Finite-time Tracking Problem Research Articles

Decentralized finite-time adaptive neural FTC with unknown powers and input constraints

This paper investigates the finite-time tracking problem of a class of nonlinear interconnected systems, where each subsystem not only is subject to actuator faults but also has unknown system input powers. Based on Lyapunov stability theory and decentralized control method, a novel finite-time adaptive fault-tolerant control (FTC) scheme is proposed such that each tracking error can converge to a small neighborhood of the origin in finite time. Different from the existing works on interconnected systems where the system input powers are assumed to be known and equal to one, the general case where the powers are unknown and larger than one is investigated in this work. Furthermore, input constraints are also applied to avoid actuator damage caused by control signal overshoot and jittering in this work. From theoretical analysis, each tracking error is proven to converge to a small neighborhood of the origin in finite time. Finally, a numerical example is given to demonstrate the validity of proposed control method.

Position and Attitude Tracking Finite-Time Adaptive Control for a VTOL Aircraft using Global Fast Terminal Sliding Mode Control

In this work, the position and attitude tracking finite-time adaptive control problem of a type of vertical take-off and landing (VTOL) aircraft system is studied. Here, the dynamic of the VTOL aircraft is subjected to external disturbances and unknown nonlinearities. Firstly, radial basis function neural networks are introduced to approximate these unknown nonlinearities, and adaptive weight update laws are proposed to replace unknown ideal weights. Secondly, for the errors generated in the approximation process and the external disturbances of the aircraft system, adaptive parameter update laws are presented. After that, based on the designed global fast terminal sliding mode control functions and adaptive update laws, we present the position tracking control laws and the roll angle control law. Then, based on this, the adaptive global fast terminal sliding control laws for the given aircraft system are finally obtained. Meanwhile, the stability of the aircraft control system is proven by using Lyapunov stability theory and designed adaptive control laws. It is not only ensured that the outputs of the aircraft system can track the given trajectories, but also ensured that the tracking errors can converge to approximately zero within a finite time. Finally, the validity of the designed adaptive control laws is verified through three numerical examples. It can be obtained that the finite-time tracking problems of the given aircraft system can be achieved at 18.8766 s and 14.6340 s under the given parameters. The results are consistent with the theoretical analysis. In addition, under the control laws proposed in this work, the aircraft system can achieve tracking after 9.443 s and 9.674 s and the tracking errors are basically close to zero, which is significantly superior to other control methods considered in this work.

Convergence analysis for iterative learning control of fractional-order nonlinear differential inclusion system

This paper considers a class of finite-time tracking problems of fractional-order uncertain system governed by nonlinear differential inclusion. We introduce a Lipschitz continuous condition into the set-valued mapping described by the closure of the convex hull of a set, and design PDγ-type and PIαDγ-type update laws with initial learning mechanisms in open loop and closed loop, respectively. Then, the Steiner-type selector and mathematical analysis tools are used to complete the convergence analysis. Finally, numerical examples are used to verify the validity of the theoretical results, and the tracking performance of system is compared for different values of γ,α and learning laws.

Distributed finite-time neural network observer-based consensus tracking control of heterogeneous underwater vehicles

This note scrutinizes the distributed finite-time tracking problem of heterogeneous multi-agent systems with uncertain dynamics and environmental disturbances. To estimate the exogenous disturbances, an adaptive neural network-based disturbance observer is developed in which the approximation error of the neural network is compensated using adaptation laws. Based on finite-time stability theory, a distributed finite-time observer is proposed for each follower in order to estimate the leader's position. Moreover, an adaptive dynamic sliding mode-based controller is also developed for each follower, which ensures finite-time convergence of the tracking error between the leader and the follower. Incorporating adaptive control into the developed composite control structure leads to reducing the chattering, as well as enhancing the robustness and accuracy. Stability analysis and finite-time convergence of the tracking error are performed using the Lyapunov theory and multiple time scale principle, respectively. Finally, simulations and comparisons are performed in order to verify the effectiveness of the developed control algorithm for a group of autonomous underwater vehicles (AUVs).

