Finite-time Stabilization Control Research Articles

Finite-time control of switched stochastic delayed neural networks with Φ-dependent average dwell time

This study focuses on the finite-time stability analysis and control for a class of switched stochastic delayed neural networks (SSDNNs), introducing the [Formula: see text]-dependent average dwell time ([Formula: see text]DADT) switching method as a novel approach for analyzing the finite-time stability of switched stochastic neural networks with time-varying delay. By applying [Formula: see text]DADT and multiple Lyapunov–Krasovskii functionals, some sufficient conditions for the finite-time stability are established. Then, a generalized partially delay-dependent controller is designed to ensure that the closed-loop system achieves stability. Finally, a numerical example is provided to illustrate the effectiveness.

Adaptive fixed-time fuzzy control for delayed recycling continuous stirred tank reactor with asymmetric time-varying full-state constraints

Recently, there are some results concerning stability and finite-time stability control for continuous stirred tank reactors (CSTR). However, when considering the control of time-delay CSTR systems or fixed-time stability of CSTR systems, there are relatively few articles involved. In this paper, we first consider the CSTR system that includes both of the above factors simultaneously, that is, the adaptive fixed-time fuzzy control design problem for a CSTR with a delayed recycle stream and asymmetric time-varying full-state constraints. Firstly, based on existing works, we present an improved practical fixed-time stability criterion, which can be applied to more complex nonlinear systems. Then, we construct time-varying asymmetric integral barrier Lyapunov functions to handle asymmetric time-varying full-state constraints. Next, fuzzy logic systems are used to approximate the unknown functions of the system, and a sliding mode differentiator is introduced to avoid the “explosion of complexity” of the time derivative of the virtual controller. Furthermore, using the improved practical fixed-time stability criterion, we present the adaptive fixed-time fuzzy controller design processes that can ensure tracking performance in a fixed-time, and states of the system never violate their constraint bounds. Finally, a simulation example is provided to verify the effectiveness of the proposed control strategy.

Finite-time stability control with hardware-in-the-loop testing of a chaotic permanent magnet synchronous motor

Stability of Permanent Magnet Synchronous Motor (PMSM) is of prime importance for the successful operation of the drive system, which is found to be dependent on initial operating conditions showing chaotic characteristic. Therefore, the paper presents the stabilization of a chaotic PMSM system through the finite-time stability approach. From this aspect, three controllers have been developed which are effective for the suppression of machine chaotic behaviour. Proposed controllers are simpler and numerically stable in comparison with previous works. Furthermore, performance comparisons of the proposed controllers are also presented in term of their settling time and peak overshoot. Selection among the proposed controllers depends on the consideration of a particular operating index (settling time or peak overshoot) wherein, performance also varies on system parameter λ. Performance evaluation of proposed controllers has been presented in MATLAB environment. In order to validate the obtained MATLAB results, a real-time analysis has been carried out using Typhoon Hardware-in-the-loop (HIL) emulator. The comparison shows that both results follow the same trend and are closely coordinated with each other, which validates the proposed controllers.

Non-overshooting tracking control for nonlinear systems with prescribed finite-time

In this study, the problem of non-overshooting tracking control (NOTC) for a class of strict-feedback systems with prescribed finite-time (FT) is studied. In order to obtain a simple closed-loop system (CLS), we first propose a criterion lemma for prescribed FT stable control. A prescribed FT controller is designed by using backstepping and the proposed criterion lemma. According to the CLS, many conditions of NOTC are analyzed. Compared with the related results, the NOTC conditions obtained in this paper are relatively extensive, which reduces conservatism. The algorithm makes the system overshoot zero, so this result increases the accuracy. The final simulation results show that this algorithm is effective.

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.

New Adaptive Super-Twisting Extended-State Observer-Based Sliding Mode Scheme with Application to FOWT Pitch Control

This paper details the transformation of the velocity or position-tracking problem of a class of uncertain systems using finite time stability control for first-order uncertain systems. A new composite extended-state observer sliding mode (ESOSM) scheme is proposed, which includes an adaptive super-twisting-like ESO and an adaptive super-twisting controller. The adaptive super-twisting controller is implemented through a barrier function-based second-order sliding mode algorithm. To further reduce control chattering and improve control performance, the adaptive super-twisting-like ESO, which employs high-order terms in the super-twisting algorithm to accelerate convergence, is designed to observe the lumped uncertainty in real time. The advantages of the proposed scheme are verified by a numerical example and application with regard to floating offshore wind turbine (FOWT) pitch control. Compared with proportional integral (PI) and adaptive super-twisting sliding mode (ASTSM) schemes, better results are obtained in velocity tracking and fatigue load suppression. For the FOWT pitch control application, the platform roll, pitch, and yaw are decreased by 3%, 2%, and 4%, respectively, compared to the PI scheme at an average turbulent wind speed of 17 m/s and turbulence intensity of 17.27%.

