Finite-time Stability Criterion Research Articles

Finite-time adaptive NN dynamic surface control for nonstrict nonlinear FOSs subject to input dead-zone and full-states constraints

This article focuses on a kind of nonstrict nonlinear fractional-order systems (FOSs) suffering from state constraints and dead-zone input. Meanwhile, a finite-time adaptive dynamic surface control (DSC) approach based on backstepping technology and approximation principle of radial basis function neural network (RBFNN) is developed. To overcome the problem of inherent computational complexity, a fractional-order filter is applied to approach the virtual controller and its fractional-order derivative in each step of the backstepping procedure. The barrier Lyapunov function (BLF) is employed to handle the state constraints, and finite-time stability criteria on the basis of fractional-order Lyapunov method are introduced to prove the finite-time convergence of the tracking error into a small region around the origin. It is shown that all the solutions of the closed-loop system are bounded, while the state constraints are satisfied within a predetermined finite time. Finally, two examples are provided to demonstrate the effectiveness of the presented control scheme.

A novel finite-time stability criteria and controller design for nonlinear impulsive systems

The issue of a novel finite-time stability and stabilization design for a class of nonlinear impulsive systems is discussed in this paper. In previous finite-time control designs for impulsive systems, the convergence rate of these control strategies is even less rapid than the exponential convergence rate when the initial state is distant from the origin. To overcome this problem, two sufficient conditions for the novel finite-time stability of impulsive systems are presented, in which the stabilizing impulses and the destabilizing impulses are considered, respectively. Meanwhile, the upper bound of the settling-time is evaluated. In addition, combining Lyapunov functions theory with impulsive control, we design a controller for impulsive dynamical systems to satisfy the novel finite-time stability. Finally, two simulation examples are given, in which the first example demonstrates the superiority of the proposed finite-time stability criterion for nonlinear impulsive systems by comparing it with traditional finite-time stability, and the second example verifies the effectiveness of the presented controller.

Further Results on Fast Finite-Time Stability Criteria and Its Application in Circuit System

Further Results on Fast Finite-Time Stability Criteria and Its Application in Circuit System

Event-Triggered Adaptive Fuzzy Control for Strict-Feedback Nonlinear FOSs Subjected to Finite-Time Full-State Constraints

In this article, an event-triggered adaptive fuzzy finite-time dynamic surface control (DSC) is presented for a class of strict-feedback nonlinear fractional-order systems (FOSs) with full-state constraints. The fuzzy logic systems (FLSs) are employed to approximate uncertain nonlinear functions in the backstepping process, the dynamic surface method is applied to overcome the inherent computational complexity from the virtual controller and its fractional-order derivative, and the barrier Lyapunov function (BLF) is used to handle the full-state constraints. By introducing the finite-time stability criteria from fractional-order Lyapunov method, it is verified that the tracking error converges to a small neighborhood near the zero and the full-state constraints are satisfied within a predetermined finite time. Moreover, reducing the communication burden can be guaranteed without the occurrence of Zeno behavior, and the example is given to demonstrate the effectiveness of the proposed controller.

Finite-Time Stability of Inertial Neural Networks with Delayed Impulses

This paper studies the finite-time stability (FTS) of the inertial neural networks (INNs) with delayed impulses. Unlike previous related works, we consider the delayed impulses and propose a new impulsive control strategy. We extend the existing FTS results to the cases with delayed impulses. We also establish some global and local FTS criteria of INNs. Moreover, we estimate the settling-time in different cases and investigate the optimization strategy. We present three numerical examples to verify the validity of our theoretical results.