Finite-Time Control of a Class of Nonlinear Underactuated Systems with Application to Underactuated Axisymmetric Spacecraft

In this paper, the finite-time control problem of a class of nonlinear underactuated systems is addressed. By using the auxiliary state generated by a time-varying oscillator-like differential equation and constructing a novel Lyapunov-like function, a time-varying dynamic feedback controller is designed for such nonlinear underactuated systems. It is proved that the state of the closed-loop system converges to zero at the finite time and the controls are bounded. As an application, the finite-time tracking problem for underactuated axisymmetric systems is solved. Numerical simulations verify the effectiveness of the proposed methods.

Investigation on energy-effective guidance-to-collision strategies for exo-atmospheric interceptors

This paper aims to investigate energy-effective guidance-to-collision strategies for an exo-atmospheric interceptor producing the normal and axial accelerations independently. According to the utilization of the two accelerations, three interception strategies are possible from the collision geometry and the nonlinear engagement kinematics. A unified form of guidance-to-collision laws realizing these interception strategies is then determined by solving a nonlinear finite-time tracking problem for the heading error based on a specific form of the error dynamics. The characteristics of the proposed guidance-to-collision laws for different interception strategies are analytically analyzed. The results show that the guidance-to-collision strategy using normal and axial acceleration simultaneously is always advantageous in control energy efficiency. Additionally, the characteristic of the guidance-to-collision law for this interception strategy is compared with existing guidance laws. It turns out that the guidance-to-collision law behaves like the true proportional navigation (TPN) guidance in a near-collision course. This fact could provide new insight into the behavior of TPN in the nonlinear engagement kinematics from the collision geometry standpoint. Additionally, analysis results also show that the proposed law is effectively working even in the presence of a large initial heading error compared to TPN due to the nonlinear nature of the proposed method in the collision geometry. Finally, our findings are verified through numerical simulations.

Fuzzy Adaptive Finite-Time Tracking for Hypersonic Flight Vehicles Using Switching Event-Triggered Methodology

The problem of event-triggered fuzzy adaptive finite-time tracking for flexible hypersonic flight vehicles is considered in this work. A new switching event-triggered mechanism is devised to mitigate the unnecessary resources waste in the process of system communication and sampled data computation. Compared with the traditional event-triggered mechanism, an exponential term with regard to tracking error is introduced into the proposed switching event-triggered function, which significantly reduces the frequencies of data transmission. To evade singularity issue typical of traditional recursive finite-time design methods, we introduce a new piecewise switching controller whose continuity and differentiability are ensured everywhere via an appropriate design. Stability of the proposed design is proved using asymmetric barrier Lyapunov functions, which are devised to tackle the fact that the operating regions of the flight state variables are asymmetric in actual engineering. Finally, comparative simulations are designed to illustrate the effectiveness and superiority of the presented methodology.

Control of high-order nonlinear systems under error-to-actuator based event-triggered framework

This paper solves the finite-time tracking problem of a class of high-order nonlinear systems under event-triggered input. Unlike existing event-triggered frameworks based on signal transmission channels from the sensor to the controller or from the controller to the actuator, these developed trigger mechanisms only compare the difference between the signal to be transmitted and the holding signal. By introducing internal trigger conditions and external trigger conditions, a novel error-to-actuator based event-triggered framework is proposed. It further considers the response of the trigger mechanism to system control performance such that the tracking performance of the system can be guaranteed while reducing the number of signal transmissions. In addition, filter-based techniques (such as the dynamic surface control method), for the first time, are utilised to eliminate some strong constraints that exist in the literature for most high-order nonlinear systems. The effectiveness of the proposed approach is evaluated on simulation examples including comparative studies and a practical example.

Robust finite-time tracking for a square fully actuated class of nonlinear systems

In this paper, the robust finite-time tracking problem is addressed for a square fully actuated class of nonlinear systems subjected to disturbances and uncertainties. Firstly, two applicable lemmas are derived and novel nonlinear sliding surfaces (manifolds) are defined by applying these lemmas. Secondly, by developing the nonsingular terminal sliding mode control, two different types of robust nonlinear control inputs are designed to meet and accomplish the aforementioned finite-time tracking objective. The global finite-time stability of the closed-loop nonlinear system is evaluated analytically and mathematically. The proposed control inputs are utilized to tackle and solve two interesting issues containing (a): the finite-time tracking problem of the unified chaotic system and (b): the finite-time synchronization of two non-identical hyperchaotic systems. Finally, based on MATLAB software, two numerical simulations are carried out to illustrate and demonstrate the effectiveness and performance of the proposed robust finite-time nonlinear control schemes.

