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This paper proposes a finite-time integral-line-of-sight (FTILOS)-based path following control scheme for 4 degree-of-freedom (4DOF) underactuated unmanned surface vehicles (USVs) in the presence of uncertain dynamics and environmental disturbances. This scheme can be divided into a guidance module and a control module. In the guidance module, a way-point-based FTILOS is proposed to address the underactuated issue and to generate a desired heading angle. Further, benefiting from the robustness of δ -modification, the saturation risk of the integral function is avoided, and the finite-time stability is realized. In the control module, with the aid of the FTILOS guidance strategy, under the design framework of backstepping, an adaptive neural control solution is proposed by combining the adaptive neural network (NN) approximation technique and the virtual parameter learning approach. To reduce the data transmission burden in the controller-to-actuator (C-A) channel, a novel self-triggered mechanism (STM) is introduced in the controller-actuator channel. Based on the Lyapunov theorem, the boundedness of all signals in the closed-loop control system are verified. Finally, the effectiveness of the proposed scheme is confirmed by the simulation studies. • An improved ILOS guidance strategy is proposed, which realizes finite-time stability. • Utilizing the NNs approximation technique and incorporating the virtual parameter learning approach, an adaptive neural control solution is developed for path following control of 4DOF underactuated USVs. • A STM is introduced into the USV path following control, which addresses the problem of continuous monitoring of triggering conditions in the ETM. [ABSTRACT FROM AUTHOR]

Aiming at the problem that multiple Unmanned Aerial Vehicles (UAVs) attack the stationary target cooperatively under time-varying velocity, the cooperative guidance law with finite time convergence on two-dimensional plan and the three-dimensional cooperative guidance laws with impact time constraint are designed separately in this paper. Firstly, based on the relative motion equation between UAV and target on two-dimensional plane, the time cooperative guidance model of multiple UAVs is established. Then based on the consistency theory and graph theory, a distributed time cooperative guidance law is designed, which can ensure that the impact time of all UAVs can be quickly consistent in a limited time. Next, the cooperative guidance problem is expanded from two-dimensional plane to three-dimensional space, the motion model between UAV and target in three-dimensional space is established and the expression of time-to-go estimation under time-varying velocity is derived. Finally, according to whether there is the communication among UAVs under the condition of time-varying velocity, a multiple UAVs three-dimensional cooperative guidance law based on desired impact time and a multiple UAVs three-dimensional cooperative guidance law based on coordination variables are designed, respectively. The simulation results show that the cooperative guidance law with finite time convergence on two-dimensional plan and the three-dimensional cooperative guidance law with impact time constraint proposed in this paper are effective, which can both realize the saturation attack under the time-varying velocity.

Abstract We investigate a finite-time synchronization problem of hybrid-coupled delayed dynamical network via pinning control. According to linear feedback principle and finite-time control theory, the finite-time synchronization can be achieved by pinning control with suitable continuous finite-time controller. Some sufficient conditions are given for finite-time synchronization of undirected and directed complex network by applying finite-time stability lemma. Numerical simulations are finally presented to demonstrate the effectiveness of the theoretical results.

The finite-time optimal output regulation problem is investigated in this paper. In order to simplify the design process of linear quadratic finite-time optimal output regulation control, a new information fusion estimation-based optimal output regulation control scheme is proposed. The information fusion estimation-based optimal output regulator converts all information into measurement equations for control input and co-state, and then obtains the optimal estimation of control input by the information fusion estimation scheme. Finally, the proposed control scheme is employed for position and velocity regulator design of a brushless linear DC motor system, and the simulation experiment illustrates the effectiveness of the proposed control strategy. [ABSTRACT FROM AUTHOR]

In this article, the problem of adaptive fuzzy finite-time command filtered control is considered for a class of nonstrict-feedback nonlinear systems. The explosion of complexity problem is dealt with by employing the command filter approach. In order to design a finite-time control scheme, a finite-time semi-global practical stability criterion is first presented. Based on this criterion, by applying the command filter technology and backstepping technique, adaptive fuzzy finite-time tracking control scheme is developed with the help of fuzzy logic systems approximation. Under the presented adaptive control scheme, all the closed-loop variables are semi-global practical finite-time stable and the tracking error goes into an adjustable neighborhood around the origin in a finite time. Finally, simulations are utilized to verify the effectiveness of designed control scheme. [ABSTRACT FROM AUTHOR]

