Finite-time Stability Research Articles

Practical finite-time command filtered backstepping control of MPCVD reactor systems with uncertainties

A practical finite-time command filtered backstepping control method is proposed in this paper for a microwave plasma chemical vapor deposition (MPCVD) reactor system. The MPCVD reactor system is modeled as a coupled nonlinear system with unknown control direction functions and unknown nonlinearities. To address the unknown nonlinearities, novel practical finite-time command filters are proposed to construct the estimations of such nonlinearities. On the other hand, an equivalent augmented system of the reactor system is proposed to address the design challenges that posed by the system unknown control direction functions. Additionally, it can be concluded that the proposed control method ensures practical finite-time stability of the reactor system tracking errors by using the practical finite-time Lyapunov stability criterion. Finally, the effectiveness of the approach is demonstrated through the simulation results.

Distributed Finite-Time Coverage Control of Multi-Quadrotor Systems with Switching Topology

This paper studies the distributed coverage control problem of multi-quadcopter systems connected with fixed and switching network topologies to guarantee the finite-time convergence. The proposed method modifies the objective function originating from the locational optimization problem to accommodate the consensus constraint and solves the problem within a given time limit. The coverage problem is solved by sending angular-rate and thrust commands to the quadcopters. By exploiting the finite-time stability theory, we ensure that the rotation and translation controllers of the quadcopters are finite-time stable both in fixed and switching communication topologies, able to be implemented distributively, and able to collaboratively drive the quadcopters towards the desired position and velocity of the Voronoi centroid independent of their initial states. After carefully designing and analyzing the performance, numerical simulations using a Robot Operating System (ROS) and Gazebo simulator are presented to validate the effectiveness of the proposed control protocols.

Filippov's Solution and Finite-Time Stability of Stochastic Systems for Discontinuous Control

In this paper, a suite of theoretic tools is provided for discontinuous control design and finite-time stability analysis of a class of stochastic differential systems. The notion of Filippov&#x0027;s solutions for stochastic differential systems is proposed, and the corresponding solution existence problem is explored. The classical It&#x00F4; differentiation formula is generalized for quasi-<inline-formula><tex-math notation="LaTeX">$C_{0}^{2}(\mathbb {R}^{n},\mathbb {R})$</tex-math></inline-formula>-class functions along Filippov&#x0027;s solutions of stochastic differential systems, and two involved set-valued stochastic integrals are introduced with a study on their properties. Some finite-time stability results of stochastic differential systems are revealed with Filippov&#x0027;s solutions, and one of them is applied to neural synchronization, together with case simulations.

Finite-Time Stability of Genetic Regulatory Networks With Nondifferential Delays

Studying the stability of genetic regulatory networks (GRNs) helps to explore the laws of automatic regulation in organisms. By designing proper controllers, the finite-time stability problem of GRNs with nondifferential discrete time-varying delays is discussed in this paper. Rather than constructing the Lyapunov functional or using the finite-time stability theorem, inequality technique and comparison method are firstly adopted in the analyzation. Then, several sufficient algebraic criteria are derived to ensure the finite-time stability of addressed delayed GRNs. The results are general and contain the exponential stability as a special case. Finally, numerical simulations are provided to illustrate the validness of theoretical 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.

Global Finite-Time Stabilization of Spacecraft Attitude With Disturbances via Continuous Nonlinear Controller

In this paper, a robust continuous controller is investigated to solve the global finite-time attitude stabilization problem of rigid spacecraft system subject to multiple disturbances. The system order is firstly increased by derivation and the derivative of the actual torque is regarded as the virtual control law to be designed. Then, a super-twisting differentiator is constructed to provide finite-time angular acceleration estimations. Finally, based on the estimated angular accelerations, a discontinuous set stabilization control law is designed as the virtual controller. The actual continuous controller is obtained by integrating the discontinuous one. Rigorous proof and stability analysis are presented based on Lyapunov analysis. Compared with most of the existing finite-time control approaches in spacecraft systems, the proposed continuous control scheme guarantees the finite-time set stability of the closed-loop system. Moreover, the system states can converge to the equilibria even in the presence of derivative-bounded disturbances. Simulation studies of the proposed controller are illustrated to demonstrate the strong disturbance rejection ability, fast convergence rate, and high steady-state precision.