Finite-time stability and applications of positive switched linear delayed impulsive systems

<abstract><p>In this paper, we study the finite-time stability and applications of positive switched linear delayed systems under synchronous impulse control, which includes two types of random switching and average dwell time switching. By constructing a type of linear time-varying co-positive Lyapunov functional, we first propose several new finite-time stability criteria. It should be emphasized that the linear term coefficient of the linear vector of the Lyapunov functional is adjusted to the difference between the weighting vector and the given vector. Then, we apply the obtained stability criteria to the linear time-varying delayed systems with impulsive effects. At last, three examples are given to demonstrate the validity of the obtained results, which includes the specific linear programming algorithm process.</p></abstract>

Adaptive finite-time output tracker design of uncertain nonlinear systems with sandwich structure and actuator saturation constraint

This paper studies the finite-time output tracking problem for a class of nonlinear sandwich systems with sandwiched dead-zone function and input actuator saturation constraint. To achieve the goal, a systematic adaptive backstepping controller is proposed based on the practical finite-time stability criterion which guarantees the output tracking even if the dead zone and saturation constraints occur, simultaneously. In the control approach to confine the system output to a predefined set, the barrier Lyapunov function is utilised. To cope with the problem of ‘explosion of complexity’, a finite-time command filter is also employed. Furthermore, the values of the unknown parameters are estimated by appropriate adaptive laws. The finite-time stability of the closed-loop system is proved based on the Lyapunov approach which ensures the boundedness of all signals. Finally, the efficiency and applicability of the proposed method are confirmed by providing the simulation results for the hydraulic servo press system.

Robust optimal triple event-triggered intermittent control for uncertain input-constrained nonlinear systems

This paper investigates the concept of finite time (FT) optimal event-triggered intermittent (ETI) control for nonlinear systems with input constraints and dynamic uncertainty. Firstly, we address a key challenge faced by existing controllers, wherein the unbounded nature of the signal function renders it impractical to handle the input-constrained FT control problem. To overcome this limitation, we derive a novel lemma of semiglobal practical finite-time stability (SGPFTS) specifically for intermittent control with the additional constant terms. By leveraging the lemma and the Hamilton–Jacobi–Bellman (HJB) equation, we obtain the optimal FT guaranteed cost intermittent control law and establish FT stability criteria for uncertain nonlinear systems. Recognizing that the general HJB theory is ill-equipped to address input-constrained optimal control problems, We introduce the model predictive control (MPC) algorithm, which has been proven to be an effective online optimization method in handling robust optimal control and constrained problems. Moreover, conventional ETI optimal control methods struggle to address intermittent control for nonlinear systems with input constraints and dynamic uncertainty. To address this limitation, we propose a triple ETI Lyapunov-based MPC strategy, which not only enhances intermittent control performance but also resolves input constraints and dynamic uncertainty issues. Finally, we present two straightforward examples of uncertain nonlinear systems to demonstrate the effectiveness of the developed strategy in practice.

Input–Output Finite-Time Stability for Switched T–S Fuzzy Delayed Systems With a Time-Dependent Lyapunov–Krasovskii Functional Approach

This research concerns the finite-time performance analysis for switched Takagi-Sugeno (T-S) fuzzy (STSF) systems subject to time-varying delay. Since the existing relevant results for finite-time synthesis of general switched systems require the finite-time stability property of the individual subsystem, a more general situation that the STSF systems comprised fully of finite-time unstable delayed subsystems are considered in the investigation. For surmounting this situation, a novel time-dependent multiple Lyapunov-Krasovskii functional (TDMLF) approach is developed by integrating a ranged dwell time switching mechanism. Then, the corresponding (input-output) finite-time stability criteria with less conservativeness are simultaneously derived for the (perturbed) STSF delayed systems to be (input-output) finite-time stable over the concerned finite-time interval. Finally, two illustrative examples are provided to demonstrate the accuracy and superiority of the developed (input-output) finite-time analysis framework.

New results on finite‐time stability and H∞ control for nonlinear Hamiltonian systems

AbstractIn this paper, we investigate the finite‐time stability (FTS) and control of nonlinear Hamiltonian systems with time‐varying state delays and output delays subject to input saturation. By introducing a new class of Lyapunov–Krasovskii (L‐K) functionals and the assumption about the Hamiltonian function, we present a delay‐dependent FTS criterion. Then, a finite‐time feedback control is designed for the nonlinear Hamiltonian systems. Finally, the validity of the proposed results is demonstrated by a numerical example.

A Fast Finite-Time Neural Network Control of Stochastic Nonlinear Systems.

