Practical Finite-time Stability Research Articles

Flight quality characteristics and observer-based anti-windup finite-time terminal sliding mode attitude control of aileron-free full-wing configuration UAV

This paper evaluates the flight quality of an aileron-free full-wing configuration UAV and proposes a highly robust attitude controller considering the typical control problems (i.e., manipulation saturation, coupling, susceptibility to the disturbance, nonlinearity, and uncertainty) of the aileron-free full-wing configuration UAV. First, the flight quality characteristics are analyzed through the change of the flight modes at different trim state points in the flight envelope. Then, the back-stepping method is introduced for decoupling and systematic control law design. Based on the Lagrange multiplier approach, the pseudoinverse control allocation is adopted to realize command decoupling and acquire the minimal 2-norm control output. In order to improve the robustness and control accuracy of the controller, a novel continuous finite-time terminal sliding mode control scheme with adaptive law is designed, which has the virtue of suppressing the chattering and avoiding singularity. In addition, an anti-windup compensator (AWC) is developed to ensure the stability of the flight state under manipulation saturation and make the manipulation output exit the saturation region quickly. To further solve the problem that the aileron-free full-wing configuration UAV is susceptible to disturbances, an adaptive super-twisting disturbance observer (ASTDO) is designed to estimate and compensate the uncertain compound disturbance including the uncertain time-varying disturbance and nonlinear dynamic term to improve control performance. The proposed observer can suppress chattering, adjust gain parameters adaptively and have high observation accuracy. Based on the Lyapunov stability theorem, the anti-windup compensation variable in the AWC and the disturbance estimation error in the ASTDO can gradually converge to neighborhoods of the equilibrium points in finite time. Moreover, the practical finite-time stability of the closed-loop control system is proved. According to the flight quality evaluation, the aileron-free full-wing configuration UAV has poor flight quality at the boundary of the flight envelope and exhibits inherent longitudinal high-frequency oscillation characteristics. The simulation results demonstrate that the designed ASTDO-AWFTTSMC guarantees strong robustness, high accuracy, and fast convergence speed for attitude tracking, solves the saturation problem and realizes state decoupling and manipulation decoupling. Moreover, the designed controller overcomes the adverse effects of disturbance, nonlinearity, and uncertainty, greatly suppresses the longitudinal high-frequency oscillation and still exhibits excellent control performance at the flight state points on the flight envelope boundary.

Practical finite-time stability of switched nonlinear time-varying systems based on initial state-dependent dwell time methods

This paper considers the problem of practical finite-time stability (PFTS) for switched nonlinear time-varying (SNTV) systems. Starting with nonlinear time-varying (NTV) systems, a new sufficient condition is proposed to verify the PFTS of systems by using an improved Lyapunov function. Then, the results obtained are extended to study the PFTS of SNTV systems. Two stability conditions are proposed for SNTV systems under arbitrary switching, moreover, the time and region of convergence are also given. Furthermore, an initial state-dependent dwell time method is introduced to study the PFTS of SNTV systems. Three stability conditions are proposed by using the methods of initial state-dependent minimum dwell time (ISD-MDT) and initial state-dependent average dwell time (ISD-ADT), respectively. The comparisons between the obtained results and the existing results are also given, and the obtained results are extended to impulsive switched nonlinear time-varying (ISNTV) systems. Finally, a numerical example is provided to illustrate the theoretical results.

Command-filter-based adaptive finite-time consensus control for nonlinear strict-feedback multi-agent systems with dynamic leader

An adaptive finite-time consensus control method is investigated for nonlinear strict-feedback multi-agent systems that contain unknown parameters and a dynamic leader with both input and output. By using command filters, the “explosion of complexity” phenomenon in traditional backstepping technique can be avoided. The filter errors can be compensated by introducing compensating signals. Adaptive finite-time controllers are constructed by a backstepping technique, command filters, and compensating signals. In addition, the consensus performance and stability of closed-loop systems can be guaranteed in finite time basd on a practical finite-time stability criterion. Finally, a simulation example demonstrates the feasibility and effectiveness of the proposed adaptive finite-time consensus control method.

Observer-based adaptive sliding mode control for steer-by-wire systems with event-triggered communication

This paper proposes an event-triggered adaptive sliding mode control for the steer-by-wire (SbW) system subject to unavailable state, time-varying disturbance, and limited communication resources. Firstly, an adaptive state observer is proposed to estimate the unmeasured state of the SbW system. The uncertain nonlinearity and the time-varying can be estimated by the adaptive fuzzy logic system and the disturbance observer, respectively. Then, considering the limited communication resources, an even-triggered adaptive sliding mode control is proposed for the SbW system. The key advantage is that the proposed control scheme can offset the observation error and the event-triggering error. Much importantly, the high-frequency switching function is nested in the control input without increasing the input–output relative degree of the controlled system, such that the chattering-free control input can be obtained. Finally, theoretical analysis shows that the practical finite-time stability of the closed-loop SbW system can be saved, and communication resources in the controller-to-actuator channel can be saved while avoiding the Zeno-behavior. Numerical simulations and experiments are given to evaluate the effectiveness of the proposed scheme.