In this paper, we consider the following pseudo-parabolic equation with variable exponents: u t - Δ u - Δ u t + ∫ 0 t g (t - τ) Δ u (x , τ) d τ = | u | p (x) - 2 u. Under suitable assumptions on the initial datium u 0 , the relaxation function g and the variable exponents p, we prove that any weak solution, with initial data at arbitrary energy level, blows up in finite time. [ABSTRACT FROM AUTHOR]

Ordinary differential equations (ODEs) have a wide range of potential applications in science and engineering with regard to nonlinear dynamic systems. Frequently, there is a focus upon locating unique solutions to ODEs, with non-unique solutions being viewed as potentially problematic. However, some have recognized the importance of examining the character of non-unique solutions as well in order to properly understand the behaviour of physical systems. In some areas of engineering, notably control theory, the latter concern has become pressing. In this paper, by studying the asymptotic stability of second-order ordinary differential systems, we present a theorem creatively and prove it strictly by two lemmas. Using the criteria for non-unique solutions of first-order ordinary differential equations at points of equilibrium, we can solve engineering problems effectively. The applicability of this novel approach to the solution of engineering problems is provided through an example relating to the optimization of finite time controllers. [ABSTRACT FROM AUTHOR]

Advanced encryption standard (AES) crypto‐algorithm design can be implemented in software and hardware. No known attacks are available that can break the AES with brute force or cryptanalysis in finite time. However, when the AES is implemented in hardware, test infrastructure such as scan chain, stimuli decompressor, response compactor and built‐in self‐test (BIST) are included in the normal design for making the crypto‐chip easily testable after manufacturing. This test infrastructure is highly susceptible to attacks. The attacker may misuse the scan‐chain content for the retrieval of secret key from AES hardware. In this study, the authors investigated scan‐chain attack based on different distributions of key‐related flip‐flops of AES hardware implementation with X‐tolerant response compactor‐based test infrastructure. The modular exponentiation security scheme as a counter measure against test infrastructure attacks is proposed. In this study, the statistical security analyses are performed with and without the proposed countermeasure in case of AES hardware followed by X‐tolerant test response compactor. The experimental result shows that the proposed countermeasure thwarts the attack with almost constant rate for different distributions of key‐related flops in the scan‐chain, and hence it is not dependent on the nature of scan‐chain architecture design. [ABSTRACT FROM AUTHOR]

In this paper, we mainly investigate the global finite-time event-triggered consensus problem for a class of second-order multi-agent systems with the power of positive odd rational number and quantized control inputs under directed network topology. Under an appropriate assumption, a novel finite-time event-triggered consensus protocol is proposed to reduce the communication burden from the controller to the actuator. Based on the backstepping method, a synthetic trigger function is derived, and it is proven theoretically that the Zeno behavior is avoided for each agent under this trigger condition. Moreover, to avoid the chattering phenomenon caused by unknown input disturbances, the hysteretic quantizers are incorporated to quantize the input signals. It is shown that the proposed finite-time event-triggered consensus protocol enables the local neighbor position error, and the velocity error between any two agents converges toward a small range of the origin in a finite time. Finally, the proposed method is validated through a numerical example. [ABSTRACT FROM AUTHOR]

For linear systems in the controllable canonical form, we introduce a prescribed-time output feedback controller which provides for easy prescription of estimation and stabilization convergence times irrespective of initial conditions and with minimal tuning of the observer and controller parameters. We show that the closed-loop output feedback system is fixed-time globally uniformly asymptotically stable as well as convergent to zero in the prescribed time. Further, we show that a separation principle holds between the prescribed-time controller and the prescribed-time observer provided the scaling power of the time-varying observer gains exceeds the scaling power of the controller gains by twice the order of the system, i.e., provided the observer is fast enough relative to the controller, irrespective of the constant gains of both. [ABSTRACT FROM AUTHOR]

