Finite-time Control Problem Research Articles

Finite-Time Control for Nonlinear Systems with Time-Varying Delay and Exogenous Disturbance

This paper is concerned with the problem of finite-time control for nonlinear systems with time-varying delay and exogenous disturbance, which can be represented by a Takagi–Sugeno (T-S) fuzzy model. First, by constructing a novel augmented Lyapunov–Krasovskii functional involving several symmetric positive definite matrices, a new delay-dependent finite-time boundedness criterion is established for the considered T-S fuzzy time-delay system by employing an improved reciprocally convex combination inequality. Then, a memory state feedback controller is designed to guarantee the finite-time boundness of the closed-loop T-S fuzzy time-delay system, which is in the framework of linear matrix inequalities (LMIs). Finally, the effectiveness and merits of the proposed results are shown by a numerical example.

Chebyshev neural network-based attitude-tracking control for rigid spacecraft with finite-time convergence

In this paper, the problem of finite-time attitude-tracking control for a rigid spacecraft is addressed. Uncertainties including unknown inertial parameters, external disturbances, actuator failures and saturation constraints are considered. Firstly, a smooth function which is different from the common saturation treatment is presented to deal with the actuator constraints. Secondly, a fast non-singular terminal sliding mode (FNTSM) manifold composed of tracking errors is constructed. To estimate the unknown function in the sliding surface derivative, Chebyshev neural network (CNN) is introduced and thus the strict assumptions on uncertainties in many related works are abolished. By designing the CNN adaptive laws, a new fault-tolerant control scheme is proposed such that the attitude tracking can be achieved within a limited time interval. Compared with the existing CNN-based achievements with finite-time convergence, the approximation errors are proved to be finite-time stable instead of uniformly ultimately bounded (UUB). Finally, simulation experiments are conducted to demonstrate the satisfactory tracking performance of the attitude controller.

Finite-time H∞ control for a class of singular Markovian jump systems subject to actuator saturation

This work considers the finite-time control problem for a class singular Markovian jump delayed systems subject to saturating actuators. By employing local sector conditions and an appropriate Lyapunov function, a observer-based state feedback controller is designed to guarantee that the resulted closed-loop constrained system is mean-square locally finite-time stabilizable. Some sufficient conditions for the solution to this problem are derived in terms of linear matrix inequalities. Finally, two numerical examples are provided to demonstrate the effectiveness of proposed method.

Finite-time trajectory control for a quadrotor aircraft using disturbance observer

In this article, we investigate the problem of finite-time trajectory tracking control for a quadrotor aircraft with unknown external disturbances. To improve convergence rate and disturbance rejection performance, a new composite controller is proposed by integrating finite-time control design and disturbance estimation attenuation technique. Explicit Lyapunov function is given to ensure the finite-time stability of the closed-loop control system. Numerical simulations also show the effectiveness of the proposed method.

Practically Finite-Time Control for Nonlinear Systems With Mismatching Conditions and Application to a Robot System

This paper is concerned with the practically finite-time (PFT) control problem for a class of more general nonlinear systems subject to mismatching time-varying disturbances. Without any extra assumptions on system nonlinearities, a composite controller is developed by introducing a disturbance observer and finite-time control technique. Based on the designed controller and Lyapunov stability theory, the PFT stability of the closed-loop system is strictly verified and proven to be a better convergence performance. Furthermore, as a byproduct of the proposed design method, the disturbance observer-based PFT control for high-order nonlinear systems is also shown to be possible. To the best of the authors’ knowledge, it is the first PFT control result for high-order nonlinear systems with external disturbances. Finally, an application example of a single-link robot system with disturbances and a numerical example are presented to demonstrate the effectiveness of the proposed scheme, respectively.