Finite‐time stabilization control of nonlinear systems with full‐state constraints

AbstractThis paper studies the finite time stabilization control (FTSC) problem of nonlinear systems with unknown functions and full‐state constraints (FSCs). A lemma dealing with unknown functions is put forward so that the assumptions and the “explosion of terms” (EOT) of backstepping are avoided. Compared with approximation algorithms, this algorithm can make the system states converge to the origin in a finite time. On the other hand, a new logarithmic constraint function is utilized to solve the drawback of barrier Lyapunov functions (BLFs). Then, combined with finite time control (FTC), an FTSC algorithm with FSCs is proposed. Finally, simulations of Chua's circuit system are given to verify the effectiveness and superiority of this algorithm. Compared with the approximation algorithm, this algorithm can theoretically make the states of Chua's circuit system to the origin in a finite time.

Finite-Time Adaptive Fuzzy Backstepping Control for Quadrotor UAV With Stochastic Disturbance

This paper proposes an adaptive fuzzy output feedback control approach for quadrotor unmanned aerial vehicles (QUAV) with stochastic disturbances, besides which we consider the unmeasurable states and unknown nonlinear functions. The QUAV system contains stochastic terms which are not bounded and not differentiable. By combining the It <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\hat{\rm \textbf{o}}$</tex-math> </inline-formula> differential equation with finite-time theory, a novel stochastic finite-time stability controller for QUAV is raised for the first time. The fuzzy logic system (FLS) is utilized to approximate the unknown nonlinear functions in the model. Dynamic surface control technology is introduced to reduce the complexity of differential. Furthermore, an observer with FLS is designed through the adaptive backstepping technique to estimate the immeasurable states. It is proved that this control approach can ensure that all states of the closed-loop QUAV system are semi-global and finite-time stable in probability. Meanwhile, the errors of system outputs and observer converge to a small neighborhood of origin. The simulation results show the effectiveness of the proposed method. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —In practical applications, many systems are often affected by internal and external disturbances, and not all of them can be described by mathematical models, so they are called stochastic disturbances. Taking the QUAV as an example, when the system is disturbed by internal parameters, external environment, system input, sensor error, and other stochastic factors, the deterministic system can no longer accurately describe the controlled object. In this paper, the QUAV is regarded as a stochastic system for the first time, and a novel controller is designed to solve the above problems. In addition, the QUAV needs fast action in some applications, such as emergency collision avoidance, which has high requirements for the convergence performance of the controller. Therefore, studying the finite-time control for QUAV systems with stochastic disturbances is necessary. At the same time, this paper also considers the problem that the state is not measurable and the system contains unknown nonlinear equations.

Finite-Time Contraction Stability and Optimal Control for Mosquito Population Suppression Model

Releasing Wolbachia-infected mosquitoes into the wild to suppress wild mosquito populations is an effective method for mosquito control. This paper investigates the finite-time contraction stability and optimal control problem of a mosquito population suppression model with different release strategies. By taking into account the average duration of one reproductive cycle and the influences of environmental fluctuations on mosquitoes, we consider two cases: one with a time delay and another perturbed by stochastic noises. By employing Lyapunov’s method and comparison theorem, the finite-time contraction stabilities of these two cases under a constant release strategy are analyzed. Sufficient conditions dependent on delay and noise for these two systems are provided, respectively. These conditions are related to the prespecified bounds in finite-time stability (FTS) and finite-time contraction stability (FTCS) of the system, and FTCS required stronger conditions than FTS. This also suggests that the specified bounds and the delay (or the noise intensity) play a critical role in the FTCS analysis. And finally, the optimal control for the stochastic mosquito population model under proportional releases is researched.

Finite-Time Stability Control of Uncertain Nonlinear Systems With Self-Limiting Control Terms.

In this brief, we define a self-limiting control term, which has the function of guaranteeing the boundedness of variables. Then, we apply it to a finite-time stability control problem. For nonstrict feedback nonlinear systems, a finite-time adaptive control scheme, which contains a piecewise differentiable function, is proposed. This scheme can eliminate the singularity of derivative of a fractional exponential function. By adding a self-limiting term to the controller and the virtual control law of each subsystem, the boundedness of the overall system state is guaranteed. Then the unknown continuous functions are estimated by neural networks (NNs). The output of the closed-loop system tracks the desired trajectory, and the tracking error converges to a small neighborhood of the equilibrium point in finite time. The theoretical results are illustrated by a simulation example.

Observer-based finite-time robust control of nonlinear time-delay uncertain systems with different power Hamiltonian function

Using the Hamiltonian function method with different powers, this paper studies the observer-based finite-time robust control problem of general nonlinear uncertain systems with time delay and presents some new results on this issue. First, by applying Hamiltonian realization method, the paper develops an equivalent Hamiltonian form of original system and designs its observer system. Then, based on the observer system, we study finite-time control problem and present several finite-time stabilization and finite-time robust stabilization results by using the augmented technology and the Lyapunov method. Finally, a real unmanned vehicle is used to verify the performance of the observer-based finite-time robust stabilization controller. Different from the existing literature on Hamiltonian method, the Hamiltonian function in the paper has different powers, which implies that the results developed in the paper have a wider range of application.