This article takes a fast finite-time control of stochastic nonlinear systems into account. The presence of unknown stochastic disturbance terms makes the traditional fast finite-time control approaches unavailable. To deal with this difficulty, by establishing an auxiliary function and using Jensen's inequality, in Lemma 6, a new criterion of fast finite-time stability is first established for the uncertain stochastic system. Based on the approximation ability of neural networks (NNs), an innovative fast finite-time strategy is put forward for stochastic nonlinear systems. Furthermore, by adopting the presented fast finite-time stability criterion, the stability of the stochastic systems is confirmed. Finally, two simulations are implemented to validate the feasibility of the presented NN control strategy.

Finite-time synchronization of intermittently controlled reaction–diffusion systems with delays: A weighted LKF method

Considering the fact that existing methodologies for finite-time control are difficult to simultaneously overcome the difficulties induced by the effects of reaction–diffusion and time delay when intermittent control is confronted, this paper explores a novel Lyapunov–Krasovskii functional (LKF) method to investigate the finite-time synchronization of delayed reaction–diffusion systems. By designing a simple intermittent control and a weighted LKF, a general finite-time stability criterion is established first. Then, sufficient conditions for the finite-time synchronization of the interested system are given, where the weight factor of the LKF has a heavy influence on the settling time. Several important corollaries are also given to specify the usefulness and generality of the weighted LKF method and the finite-time stability criterion. Finally, a numerical example is provided to verify the new findings, and an image encryption algorithm is presented to validate the useful application of theoretical results.

Stochastic finite-time stability and stabilization for stochastic nonlinear systems with impulse effects

In this paper, some unified stochastic finite-time stability (SFTS) criteria are derived for the impulsive stochastic nonlinear systems by using the stochastic analysis theory, stopping time technology, Lyapunov approach and limit average dwell time (LADT) technology when the impulse effect is destabilizing impulse or stabilizing impulse. Meanwhile, in order to achieve stochastic finite-time stabilization for stochastic nonlinear systems, the impulse control approach is also obtained, which can be divided into two cases: (1) A stochastic finite-time instable (SFTI) stochastic system can become SFTS under the impulse control strategy; (2) A SFTS stochastic system can keep the SFTS under the impulsive disturbance. Furthermore, by using the impulse dependent average dwell time (IDADT) technology, the results are also established for the multiple impulse effects, i.e. destabilizing impulse and stabilizing impulse exist in the system simultaneously. Finally, two useful examples are provided.

Finite-Time Adaptive Fuzzy Event-Triggered Output-Feedback Containment Control for Nonlinear Multiagent Systems With Input Saturation

This paper considers the finite-time containment output-feedback control problem for a class of nonlinear multi-agent systems (MASs) with unmeasurable states and input saturation. Fuzzy logic systems (FLSs) and a smooth function are first employed to model unknown agent's subsystems and input saturation, respectively. Then, a novel fuzzy state observer is established via the intermittent output signal. By introducing first-order filter and using the sampled estimating states and triggered output signals, an event-triggered mechanism consisting of the sensor-to-controller and controller-to-actuator is formulated. Consequently, under the framework of the finite-time stability criterion and adaptive backstepping control design technique, a finite-time adaptive fuzzy event-triggered output-feedback containment control design method is proposed and the semiglobal finite-time stability of the controlled system is rigorously proved. Finally, the simulation results are given to confirm the effectiveness of the proposed control scheme.

Criteria for finite-time stability of singular large-scale discrete-time delay systems

This paper concerns a problem of finite-time stability for a class of linear singular large-scale systems with delays. Based on matrix transformations, Lyapunov function method combined with new estimation techniques, we derive sufficient conditions for solving the finite-time stability of the system. A numerical example is given to illustrate the validity and effectiveness of the theoretical results.