Command-Filter-Based Adaptive Fuzzy Finite-Time Control for Switched Nonlinear Systems Using State-Dependent Switching Method

The adaptive fuzzy finite-time tracking control problem of a class of switched nonlinear systems is investigated in this study. Fuzzy logic systems are introduced to handle the unknown nonlinear terms in the considered system. To overcome the drawback in the recursive design method, a finite-time command filter is employed. By constructing a new state-dependent switching law and adaptive fuzzy control signal, the existing restrictions on subsystems of switched systems are relaxed, all subsystems of the considered system are allowed to be unstabilizable. To avoid the Zeno behavior, a new hysteresis switching law is derived. It is proven that all states of the closed-loop system are bounded in finite time under the proposed fuzzy finite-time control scheme. Additionally, the proposed control method is extended to a class of more general switched large-scale nonlinear systems. Finally, two examples are provided to verify the developed method's effectiveness.

Adaptive neural finite-time containment control for nonlower triangular nonlinear multi-agent systems with dynamics uncertainties

This paper considers the finite-time containment control problem for nonstrict-feedback nonlinear multi-agent systems (MASs) in the presence of unmodeled dynamics. A new variable separation approach is developed to overcome the difficulty of unknown functions with nonstrict-feedback structure in the backstepping design process. The second-order tracking differentiator is extended to the nonstrict-feedback nonlinear MASs for avoiding the problem of “explosion of complexity”. Neural networks are used to approximate the unknown nonlinear functions. With introducing a dynamic signal, the difficulty from the unmodeled dynamics is successfully solved. And, by introducing a finite-time stability criterion, an new adaptive finite-time containment control scheme is designed, which ensures all signals are bounded. Moreover, the output signals of all followers converge to a convex hull spanned by the outputs of the leaders. Finally, a simulation example illustrates the effectiveness of the developed control scheme.

Practical finite time adaptive robust flight control system for quad-copter UAVs

This paper investigates the practical finite time control problem with uncertain parameters, external disturbances, and input saturation for quad-copter unmanned aerial vehicle systems. Firstly, an adaptive robust controller based on backstepping with fast terminal sliding mode control is designed for the major control loops. Secondly, only four adaptation laws are used to estimate the quad-copter uncertain parameters while a projector algorithm is used to guarantee the estimation within a prescribed range. Thirdly, an adaptive switching gain is developed to compensate the lumped disturbances. Finally, a compensator term is introduced in control design to reduce the adverse effect caused by the input saturation. The proposed control scheme can attenuate chattering phenomenon and guarantee that all states of the closed-loop system are practical finite time stable. The validity of the proposed flight control system is confirmed by using several flight scenarios under various conditions and a comparison study with other works is made showing the effectiveness, robustness, adaptiveness, and energy efficiency of the proposed approach.

Finite-time synchronization of hyperchaotic systems based on feedback passivation

Abstract This paper proposes a scheme to realize finite-time synchronization of hyperchaotic systems using a feedback passivation technique. Although the technique is widely known, its utilization for finite-time control problems is still considered to be new since finite-time passivity has been just recently introduced. The proposed scheme consists of few design steps. First, a feedback is designed such that it yields finite-time stability for the zero-dynamics of the synchronization errors. Then, the synchronization errors is transformed into a finite-time passive system by an additional feedback. Consequently, the finite-time convergence of the synchronization errors is obtained. The hyperchaotic Lu system and a 5D Lorenz-like system are used as examples to demonstrate the effectiveness of the scheme.

Scalable distributed optimal control of vibrating modular structures

A scalable optimal control method for structural vibration mitigation is studied. The method relies on a structure's partitioning that leads to a set of dynamically interconnected subsystems. Each subsystem is operated with an individual subcontroller that collects the local state information and collaborates with the neighboring subcontrollers to estimate a short time prediction of the interconnecting forces defining the subsystem's boundary conditions. Using the extended model that represents the subsystem's dynamics together with the evolution of its boundary conditions, each subcontroller computes the control decision based on the solution to a finite-time horizon optimal control problem. In order to cope with the changes in the boundary conditions, the optimal solution is computed repetitively according to the receding horizon scheme. The method is validated numerically for a cantilever structure equipped with actively controlled electromagnetic actuators and subjected to a variety of initial condition scenarios. The performance of the designed controller is tested by comparisons to the centralized and isolated decentralized controllers. The introduced system partitioning and distributed controller allow performing parallel computing which makes the method fully scalable and applicable to large-scale structures. The computational complexity of the designed distributed control is studied for different settings in the modeling of the subsystem's boundary conditions.