Output tracker design for uncertain nonlinear sandwich systems with sandwiched dead-zone nonlinearity based on adaptive finite-time control

This paper addresses the adaptive finite-time tracking problem for nonlinear sandwich systems with dead-zone nonlinearity and full state constraints. The existence of the non-smooth dead-zone nonlinearity between the subsystems of the sandwich system makes the controller design as a challenging task. In this paper, a novel adaptive backstepping controller is proposed by employing the finite-time stability theorem and based on the barrier Lyapunov functions and finite-time command filters. The proposed controller guarantees the output tracking of the specified time-varying reference signal with the sufficiently small bounded tracking error in a finite-time. Moreover, all states of the controlled system are confined to predefined compact sets. To verify the theoretical achievements and show the applicability of the proposed method, simulation results are provided for both numerical and practical examples.

Finite-time tracking control for autonomous underwater vehicle based on an improved non-singular terminal sliding mode manifold

This paper investigates the finite-time tracking problem for autonomous underwater vehicles (AUVs) in the presence of external disturbance and modelling uncertainty. A finite-time tracking control scheme is proposed based on an improved non-singular terminal sliding mode manifold. Firstly, in order to achieve finite-time stability and avoid singular problem, a continuous and smooth non-singular terminal sliding mode manifold is designed based on a piecewise function. And then a continuous control law is designed by indirectly estimating the bound of the general uncertainty, to compensate the external disturbance and modelling uncertainty. Based on the Lyapunov stability analysis, it is verified that the tracking error can converge to a certain range near zero in a finite time. Finally, the proposed control scheme is applied to ODIN AUV and compared with another two finite-time tracking controllers. Simulation results show the effectiveness of the proposed control scheme.

PWM-Based Finite-Time Tracking of Switched Buck Power Converters

In this paper, the problem of finite-time tracking is investigated for switched buck power converters based on the pulse width modulation (PWM) technique. For the continuous model, an equivalent continuous controller is solved by the backstepping technique, such that all signals are finite-time stable. PWM-based finite-time tracking with the equivalent control input is proposed for the switched buck converter, such that the tracking error converges to an arbitrarily small neighborhood of the origin in finite time, and the origin of the closed-loop system is practically finite-time stable. Simulation results are given to demonstrate the effectiveness of the proposed schemes.

Continuous Integral Terminal Sliding Mode Control for Double-Layer Peltier System Based on Finite-Time Observer

This paper addresses the finite-time tracking problem for the double-layer Peltier system. Peltier is a semiconductor thermoelectrical transform device. It is widely used in the thermal tactile reappearance area. To expand temperature differences, Peltier is usually used in the form of double layers. There are some uncertain factors such as state coupling, external disturbance, and parameter perturbation in double-layer Peltier. Therefore, it is of great theoretical and practical significance to design a controller with superior performance. To this end, a compound continuous integral terminal sliding mode control strategy is proposed here. Firstly, finite-time disturbance observers are designed for feedforward compensation and evaluating the external disturbances. Secondly, the strong robustness of the sliding mode control enhances the disturbance rejection of the system. The continuous integral sliding mode makes the input continuous and weakens the chattering. Also, the terminal sliding mode improves the convergence speed of the system on the sliding surface significantly. The performance of the proposed method is analyzed through Lyapunov stability analysis, simulations, and experiments. Compared to nonsmooth finite-time control, the continuous integral terminal sliding mode control achieves rapid temperature stability and better disturbance rejection under the same condition of finite-time convergence.

Finite-time adaptive fuzzy command filtered control for nonlinear systems with indifferentiable non-affine functions

This paper mainly addresses the finite-time tracking problem of pure-feedback systems with indifferentiable non-affine functions. A novel adaptive fuzzy finite-time command filtered scheme is proposed by remodeling the non-affine functions. The control scheme consists of the fuzzy logic systems with modified minimal learning parameter technique, the command filtered scheme and the finite-time error compensation system. The finite-time convergences of tracking error and all closed-loop signals are proved by using the finite-time stability theory. The contributions of this paper are that the new controller can achieve finite-time convergence, relax the restriction conditions that the non-affine functions must be derivative and strictly positive or negative and reduce the computational load significantly. Finally, a simulation example is given to validate the effectiveness of the developed control technique.

