Finite-time Stability Research Articles

Local set stability and target control of probabilistic Boolean networks

This paper analyzes the local set stability of probabilistic Boolean networks (PBNs), including local finite-time set stability with probability one (FSSPO) and local asymptotic set stability with probability one (ASSPO). Firstly, a necessary and sufficient condition is proposed for the local FSSPO of PBNs. Then, a reachable set with probability one is constructed, based on which, the largest domain of attraction for the local FSSPO of PBNs is determined. Secondly, by constructing two parameterized sets, the transition probability matrix of PBNs is properly partitioned, and the largest domain of attraction for the ASSPO is depicted. Finally, for PBNs which are locally stable, the target control is introduced to achieve the global FSSPO and global ASSPO of PBNs, respectively.

Observer based finite-time adaptive fractional-order sliding mode control of DFIG wind turbines with unknown dynamic parameters

In this study, we investigate adaptive finite-time fractional-order sliding mode control (AFFSMC) of DFIG wind turbines (DWTs) under model uncertainty in finite time. A fractional-order sliding surface is first constructed to develop the concept. A robust terminal adaptive sliding mode controller is then designed for pitch angle control of wind turbine to achieve finite-time stability at high wind speeds to regulate the produced electric power in Zone III of the turbine’s working range. This is all with this assumption that there is no any information about the dynamics of the turbine due to the significant uncertainties. Through the use of a stable adaptive law, the vector of the wind turbine’s unknown dynamic parameters is approximated in this method. An observer is also proposed to estimate both turbine speed and external disturbances term. The closed-loop system’s finite-time stability study and the finite-time convergence of the turbine output were both carried out using the dynamic model of the system and the proposed Lyapunov theory. Some numerical examples are also presented together with a comparison to the standard integer sliding mode control to demonstrate the correctness of the control law.

New method for stability of probabilistic Boolean networks with inequality constraints

This paper studies the stability of probabilistic Boolean networks (PBNs) with state inequality constraints by establishing a new algebraic representation. On one hand, combining with the semi-tensor product (STP) of matrices and the law of total expectation, the algebraic representation of PBNs is established. On the other hand, based on the STP of matrices, an algorithm is proposed to determine the solution set of the state inequality constraints. Then, based on the algebraic representation and the inequality constrained solution set, a new form of transition probability matrix is constructed for PBNs. Finally, by the proposed transition probability matrix, new criteria are proposed for the finite-time stability with positive probability of PBNs. Several simulation examples are used to illustrate the effectiveness of the obtained results.

Generalized Homogeneous Formation Control for Unicycle Multi-Agent Systems

In this paper, the formation control problem for unicycle multi-agent systems is considered. The design of a generalized homogeneous leader–follower formation control protocol is studied which shows that such a control protocol can be obtained by “upgrading” from the classical linear control. With this proposed control protocol, a finite-time stability of the formation error is ensured if the acceleration of the leader is bounded by some known value. In addition, if the leader acceleration is unknown but bounded, the robust formation is achieved by ensuring the formation error’s input-to-state stability. Simulations are carried out to verify the effectiveness of the proposed control protocol.

New delay‐dependent finite‐time stabilization of Takagi–Sugeno fuzzy approaches for delayed nonlinear systems

AbstractIn this paper, the finite‐time stability and stabilization of nonlinear systems with delays is studied, via a Takagi–Sugeno approach. By using a novel Lyapunov–Krasovskii functional and introducing some fuzzy free‐weighting matrices, sufficient conditions are derived, for bounded and differentiable time‐varying delays in terms of an upper bound of the delay derivatives. Then, we achieve closed‐loop stabilization in finite time through an efficient parallel distributed compensation design. The sufficient conditions are formulated as linear matrix inequalities to achieve the desired performance. Finally, the proposed methodology is applied to various case studies, highlighting its significance.

Finite-time and fixed-time stability for nonlinear systems via aperiodically intermittent control

Finite-time and fixed-time stability for nonlinear systems via aperiodically intermittent control

Finite-time output feedback control for a class of stochastic low-order nonlinear systems with output function

This paper studies the problem of finite-time output feedback stabilisation for a class of stochastic low-order nonlinear systems with output function. Under the assumption that output function is continuous, by generalising the adding a power integrator technique, constructing a new implementable reduced-order observer and using the stochastic finite-time stability criterion, the maximal open sector Ω of output function is given. As long as output function belongs to any closed sector included in Ω, an output feedback controller can be developed to guarantee finite-time stability in probability of the closed-loop system. A simulation example is provided to verify the effectiveness of the proposed design method.

Finite Time Stability Analysis and Feedback Control for Takagi–Sugeno Fuzzy Time Delay Fractional-Order Systems

This study treats the problem of Finite Time Stability Analysis (FTSA) and Finite Time Feedback Control (FTFC), using a Linear Matrix Inequalities Approach (LMIA). It specifically focuses on Takagi–Sugeno fuzzy Time Delay Fractional-Order Systems (TDFOS) that include nonlinear perturbations and interval Time Varying Delays (ITVDs). We consider the case of the Caputo Tempered Fractional Derivative (CTFD), which generalizes the Caputo Fractional Derivative (CFD). Two main results are presented: a two-step procedure is provided, followed by a more relaxed single-step procedure. Two examples are presented to show the reduction in conservatism achieved by the proposed methods. The first is a numerical example, while the second involves the FTFC of an inverted pendulum, which exhibits both symmetrical dynamics for small angular displacements and asymmetrical dynamics for larger deviations.