On Stabilizability of Nonbilinear Perturbed Descriptor Systems

One way in which nonlinear descriptor systems of (index-k) naturally arise is through semiexplicit differential-algebraic equations. The study considers the nonbilinear dynamical systems which are described by the class of higher-index differential-algebraic equations (DAEs). Their nature is analysed both quantitatively and qualitatively, and stability characteristics are presented for their solution. Higher-index differential-algebraic systems seem to show inherent shaky around their solution manifolds. The often use of logarithmic norms is for the estimation of stability and perturbation bounds in linear ordinary differential equations (ODEs). The question of how to apply the notation of logarithmic norms to nonlinear DAEs has long been an open question. Other problem extensions including nonlinear dynamics and nonbilinear DAEs need subtle modification of the logarithmic norms. The logarithmic norm is combined by conceptual focus with the finite-time stability criterion in order to treat nonbilinear DAEs with the aim of covering some unbounded operators. This means we obtain the perturbation bounds from differential inequalities for a norm by the use of the relationship between Dini derivatives and semi-inner products. A numerical result obtained when tested on the nonbilinear mechanical system with a larger scale showed that the method was highly efficient and accurate and particularly suitable for nonbilinear DAEs.

GKL‐finite‐time stability via comparison principles for stochastic impulsive systems

AbstractThis paper studies the finite‐time stability (FTS) for stochastic impulsive systems (SIS). The notions of FTS including ‐FTS and event‐ ‐FTS are proposed for SIS. The comparison principles for ‐FTS and event‐ ‐FTS are established, respectively. Then the FTS criteria with the settling time estimates are derived. The criteria of ‐FTS and event‐ ‐FTS relax the requirements on stabilizing flow and jump for FTS in the literature. Finally, two examples are presented to demonstrate the obtained results.

Finite-Time Event-Triggered Stabilization for Discrete-Time Fuzzy Markov Jump Singularly Perturbed Systems.

The finite-time event-triggered stabilization is studied for a class of discrete-time nonlinear Markov jump singularly perturbed models with partially unknown transition probabilities (TPs). T-S fuzzy strategy is adopted to characterize the related nonlinear Markov jump singularly perturbed models. The control objective is to make sure that the system states remain within a bounded domain during a fixed-time interval. First, a mode-dependent event-triggered scheme is constructed to reduce the communication burden and save the network bandwidth. On that basis, by using a new Lyapunov function, a developed finite-time stability criterion is derived for the corresponding system to avoid an ill-conditioned issue due to a small singular perturbation parameter. Moreover, the mode-dependent fuzzy controller gain and the event-triggered parameter are co-designed under the framework of partially unknown TPs. Finally, the feasibility of the main results is provided to verify the finite-time event-triggered control strategy.

Further results on the finite-time static output feedback control for nonlinear singular systems

This paper studies the finite-time static output feedback control for a class of nonlinear singular systems. Finite-time stability criterion for the closed singular systems is proposed by static output feedback technique. Based on the properties of structure of the singular system, static output feedback control gain is obtained by using singular value decomposition technique. Meanwhile, different from the existing results of normal systems, the presented scheme reduces the conservatism and complexity during the calculation process. Furthermore, static output feedback H∞ controller is designed and finite time stability criterion is proposed for the nonlinear singular systems with external disturbance. Finally, the applicability and effectiveness of the proposed strategy are illustrated by a circuit system simulation.

Finite-time stability analysis and control of stochastic SIR epidemic model: A study of COVID-19

Finite-time stability analysis is a powerful tool for understanding the long-term behavior of epidemiological models and has been widely used to study the spread of infectious diseases such as COVID-19. In this paper, we present a finite-time stability analysis of a stochastic susceptible–infected–recovered (SIR) epidemic compartmental model with switching signals. The model includes a linear parameter variation (LPV) and switching system that represents the impact of external factors, such as changes in public health policies or seasonal variations, on the transmission rate of the disease. We use the Lyapunov stability theory to examine the long-term behavior of the model and determine conditions under which the disease is likely to die out or persist in the population. By taking advantage of the average dwell time method and Lyapunov functional (LF) method, and using novel inequality techniques the finite-time stability (FTS) criterion in linear matrix inequalities (LMIs) is developed. The finite-time stability of the resultant closed-loop system, with interval and linear parameter variation (LPV), is then guaranteed by state feedback controllers. By analyzing the modified SIR model with these interventions, we are able to examine the efficiency of different control measures and determine the most appropriate response to the COVID-19 pandemic and demonstrate the efficacy of the suggested strategy through simulation results.