Finite-Time Predictive Consensus for Discrete-Time Heterogeneous Multi-Agent Systems Over Switching Digraphs

This brief investigates the finite-time consensus of discrete-time heterogeneous multi-agent systems with the predictive mechanism on switching digraphs. By optimizing the consensus problem, a fully distributed model predictive controller in the analytical form is developed. Moreover, sufficient conditions are obtained, and the finite-time stability is guaranteed with an explicit settling time. Numerical examples illustrate the effectiveness of the designed controller and the validity of the derived theoretical results.

Finite-Time Control of High-Order Nonlinear Random Systems Using State Triggering Signals

In order to improve the efficiency of data transmission and save communication resources, the problems of double event-triggered control are investigated for a class of high-order nonlinear random systems. Under more general system conditions, in addition to overcoming the difficulty of recursive design caused by signal discontinuity, the effects of high-order nonlinearity and random disturbances also need to be addressed. Based on the adding power integral technique, a practical finite-time stable result is established for the nonlinear random systems under a double event-triggered mechanism (ETM) and proved that there is no Zeno phenomenon. Compared with the existing results, the update frequency of the signals is effectively reduced, and the upper bound of the stable error is independent of trigger parameters, thus can be made sufficiently small by tuning design parameters. Furthermore, the result is expanded to finite-time stabilization, state variables converge to the origin in a finite time. Finally, numerical simulations verify the effectiveness of the proposed algorithm.

Adaptive Performance-Constrained Synchronization Control for Hypersonic Flight Vehicle Swarms: A Novel Finite-Time Convergence Protocol Methodology

This paper proposes a novel neural adaptive performance-constrained synchronization tracking control algorithm for multiple hypersonic flight vehicles (HFVs), which are subject to actuator faults and full-state constraints. The proposed method is based on advanced Lyapunov finite-time stability theory and a sophisticated backstepping design scheme. The longitudinal model of HFV is converted into velocity and altitude subsystems through functional decomposition. Our method presents three significant contributions over the existing state-of-the-art approaches: (a) ensuring finite-time convergence of HFVs systems by guaranteeing that the setting time is lower bounded by a positive constant that is related to the initial states; (b) utilizing a tan-type Barrier Lyapunov function (BLF) to ensure that the synchronization tracking errors of velocity, altitude, flight path angle, angle of attack, and pitch angle rate are maintained within certain performance bounds; and (c) designing a neural adaptive control algorithm and adaptive parameter laws by combining the backstepping design technique and radial basis function neural networks (RBFNNs) to handle unknown actuator faults and modeling uncertainties. Finally, comparative simulations are conducted to validate the efficacy of the proposed scheme.

Finite-Time Output Feedback Cooperative Formation Control for Marine Surface Vessels With Unknown Actuator Faults

This article studies the finite-time output-feedback cooperative formation problem of multiple marine surface vessels (MSVs) without using velocity information, where each MSV contains unknown time-varying actuator faults, ocean disturbances, and model uncertainties. Considering the performance specifications and requirements in practice, the formation errors and velocities are also required to change in a predefined compact set. Aiming at the challenge of unknown input gain caused by unknown time-varying multiplicative faults, a novel nonlinear extended state observer with an adaptive law is first constructed, which cannot only recover unmeasurable velocities from position-heading information but also simultaneously compensate for ocean disturbances, model uncertainties, and additive faults. Subsequently, combining the barrier Lyapunov function and the nonlinear tracking differentiator technique, a unified finite-time output-feedback cooperative control framework is developed, including both kinematics and kinetics, to prevent constraint deviation and avoid the computational complexity of the traditional backstepping method. Using finite-time stability theory, the designed output feedback cooperative controller can ensure that the desired cooperative performance is achieved within a finite time and tracking errors converge to a small neighborhood of the origin while ensuring that the closed-loop system is semiglobally uniformly ultimately bounded. Simulation examples are shown to demonstrate the effectiveness of the proposed control scheme.