Finite-time optimal control for a class of nonlinear systems with performance constraints via critic-only ADP: Theory and experiments

This paper addresses the optimal control problem within the framework of adaptive dynamic programming (ADP) for a class of nonlinear systems subjected to performance constraints. A new finite-time optimal control scheme is developed to stabilize the system by using the critic-only neural network ADP method. Compared with the existing ADP-based optimal control methods with uniformly ultimately bounded stability, the provided control scheme ensures that the controlled system's state and neural network weight estimation error are finite-time stable. It can ensure optimality, prescribed performance, and finite-time stability of the closed-loop control system simultaneously through an integration of ADP, the prescribed performance control technique, and Lyapunov theory. The designed adaptive neural network weight update law can relax the persisting excitation condition. The proposed control scheme is implemented on a robotic experiment platform to achieve trajectory tracking and verify its effectiveness.

Robust finite-time output feedback stabilisation for a class of uncertain planar systems with asymmetric output constraints

This paper considers the finite-time output feedback stabilisation (FTOFS) problem for a class of uncertain planar systems with asymmetric output constraints. The presence of unknown control coefficients, unknown measurement sensitivity and asymmetric output constraints makes the system under consideration essentially different from those in the existing related works. By constructing a new barrier Lyapunov function and applying homogeneous system theory, a simple proportional-derivative like finite-time output feedback controller is explicitly constructed, which only utilises the output information. A rigorous proof demonstrates that not only the closed-loop system is finite time stable, but also the requirement of asymmetric output constraint can be achieved. The novelty of the control approach lies in that it is capable to handle the FTOFS problem for uncertain planar systems with or without asymmetric output constraints in a unified manner, without changing the control structure. The efficiency of the proposed theoretical results are confirmed by simulation results.

Finite-Time Adaptive Control for Electro-Hydraulic Braking Gear Transmission Mechanism with Unilateral Dead Zone Nonlinearity

Autonomous vehicles require more precise and reliable braking control, and electro-hydraulic braking (EHB) systems are better adapted to the development of autonomous driving. However, EHB systems inevitably suffer from unilateral dead zone nonlinearity, which adversely affects the position tracking control. Therefore, a finite-time adaptive control strategy was designed for unilateral dead zone nonlinearity. Initially, the unilateral dead zone nonlinearity was reformulated into a matched disturbance term and an unmatched disturbance term to reduce the adverse effects of disturbances, thereby enhancing system controllability. Then, the “complexity explosion” in the design of the control strategy was avoided by command filtering, and the design process of the controller was simplified. Furthermore, the finite-time control theory was employed to boost the system’s convergence speed, thereby enhancing control performance. In order to ensure the stability of the system under the dead zone disturbance, the unknown disturbance terms were estimated. The stability of the control strategy was validated through the finite-time stability theorem and the Lyapunov function. Eventually, simulations and hardware-in-the-loop (HIL) experiments validated the feasibility and availability of the finite-time adaptive control strategy.

Finite-Time Stability Analysis and Stabilization of Switched Affine Systems via an Event-Triggered Strategy.

This article investigates the finite-time control problem of the switched affine systems via an event-triggered strategy. It is well known that the existence of affine terms brings great difficulties in analysis of the finite-time property of such systems. Furthermore, the design of the globally feasible event-triggered mechanism (ETM) under a finite-time control framework is challenging. Thus, a two-step hybrid control scheme is proposed in this article. The first step focuses on the event-triggered finite-time control for practical stability, while the second step aims to achieve finite-time stabilization. Particularly, in step one, by constructing the intersection between the affine term's threshold and feasible state region of the established ETM, it is verified that the Zeno behavior can be excluded. Thereafter, an affine state-dependent switching law and sufficient conditions are provided for achieving practical stability. Meanwhile, an estimation for the practical settling time to enter the bounded set is provided. In step two, the criteria for finite-time stabilization of the considered systems are further presented, and an overall settling-time upper bound is derived. Finally, a numerical example is illustrated to demonstrate the effectiveness of our proposed method.

Enhanced Impedance Control of Cable-Driven Unmanned Aerial Manipulators Using Fractional-Order Nonsingular Terminal Sliding Mode Control with Disturbance Observer Integration

The article presents a novel control strategy for cable-driven aerial manipulators (UAMs) aimed at enhancing impedance control during contact operations in complex environments. A fractional-order nonsingular terminal sliding mode control (FONTSMC) integrated with a disturbance observer (DOB) is proposed to improve the robustness and precision of the UAM under lumped disturbances. This developed approach utilizes the flexibility of fractional calculus, the finite-time stability of nonsingular terminal sliding mode, and the real-time disturbance estimation capabilities of the DOB to ensure smooth and compliant contact interactions. The effectiveness of the proposed control strategy is validated through comprehensive simulation studies, which demonstrate significant improvements in control performance, stability, and disturbance rejection when compared to traditional methods. The results indicate that the FONTSMC-DOB framework is highly suitable for complex aerial manipulation tasks, offering both theoretical and practical insights into the design of advanced control systems for UAMs.