This study deals with the problem of relative motion control with 6 degrees of freedom (6DOF) for spacecrafts without a priori knowledge of the inertia parameters. Considering the system natural couplings, the integrated rotational and translational dynamics of the spacecraft are achieved. By a series of first‐order filter operations, an expression of the parameter estimation error is derived and then used for the design of an integrated finite‐time tracking controller applying adaptive backstepping technique. Proven by the Lyapunov theory, the proposed controller can guarantee that the errors of trajectory tracking and parameter identification simultaneously converge to zero in finite time. Furthermore, to be applied in practice, the controller is adapted for the spacecraft subject to external disturbance and input saturation. Compared with the previous control designs, the proposed control strategy can realise inertia parameter identification together with tracking of command position and attitude in finite time, in the presence of input saturation and external disturbance. The effectiveness of the control law is finally demonstrated by numerical simulations. [ABSTRACT FROM AUTHOR]

For the multiple missiles intercepting a maneuvering target cooperatively, a cooperative guidance method considering a cooperative detection geometry configuration is designed based on the finite-time control theory. For the first-order dynamics of the missiles, a cooperative interception model with detection geometry configuration is established according to the relative motion equations of particles and the principle of cooperative detection. The sufficient conditions for the finite time boundedness of system state and the finite time stability of system input and output are given based on the differential inequality theory. And on this basis, a finite time cooperative guidance method is designed. The proposed method uses the measurement matrix to characterize the dynamic quality of system state and output, and can ensure that the state and output of guidance system are bounded and stable within a finite time interval. The simulated results show that the proposed guidance method can ensure that the LOS separation angle converges to the preset angle, the LOS angular rate converges to zero, and the acceleration does not exceed the maximum physical limit when a target is maneuvering. Compared with proportional navigation and optimal guidance law, the proposed method has the advantages in cooperative detection and guidance. [ABSTRACT FROM AUTHOR]

This paper concentrates on the study of finite time control for nonlinear switched systems. Based on a newly introduced adding a barrier integrator technique, a novel adaptive fuzzy control strategy is proposed for a class of nonlinear switched systems. Compared with the existing adaptive control methods, the proposed method has several distinguishing features. Finite time control: the proposed adaptive control method can solve the exact finite time control problem for the stabilization and some types of tracking issues. Namely, the errors will converge to zero in finite time. For a general tracking problem, the practical finite time control can be achieved. More general systems: the proposed method is suitable for high order nonlinear switched systems with arbitrary switching and unknown control gains. Some strict assumptions on the system dynamics are relaxed. Full state constraints: the proposed method can be utilized to deal with the full state constraints problem. Simple controller structure: the “explosion of the complexity” in the backstepping design is avoided. Singularity free design: the singularity problem is carefully handled during the whole design procedure. Examples are presented to illustrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

Abstract In this paper, we present a finite-time model order reduction method for linear systems via shifted Legendre polynomials. The main idea of the approach is to use finite-time empirical Gramians, which are constructed from impulse responses by solving block tridiagonal linear systems, to generate approximate balanced system for the large-scale system. The balancing transformation is directly computed from the expansion coefficients of impulse responses in the space spanned by shifted Legendre polynomials, without individual reduction of the Gramians and a separate eigenvector solve. Then, the reduced-order model is constructed by truncating the states corresponding to the small approximate Hankel singular values (HSVs). The stability preservation of the reduced model is briefly discussed. And in combination with the dominant subspace projection method, we modify the reduction procedure to alleviate the shortcomings of the above method, which may unexpectedly lead to unstable systems even though the original one is stable. Furthermore, the properties of the resulting reduced models are considered. Finally, numerical experiments are given to demonstrate the effectiveness of the proposed methods. [ABSTRACT FROM AUTHOR]

In this study, the finite‐time cooperative tracking issue for non‐linear multi‐agent systems with stochastic disturbances is addressed. Different from the existing asymptotical stable control, the finite‐time cooperative control can ensure the outputs of agents reach agree in finite time by raising a novel finite‐time stability criterion. The radial basis function neural networks are employed to cope with the unknown non‐linearities caused by the non‐linear non‐strict feedback form. Moreover, this study designs a new adaptive quantised control strategy to reduce communication burden. With such a control scheme, the tracking errors converge to a small area of the origin in finite time. Finally, some numerical simulation results are presented to testify the effectiveness of the approach proposed in this study. [ABSTRACT FROM AUTHOR]