Collision-Free Adaptive Constrained Tracking of Satellite Clusters Under Time-Receding Horizons

The satellite cluster flying (SCF) technology is essential in contemporary space engineering, while escalating requirements and clustering scales pose challenges for control implementation. This paper provides a low-complexity adaptive control scheme for asymptotic tracking of the SCF system, aiming to drive satellites to form a scalable formation lattice (F-lattice) around the virtual global center (VGC). The topological relations denoted by graphic matrices are replaced with a set of well-defined bump functions, which are also utilized to generate finite cut-off potential functions for preventing collisions. Then, a set of time-receding horizons (TRH) stitched with quadratic Lyapunov functions (QLF) are presented for constrained dynamic performance, relaxing the initial dependencies and specifying the practically preset finite-time stability (PPFS) of the perturbed SCF throughout. In addition, by integrating specific inequality and adaptive estimators, disturbances and recursive derivatives are compensated online without “complexity explosion.” At last, simulations built upon a satellite cluster illustrate the effectiveness and superiority of the proposed method.

Finite-Time Synchronization of Neural Networks With Infinite Discrete Time-Varying Delays and Discontinuous Activations.

This article investigates finite-time synchronization of neural networks (NNs) with infinite discrete time-varying delays and discontinuous activations (DDNNs). By virtue of theory of differential inclusions, comparison strategies, and inequality techniques, finite-time synchronization of the underlying DDNNs can be developed via a discontinuous state feedback control law, and the synchronous settling time can be estimated. The delayed state feedback controller and finite-time stability theorem are not employed during the analysis. As a special case, finite-time synchronization of NNs with bounded delays and discontinuous activations is given. Finally, two examples are provided to illustrate the validity of the theories.

Event-Based Finite-Time Control for Nonlinear Multiagent Systems With Asymptotic Tracking

In this paper, an adaptive neural finite-time event-triggered consensus tracking problem is studied for nonlinear multi-agent systems (MASs) under directed graphs. Firstly, the unknown nonlinear functions of MASs can be approximated by neural networks. Then, a distributed adaptive event-triggered control (ETC) scheme is proposed via command filter and backstepping technique. The newly designed control scheme can not only circumvent the problem of the explosion of complexity, but also remove the singularity issue typical of conventional backstepping technique. In the meanwhile, an event-triggered mechanism with a dynamic threshold is devised to reduce the waste of network resources. Moreover, by using a novel finite-time stability criterion, it can be proved that the closed-loop system is finite-time stable and the consensus tracking errors can reach zero as time approaches to infinity. Finally, a numerical example is given to validate the feasibility of the proposed scheme.

Backstepping-Based Finite-Time Control for High-Order Discrete-Time Systems

This paper studies the finite-time control of high-order discrete-time nonlinear systems. A novel backstepping based nonsmooth finite-time controller design method is established through recursive computation. Under proposed control scheme, the finite-time stability analysis is given from the last subsystem to the first subsystem, and the settling time can be estimated. An example is given to verify the method.

Finite-Time Fault-Tolerant Control for Swashplate of Integrated Hydraulic Transformer With Uncertain Mismatched Interference

The precision position control for the swashplate servomechanism of the integrated hydraulic transformer (IHT) with mismatched interference is considered in this paper. Compared with the type of port-plate-rotating IHT, the swashplate-rotating IHT has smaller leakage and higher efficiency, but suffers from parameters uncertainty, and time-varying uncertain torque from the plungers. To enhance the robustness of the proposed system, a novel robust control scheme based on a finite-time extended state observer (FTESO) is developed. In the proposed control scheme, the system nonlinearities, parameter uncertainty, actuator failure are both taken into account. And a novel FTESO is established to obtain the state variables, load torque, and failure signals. By introducing the nonsingular terminal sliding mode surface and finite-time technique in each step of the backstepping design, the novel control scheme is able to enhance the robustness of servomechanism and realize finite-time stability of the tracking errors. Finally, the comparative experiment is performed to verify the effectiveness of the controller design.