Further finite-time stability analysis of neural networks with proportional delay

Different from fixed delays between neurons, proportional delay is a time-varying unbounded delay. In this paper, the issue of finite-time stability of fractional-order neural networks with proportional delay is investigated. To address the proportional delay terms in the system, a new Gronwall-type inequality with delay is proposed. Based on this inequality, order-related criterion for finite-time stability of fractional-order neural networks with proportional delay is obtained. Finally, some numerical experiments demonstrate the effectiveness and superiority of the results.

Collaborative attitude stabilization and distributed vibration suppression of satellite with ultra–large flexible antenna

Large flexible radar satellites are widely used in space–based remote sensing for wide–area target observation and high–capacity information transmission. To achieve accurate earth observation and structural stability of an ultra–large flexible satellite in hundred–meter length concurrently, this paper presents two–time–scale collaboration for attitude stabilization and vibration suppression. First, the coupling dynamic model of the satellite with ultra–large flexible antenna is established under space disturbances. Next, singular perturbation with boundary layer correction is employed to decompose attitude and vibration controls in different time scales, respectively. Given the respective decoupling models, the slow subsystem employs an angles–only terminal sliding–mode controller with adaptive switching and input saturation to accomplish high–robustness triaxial attitude stabilization in finite time. For the fast subsystem, distributed piezoelectric actuators with leader–follower consensus and feedback control are applicable to rapid and stable vibration suppression of the ultra–large structure. Finally, simulation results validate the effectiveness and superiority of these control methods on the satellite, where collaborative control effects on multiple key indices including attitude and vibration control accuracy and settling time are significant. This work facilitates high–accuracy and –stability collaborative control of future ultra–large satellites.

Fuzzy adaptive finite-time formation control of unmanned ground vehicles with performance and feasibility constraints

This paper investigates the problem of fuzzy adaptive finite-time formation tracking control for unmanned ground vehicles (UGVs) systems with two different constraints. By utilizing the distance tracking error between the actual trajectory and the desired trajectory of each UGV, as well as the constraints of bearing angle, to achieve the performance and feasibility constraints, respectively. Furthermore, the fuzzy logic systems (FLSs) are used to approximate unknown nonlinear functions. Due to the limitations of the field of view and communication distance of UGVs, the controller is designed by using finite time stability theory and universal barrier function. Under the proposed control scheme, the stability of the closed-loop system can be ensured, feasibility and performance constraints are also achieved. Finally, the effectiveness of the proposed control design is verified through simulation results.

Finite-time SMC-based admittance controller design of macro-micro robotic system for complex surface polishing operations

In the field of robotic polishing, achieving uniform material removal typically involves addressing the issue of constant contact force control. However, multi-source external disturbances in the polishing scenarios of complex workpiece surfaces can severely affect the robot’s force control accuracy. To enhance the responsiveness and disturbance rejection capabilities of robots in the compliant polishing process, this paper proposes an adaptive admittance controller with practical finite-time stability. A virtual control input is introduced into the basic admittance control framework in light of the state space theory, aiming to provide flexibility for common adaptive law designs. On this basis, a robust sliding mode control (SMC) algorithm is proposed to suppress external disturbances. The force tracking error is theoretically proven to achieve finite-time convergence when applying the proposed control strategy. Experimental results across various polishing scenarios demonstrate that, compared with the existing admittance control strategies, the proposed method can reduce fluctuations of the polishing force and improve the surface quality, thus verifying its effectiveness.

Finite-time ontractive stability for Fractional-Order Nonlinear Systems with delayed impulses: Applications to neural networks

This paper deals with finite-time stability (FTS) and finite-time contractive stability (FTCS) criteria of fractional-order nonlinear systems (FONSs), where the state of the systems consists of a finite number of delayed impulsive instants. To achieve these results, we have extended the theories on FTS and FTCS criteria from integer-order NSs to fractional-order systems. Employing the fractional-order Lyapunov stability theory, the sufficient conditions of the above-mentioned stability criteria are derived for a class of FONSs with state-dependent delayed impulses. Then, to ensure the applicability of the proposed results, we have analyzed the desired performances for several neural network (NN) models, such as non-autonomous NNs (NANNs), Cohen-Grossberg NNs (CGNNs), switched NNs (SNNs) and Bidirectional associative memory NNs (BAMNNs). Finally, four representative numerical examples are illustrated to demonstrate the assurance of the obtained stability conditions of the respective state-dependent impulsive fractional-order NNs (FONNs).

Finite-Time Stability Properties of Lur'e Systems With Piecewise Continuous Nonlinearities

Finite-Time Stability Properties of Lur'e Systems With Piecewise Continuous Nonlinearities

Finite-time Stabilization of Fractional-order Impulsive Switched Systems With Saturated Control Input

Finite-time Stabilization of Fractional-order Impulsive Switched Systems With Saturated Control Input