This paper investigates the finite time simultaneous attack problem for a maneuvering target with unknown acceleration when the multiple attackers move slower than the target at the initial stage under a communication network having a spanning tree. Attackers can reach agreement before the precise strike when the upper bound on time to consensus is calculated beforehand. The unknown acceleration of the target can be estimated by a disturbance observer, and a cooperation protocol is designed to decrease chattering. Numerical simulations with comparisons demonstrate the effectiveness and the superiority of the proposed method. [ABSTRACT FROM AUTHOR]

Summary: This paper presents a novel adaptive sliding‐mode control (ASMC) method for Mars entry guidance and the finite‐time convergence in the presence of large uncertainties can be guaranteed. With the help of gain adaptive law, the nonoverestimating value of control gains can be achieved, and then, the chattering can be attenuated by the proposed ASMC method. Meanwhile, the extended state observer is introduced to estimate and compensate for uncertainties and the nonoverestimating problem is resolved further. In addition, the proposed method does not require any knowledge on the upper bound of uncertainty, which yields to be used in practical systems. Finally, the numerical simulation results are given to demonstrate the effectiveness of the proposed guidance law. [ABSTRACT FROM AUTHOR]

In this study, the anti‐swing control is investigated for a suspension cable system of a helicopter subject to external disturbance. First, a disturbance observer is designed to compensate for the effect of the external disturbance in finite time. Next, based on the proposed disturbance observer and the given desired trajectory, a unilateral boundary control law is proposed to eliminate the vibration by using Lyapunov's direct method. Under the designed control scheme, the ultimately boundedness of closed‐loop is guaranteed. Moreover, the vibration range and trajectory tracking error will converge to a small neighbourhood of zero by selecting suitable parameters. Simulation results verify the rationality and validity of proposed control scheme. [ABSTRACT FROM AUTHOR]

This paper develops a unified framework to study the finite-time and fixed-time stabilization (FFTS) of neural networks (NNs) with general activations and external disturbances. A new distributed control algorithm is designed to achieve the goal of FFTS for the NNs with either continuous or discontinuous activations. An upper-bound of the stabilization time is determined based on the control parameters. Numerical simulations are provided to demonstrate the robustness and disturbance rejection of the proposed control algorithm. [ABSTRACT FROM AUTHOR]

The yaw system is one of the important parts of the horizontal axis wind turbines. In this paper, a novel maglev yaw system (MYS) is introduced, a novel robust controller based on nonlinear disturbance observer (NDOB) is proposed to improve the dynamic suspension stability of the MYS in its levitating and landing process. First, the dynamic model of the MYS is built and analyzed as well as the model of the force caused by crosswind exerting on the MYS, and then the mathematical model of the MYS is derived from its dynamic model. Second, since the uncertain internal disturbance originated from the MYS itself exists, in order to realize the finite time convergence and improve the robustness of the MYS, a NDOB‐based robust controller is designed via like nonsingular terminal sliding mode (LNTSM) method with the aid of backstepping design idea (BDI) to guarantee that the system output asymptotically tracks the reference trajectory, and the levitating and landing velocities of the MYS converge to their expectations globally and asymptotically in finite time. Finally, compared the conventional backstepping control (BC), the extensive simulation results show that the proposed robust controller has a better robustness and the MYS can realize smooth and reliable operations in its levitating and landing process in finite time, therefore the novel robust controller is substantiated to be effective and feasible. [ABSTRACT FROM AUTHOR]

A backstepping nonsingular fast terminal sliding mode control with the extended state observer (ESO) is proposed for the uncertain factors of nonlinear spinning missile. Based on Lyapunov stability theory, the virtual control as sliding mode is taken in the backstepping design and then the tracking differentiator (TD) is employed to eliminate the "explosion of terms". In the last step of the backstepping design, nonsingular fast terminal sliding mode control is utilized to drive the angular velocity tracking error to converge to the origin in a finite period of time. To estimate the chattering phenomenon caused by disturbance influence variable in the system, an ESO is applied to estimate and compensate the impact from uncertainties and disturbances. The stability of the closed-loop system is proved. The simulation results show the effectiveness of the proposed control method and the stability of the controller. [ABSTRACT FROM AUTHOR]

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