Finite-time terminal synergetic control of a class of nonlinear systems with unmatched uncertainties

Abstract In this paper, the problem of finite-time tracking for nth-order uncertain nonlinear systems with unmatched uncertainties is addressed. Using a terminal synergetic manifold, a controller is provided to force the tracking error to the origin in finite time in the presence of unmatched uncertainties. With this method, chattering problem is completely removed without defining a new function. Lyapunov theory is used to prove the stability of the proposed method. The proposed controller provides the convergence of finite-time tracking error to zero by suitable performance that is theoretically analysed and proved through simulation.

Finite-Time Control of One Dimensional Crowd Evacuation System

This paper pertains to the study of finite-time control of one dimensional crowd evacuation system. Benefiting from the research of fluid dynamics and vehicle traffic, a one dimensional crowd evacuation system is constructed, whose density-velocity relationship is represented by a diffusion model. In order to deal with the nondirectionality of crowd movement, the free flow speed is chosen as a control variable. Since the control variable is included in a partial derivative, it increases the difficulty of designing the controller. In this paper, finite-time controller is designed, which not only guarantees the effective evacuation, but also obtains the estimation of evacuation time. Then, finite-time tracking problem is solved, which makes the density converge to a given density. Finally, numerical examples illustrate the effectiveness of the controllers.

Distributed finite-time tracking for multiple uncertain mechanical systems with dead-zone input and external disturbances

This paper addresses the distributed finite-time tracking problem for multiple uncertain mechanical systems with dead-zone input and external disturbances. An observer-based adaptive finite-time consensus protocol is designed, which consists of two steps. Firstly, distributed observers are developed such that all the mechanical systems can obtain the leader’s state in finite settling time. Then, based on backstepping method and adding a power integrator technique, the finite-time consensus protocol and appropriate adaptive laws are designed to track the estimated leader’s state. Rigorous proofs show that the tracking errors between each mechanical system and the leader can converge to a small neighborhood of origin in finite time despite the presence of dead-zone nonlinearity and external disturbances. Finally, simulation example is provided to demonstrate the effectiveness of the proposed scheme.

Global saturated velocity‐free finite‐time control for attitude tracking of spacecraft

This study investigates the problem of global finite-time attitude tracking for spacecraft subject to actuator constraints and attitude measurements only. A velocity-free saturated hybrid proportional-derivative (PD) plus spacecraft dynamics (PD+) control is proposed. Benefiting from the hybrid control technique, the unwinding phenomenon is completely avoided and the global stability is achieved. Lyapunov stability theory and homogeneous method are employed to show global finite-time tracking. Advantages of the proposed control include simple and intuitive structure and the absence of velocity measurements, and thus it is ready to implement. An additive feature is that the proposed control is explicitly upper bounded and hence it can assure that actuator constraints will not be violated by selecting the control gains a priori. Simulations are performed to illustrate the effectiveness and improved performance of the proposed approach.

Robust Finite-Time Stabilizers for a Connected Chain of Nonlinear Double-Integrator Systems

In this paper, the robust finite-time stabilization problem is addressed for a wide group of fully actuated nonlinear systems containing dependent double-integrator subsystems in the presence of unbounded uncertainties. Based on the nonsingular terminal sliding mode control, three types of stabilizers are proposed to steer the system states to zero within adjustable convergence finite times. Moreover, several inequalities are obtained to determine the conservative upper bounds for these convergence finite times. To clarify the applicability of the suggested stabilization methods, a finite-time tracking problem for robotic manipulators is discussed and handled by applying three introduced stabilizers. Finally, a numerical simulation related to this tracking problem is provided.

Finite-Time Switching Control of Nonholonomic Mobile Robots for Moving Target Tracking Based on Polar Coordinates

In this paper, finite-time tracking problem of nonholonomic mobile robots for a moving target is considered. First of all, polar coordinates are used to characterize the distance and azimuth between the moving target and the robot. Then, based on the distance and azimuth transported from the sensor installed on the robot, a finite-time tracking control law is designed for the nonholonomic mobile robot by the switching control method. Rigorous proof shows that the tracking error converges to zero in a finite time. Numerical simulation demonstrates the effectiveness of the proposed control method.