Finite-time H∞ control under the Round-Robin protocol for switched linear systems with admissible edge-dependent average dwell time

This article focuses on finite-time [Formula: see text] control under the Round-Robin protocol for switched linear systems with admissible edge-dependent average dwell time. To relieve the bandwidth pressure of the sensor, a Round-Robin protocol is constructed to decide the access rights of each node of the sensor. Under the Round-Robin protocol-based control structure, admissible edge-dependent average dwell time is applied to describe the transition relationship between the modes of the subsystem and release the restrictions of mode-dependent average dwell time. Moreover, the finite-time stability and [Formula: see text] performance of switched system with Round-Robin protocol are analyzed by using multiple Lyapunov function method combined with the admissible edge-dependent average dwell time switching. Sufficient conditions for the solution to finite-time control problem are derived which consider the [Formula: see text] performance index. Finally, the availability of the control synthesis methods is verified by the circuit model of Buck–Boost converter.

Finite-Interval Stability Analysis of Impulsive Fractional-Delay Dynamical System

Stability analysis over a finite time interval is a well-formulated technique to study the dynamical behaviour of a system. This article provides a novel analysis on the finite-time stability of a fractional-order system using the approach of the delayed-type matrix Mittag-Leffler function. At first, we discuss the solution’s existence and uniqueness for our considered fractional model. Then standard form of integral inequality of Gronwall’s type is used along with the application of the delayed Mittag-Leffler argument to derive the sufficient bounds for the stability of the dynamical system. The analysis of the system is extended and studied with impulsive perturbations. Further, we illustrate the numerical simulations of our analytical study using relevant examples.

An adaptive finite-time control method for antilock braking system with experimental analysis

The antilock braking system (ABS) is a representative technology to improve the safety of hard braking in automobiles. The slip rate control has been a challenging issue due to the complicated characteristics of tires and the strong nonlinearity of the system. In this paper, a novel adaptive finite-time controller for ABS is developed to improve braking performance. Different from the current control strategies for ABS, the extended finite-time stability theory and state constraint are comprehensively considered in the proposed control strategy. The extended finite-time stability theory is applied to deal with the system uncertainties, by which the convergence of slip rate tracking error is achieved. And the asymmetric tan-type barrier Lyapunov function (BLF) is used to ensure that the wheel slip ratio is within a smaller and more stable area. Finally, according to the simulation and experiment, compared with the existing BLF controller, a faster convergence rate, better robustness and anti-disturbance performance of ABS can be achieved with the proposed strategy.

Multiple interval delay-dependent finite-time control of fuzzy stochastic systems

This work is concerned with multiple interval delay-dependent stochastic finite-time boundedness as well as input-output finite-time mean square stabilization for fuzzy plants against state constraints as well as input constraints. Nonlinear dynamics, intermittent actuator faults, exogenous disturbances, model uncertainties and intermittent sensor faults appear in the multiplicative form in these systems. The switching between the faulty and healthy conditions is described via semi-Markov chain. First, a semi-Markovian fault-tolerant controller is researched. Next, the closed-loop model is gathered. The issue of robust stochastic finite-time boundedness as well as input-output finite-time mean square stabilization against H∞ performance is realized via fuzzy stochastic Lyapunov function. Meanwhile, sufficient conditions are presented with linear matrix inequalities. At last, this validity of this approach in this paper is proved by two examples.

Finite-time peak-to-peak analysis for switched generalized neural networks comprised of finite-time unstable subnetworks

This research is concerned with finite-time stability and peak-to-peak performance analysis for the discrete-time switched generalized neural networks (SGNNs) with time-varying delay. Compared with the reported results, each individual subnetwork of the SGNNs is considered to be finite-time unstable in the present study. To accomplish the anticipatory objective, the quasi-time-dependent Lyapunov–Krasovskii functional is constructed, and the associated sufficient conditions are simultaneously formulated to confirm that the disturbance-free SGNNs are finite-time stable when the subnetwork satisfies a certain switching time interval. In addition, a prescribed disturbance attenuation level is also achieved for the perturbed SGNNs in the sense of peak-to-peak performance. Finally, the provided simulation example corroborates the effectiveness and applicability of the established finite-time analysis framework in the absence of finite-time stable subnetworks.