Observer-based finite-time robust control for nonlinear systems with different power Hamiltonian functions

This work uses the Hamiltonian function approach to investigate the observer-based finite-time robust control problem of a broad nonlinear system and presents various new results. To begin, the Hamiltonian technique is used to convert the original system to its equivalent form, and then the observer system is designed. Afterward, utilizing the technology and the Lyapunov method, we investigate the finite-time control issue and give several finite-time stabilization results based on the observer method. Finally, a real unmanned vehicle is used to verify the performance of the observer-based finite-time robust stabilization controller. Different from the existing literature on the Hamiltonian method, the Hamiltonian function in this article has different powers, which implies that the results developed in this article have a wider range of application.

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.

Finite-Time Stabilization and Impulse Control of Heat Equation with Dynamic Boundary Conditions

In this paper, we study the impulse controllability of a multi-dimensional heat equation with dynamic boundary conditions in a bounded smooth domain. Using a recent approach based on finite-time stabilization, we show that the system is impulse null controllable at any positive time via impulse controls supported in a nonempty open subset of the physical domain. Furthermore, we infer an explicit estimate for the exponential decay of the solution. The proof of the main result combines a logarithmic convexity estimate and some spectral properties associated to dynamic boundary conditions. In our setting, the nature of the equations, which couple intern-boundary phenomena, makes it necessary to go into quite sophisticated estimates incorporating several boundary terms.

Finite-time stability and observer-based control for nonlinear uncertain discrete-time switched system

Finite-time stability and observer-based control for nonlinear uncertain discrete-time switched system

Velocity-based tuning of degree of homogeneity for finite-time stabilization and fault tolerant control of an ROV in the presence of thruster saturation and rate limits

Velocity-based tuning of degree of homogeneity for finite-time stabilization and fault tolerant control of an ROV in the presence of thruster saturation and rate limits

Constrained Reference Tracking via Structured Input–Output Finite-Time Stability

In this article, the control approach based on structured input–output finite-time stability (IO-FTS) is extended to tackle the reference tracking problem. IO-FTS was originally introduced to deal with the disturbance rejection problem. By applying the finite-time stability control to a properly augmented system, we show that it is possible to enforce a set of specific requirements on the response of the closed-loop system during the transients, taking also into account saturation constraints on the actuators. Adding IO-FTS constraints to classic-state-feedback control law leads to a feasibility problem with bilinear matrix inequality (BMI) constraints. Herein, we show how the original BMI problem can be relaxed to a linear matrix inequality (LMI) one, which comes at a price of more conservatism, but turns out to be computationally more efficient. To prove the effectiveness of the proposed approach, we consider the case of the longitudinal control of a missile.

Finite-time robust stabilization of manipulator system with uncertainty via observer method

Via Hamiltonian function method, the article studies the observer-based finite-time robust stabilization problem of a class of two joint uncertain manipulator system under external disturbance. First, we present an equivalent Hamiltonian model for the two-degree-of-freedom manipulator system and design its finite-time observer and develop a finite-time robust stabilization control result by using Lyapunov stability theory and dimension expansion technique for the manipulator system with external disturbance. On this basis, we further study the robust control problem of the mechanical system containing uncertainty and external disturbance simultaneously and develop several corresponding robust control results for the system. Finally, the control effect is proved by an example simulation. Compared with the existing observer-based infinite time stability control results, an observer and a finite time controller are designed in this article. The system has good robustness to external disturbances and can converge quickly.

The Optimization of Mathematics Teaching Models in Colleges and Universities Based on Nonlinear Differential Equations

Abstract Nonlinear fractional differential equations are an important part of advanced mathematics teaching. The existence and uniqueness of its positive solution have always been a hot topic of academic discussion. This article uses differential inclusion theory and the Lyapunov stability method to analyze the finite-time stabilization control problem of the discontinuous mathematical adjustment model. The article uses a modified decomposition method and convergence acceleration technology in the application of fractional differential equations. The method gives an analytical approximate solution sequence that is easy to calculate, verify, and quickly converge. Finally, examples of Lyapunov stability and the construction of the V function can inspire students to understand ordinary differential equations and increase their interest in learning.

Finite-time stabilization of memristive neural networks via two-phase method

The finite-time stability and stabilization issues of memristive neural networks with time delays are studied via two-phase method, based on impulsive control and state feedback control. Different from classical control design, the control scheme here consists of two phases, i. e. the state can reach the inner of the unit ball exponentially from any initial condition in the first phase, and the then it can arrive at zero equilibrium from the inner of the unit ball in a finite-time. By using different Lyapunov function in two phases, both the finite-time stability criteria based on algebra inequality and the settling time dependent on the initial condition are obtained simultaneously. Compare with the finite-time control strategy in the literature, the finite-time stability and finite-time controller for stabilization of memristive neural networks are used in the second phase only, rather than the whole control process. In addition, the pinning control based on our novel control scheme is designed to obtain the finite-time stabilization of memristive neural networks.