Finite-Time Incremental Passivity and Output Tracking Control for Switched Nonlinear Systems

This paper studies the finite-time incremental passivity of switched nonlinear systems. Then, the established theory is applied to solve the finite-time output tracking control problem of switched nonlinear systems. First, finite-time incremental passivity is firstly defined for switched nonlinear systems. Each subsystem is finite-time incrementally passive during its active time interval. Unlike incremental passivity, the state trajectories of finite-time incrementally passive system with no external supplied energy can converge to each other in finite time. Second, the criterion of finite-time incremental passivity is established. Third, finite-time incremental passivity is shown to be preserved under the feedback interconnection. A composite switching law design method is provided. Under this switching law, the interconnected switched systems can switch asynchronously. Finally, the finite-time output tracking control problem was solved by the established finite-time incremental passivity theory of the switched nonlinear systems, even if the finite-time output tracking control of individual subsytem is not solvable. The effectiveness of the proposed method is verified by an example.

Finite-Time Non-Fragile Extended Dissipative Control of Periodic Piecewise Time-Varying Systems

This paper studies the problem of finite-time non-fragile extended dissipative control for the periodic piecewise time-varying systems. First, based on the time-varying Lyapunov matrix and the matrix polynomial condition, a sufficient condition of finite-time boundedness for periodic piecewise time-varying subsystem is derived, and the finite-time extended dissipative performance is then analyzed. Furthermore, considering two types of time-varying controller perturbations, the non-fragile controllers are developed, which can guarantee the finite-time boundedness of periodic piecewise time-varying systems and satisfy the extended dissipative performance at the same time. Finally, numerical examples demonstrate the effectiveness of the proposed methods.

Robust finite-time control of impulsive positive systems under ℒ1-gain performance

This paper is concerned with robust finite-time ℒ1-gain control problem for impulsive positive systems (IPSs). By adopting the average impulsive interval technique, sufficient conditions ensuring the finite-time boundedness of IPSs under ℒ1-gain characterization are formulated. The design of a feedback controller is also addressed to make the closed-loop system be positive, finite-time bounded (FTB), and have ℒ1-gain characterization. Results are presented in the form of linear programming (LP) inequalities. Finally, a numerical example is given to demonstrate the efficiency of the proposed design.

Adaptive Fuzzy Finite-Time Tracking Control of Uncertain Non-Affine Multi-Agent Systems With Input Quantization

In this paper, the finite-time tracking control problem of a class of multi-agent systems with nonaffine functions and uncertain nonlinearity is investigated, which is different from the existing on high-order multi-agent systems with pure feedback forms. The multi-agent systems considered in this paper, moreover, the nonaffine functions and uncertain nonlinearities are completely unknown, and the input of each follower agent is quantized through a hysteresis quantizer. Based on the help of the fuzzy logic systems approximator, an adaptive fuzzy finite-time tracking control protocol with adaptive update laws is presented by the backstepping technique. On the basis of the finite-time stability strategy and Bhat and Bernstein theorem, the finite-time stability of designed control protocol is fully analyzed. Under the proposed control protocol, it is indicated that the tracking error of each follower agent can press on a small neighborhood in a finite time. Finally, the effectiveness of designed control protocol in this paper is analyzed by numerical examples.

Observer-Based Adaptive Finite-Time Tracking Control for a Class of Switched Nonlinear Systems With Unmodeled Dynamics

This paper investigates the adaptive finite-time tracking control problem for a class of switched nonlinear systems with unmodeled dynamics. In practical applications, switched systems usually possess unfavourable factors, such as unmeasured states and unmodeled dynamics both of which are taken into account in this paper. A dynamic signal defined with a special property is introduced in this paper to improve control performance while garanteeing stability of the controlled system. By designing an observer, a finite-time adaptive output-feedback tracking controller is constructed via the backstepping technique. Then, the finite-time stability problem of the considered systems is studied. It is shown that all the signals in the closed-loop system are semi-globally uniformly finite-time bounded (SGFUB), and the observer errors and tracking errors can be regulated to a small neighborhood of the origin by choosing appropriate parameters. It is noted that, the design process is less complex than some existing results on tackling control problems of nonlinear systems with unmodeled dynamics. In the example, the simulation result testifies the effectiveness of the proposed method.

