knows, strict mode‐dependent event‐triggered mechanism (MDETM) is rarely studied for switched systems due to the difficulty in settling down the relationship between the dwell time (DT) and triggered intervals. This problem is satisfactorily solved by considering the exponential stabilization via observer‐based dual MDETMs in switched linear systems. The dual MDETMs on the sensor‐controller (S‐C) channel and controller‐actuator (C‐A) channel are designed respectively according to mode‐dependent average dwell time (MDADT). The MDETMs on the C‐A channel are generated based on the MDETMs on the S‐C channel, which makes the new control technique strict mode‐dependent and reduces conservatism as much as possible. Furthermore, when there exists external disturbance, a non‐weighted ‐gain with better performance than existing results is given. By studying an augmented system, exponential stabilization is achieved through a new event‐triggered state estimation (ETSE) and dual MDETMs. The observer gain, controller gain, and non‐weighted ‐gain are derived through an effective algorithm. Finally, two numerical examples are given to illustrate the effectiveness of theoretical research.

A novel adaptive control design for exponential stabilization of memristor‐based CVNNs with time‐varying delays using matrix measures

AbstractThe present study introduces a new adaptive control framework that aims to attain exponential stability in complex‐valued neural network systems utilizing memristors while accounting for time‐varying delays. The control issues in systems of this nature are mostly attributed to the presence of memristors and time‐varying latency. To overcome these challenges and achieve stabilization outcomes, a methodology is employed that integrates adaptive control approaches inside a matrix‐based framework. This study employs Lyapunov's stability theory to establish exponential stabilization conditions and conduct convergence analysis. The efficacy of the suggested control algorithm in achieving exponential stabilization and robustness under varied delays is demonstrated through numerical simulations.

Novel Exponential Stability Criteria for Switched Neutral-Type Neural Networks With Mixed Delays

Novel Exponential Stability Criteria for Switched Neutral-Type Neural Networks With Mixed Delays