Command-Filtering-Based Adaptive Finite-Time Tracking Control for Ball and Plate System

The finite-time tracking control problem is studied for non-strict feedback ball and plate systems considering friction, coupling term and external disturbance comprehensively. An adaptive finite-time tracking control strategy based on command filtering is proposed, and the adaptive neural finite-time tracking controller is given for the ball and plate system with unknown input saturation. The designed controller can guarantee that the tracking error of the system can converge to a small neighborhood of the origin within finite time, and all signals in the closed loop system are bounded in the finite time. Finally, a simulation for the designed controller is given, and the simulation results verify the effectiveness and superiority of the proposed control scheme.

Finite-time fuzzy output-feedback control for $ p $-norm stochastic nonlinear systems with output constraints

<abstract> <p>This paper investigates the finite-time control problem of $ p $-norm stochastic nonlinear systems subject to output constraint. Combining a tan-type barrier Lyapunov function (BLF) with the adding a power integrator technique, a fuzzy state-feedback controller is constructed. Then, an output-feedback controller design scheme is developed by the constructed state-feedback controller and a reduce-order observer. Finally, both the rigorous analysis and the simulation results demonstrate that the designed output-feedback controller not only guarantees that the output constraint is not violated, but also ensures that the system is semi-global finite-time stable in probability (SGFSP).</p> </abstract>

Finite-time Control for Takagi-Sugeno Fuzzy Systems with Time-varying Delay

This paper focuses on the problem of finite-time control for Takagi-Sugeno (T-S) fuzzy systems with time-varying delay and norm-bounded disturbance. By constructing a new augmented Lyapunov-Krasovskii functional, a delay-dependent finite-time boundedness criterion is derived for the T-S fuzzy time-delay system by aid of the auxiliary function-based integral inequalities and the reciprocally convex combination technique. Then, based on the parallel distributed compensation scheme, a state feedback controller is designed to ensure finite-time boundness of the closed-loop T-S fuzzy system, which can be obtained by solving a set of linear matrix inequalities (LMIs). Finally, two numerical examples are given to demonstrate the effectiveness and advantages of the proposed results.

Annular finite-time stability analysis and synthesis of stochastic linear time-varying systems

In this paper, we investigate some finite-time control problems for stochastic linear time-varying systems, described by an Itô type differential equation. In particular, the annular stochastic finite-time stability control problem is dealt with. In this context, it is required that the norm of the state variables remains bounded between an inner and an outer ellipsoid, during a finite-interval of time. The first contribution of the paper consists of two sufficient conditions for stability, which are derived by exploiting an approach based on time-varying quadratic Lyapunov functions. The first condition requires the solution of two generalised differential Lyapunov equations; the latter the existence of a feasible solution to a pair of differential linear matrix inequalities. As particular cases, we obtain sufficient conditions for stochastic finite-time stability (in this last case, the lower ellipsoid collapses to the origin). From the analysis conditions, a sufficient condition is derived for the annular stochastic finite-time stabilisation via both state and output feedback. Some numerical examples illustrate the application of the proposed methodology and show that our approach attains less conservative results than those obtainable with the existing literature. Moreover, an application of the annular stochastic finite-time stability approach to the stabilisation problem of a satellite with respect to the geomagnetic field is presented.

Adaptive finite-time prescribed performance control of switched nonlinear systems with unknown actuator dead-zone

ABSTRACTThis paper focuses on the adaptive finite-time tracking control problem for a class of nonstrict-feedback switched nonlinear systems with unknown nonsymmetric actuator dead-zone. By utilising a novel finite-time performance function (FTPF), the finite-time prescribed performance control (FTPPC) algorithm is first proposed for the considered system. In this design, the neural networks (NNs) are directly utilised to cope with the completely unknown nonlinear functions of the systems. Different from the existing results, the proposed scheme is able to guarantee that the tracking error converges to a prescribed zone at a finite-time and all the signals of the closed-loop system remain semi-globally practical finite-time stable (SGPF-stable). Simulation results are offered to illustrate the feasibility of the newly designed scheme.