Adaptive type-2 fuzzy sliding mode control of steer-by-wire systems with event-triggered communication

The steering-by-wire (SbW) system is one of the main subsystems of automatic vehicles, realizing the steering control of autonomous vehicles. This paper proposes an event-triggered adaptive sliding mode control for the SbW system subject to the uncertain nonlinearity, time-varying disturbance, and limited communication resources. Firstly, an event-triggered nested adaptive sliding mode control is proposed for SbW systems. The uncertain nonlinearity is approximated by the interval type-2 fuzzy logic system (IT2 FLS). The time-varying disturbance, modeling error, and event-triggering error can be offset by robust terms of sliding mode control. The key advantage is that the high-frequency switching of sliding mode control only appears on the time derivate of control input without increasing the input-output relative degree of closed-loop SbW systems, such that the chattering phenomenon can be eliminated. Finally, theoretical analysis shows that the practical finite-time stability of the closed-loop SbW system can be achieved, and communication resources in the controller-to-actuator channels can be saved while avoiding the Zeno-behavior. Numerical simulations and experiments are given to evaluate the effectiveness of the proposed method.

Event-Triggered Adaptive Higher-Order Sliding Mode Tracking Control for Steer-by-Wire Systems

Abstract The model uncertainty of the steer-by-wire (SbW) system and the limitation of communication bandwidth will have a negative effect on its control performance. For this reason, this paper proposes an event-triggered high-order sliding mode control for uncertain SbW systems. First, to save communication and computing resources, an event-triggering mechanism that depends on the system state is proposed for the SbW system, such that both communication and computing resources can be saved. Second, an event-triggered adaptive higher-order sliding mode (ET-AHOSM) control is proposed for the closed-loop SbW system. The assumptions about the global Lipschitz of nonlinearity and the a priori bounds of the disturbance are no longer required in the control design. Much importantly, the control input continuity can be guaranteed even there is the event-triggering communication in the controller-to-actuator channel. Theoretical analysis shows that the global practical finite-time stability of the closed-loop SbW system can be obtained while avoiding Zeno behavior of the event-triggered control system. Finally, numerical simulation and experiments show that the designed control method can reduce more than 1/2 of the calculation and communication resources while ensuring satisfactory tracking accuracy.

Neural network controller design for fractional-order systems with input nonlinearities and asymmetric time-varying Pseudo-state constraints

Abstract This article considers the neural adaptive control issues of a category of non-integer-order non-square plants with actuator Nonlinearities and Asymmetric Time-Varying pseudo-State Constraints. First, the original non-square non-affine system with input nonlinearities is transformed into an equivalent affine-in-control square model by defining a set of auxiliary variables and by employing the mean-value theorem. Second, Neural networks and Nussbaum functions are exploited to obviate the requirement of a complete knowledge of the system dynamics and the control directions, respectively. Third, a novel adaptive dynamic surface control method based on Caputo fractional derivative definitions and fractional order filters is developed to overcome the “explosion of complexity” problem in the traditional backstepping design process and to determine the parameter update laws and control signals, concurrently. Then, Asymmetric Barrier Lyapunov Functions with error variables are adopted to ensure the uniform stability of the closed-loop system and to prevent the violation of the full pseudo-State constraints. The novelties and contributions of this article are: (1) through the introduction of new technical Lemmas and corollaries, existing control design and stability theories linked to integer-order square systems are developed and extended to non-square non-integer-order ones. (2) all signals, including variables and errors in the closed-loop system are semi-global practical finite-time stability whereas the the tracking errors are asymptotically driven to zero without transgression of the constraints. Finally, the effectiveness and potential of the proposed control approach are substantiated by two example simulations.

Disturbance-observer-based finite-time adaptive fuzzy control for non-triangular switched nonlinear systems with input saturation

This paper investigates finite-time adaptive fuzzy control for a class of non-triangular switched nonlinear systems with asymmetric input saturation and mismatched external disturbances. Firstly, the mismatched external disturbances and fuzzy approximation errors are regarded as total disturbances of the system, which are estimated accurately via the finite-time exact disturbance observer. Secondly, the prescribed performance function is adopted to constrain the system output to meet the prescribed dynamic properties. To cope with the obstacle arising from asymmetric input saturation, a smooth nonlinear function is applied to approximate the actuator nonlinearity by utilizing the mean-value theorem. Thirdly, on the basis of the fast practical finite-time stability criteria, a finite-time adaptive fuzzy control where the adaptive parameter laws contain fractional-order item is developed. Meanwhile, the stability analysis verifies that all the signals in closed-loop system are bounded and error signals can converge to the prescribed small compact sets in finite time. Finally, a simulation example is included to further demonstrate the effectiveness of the proposed control strategies.

Adaptive Neural Network-Based Finite-Time Online Optimal Tracking Control of the Nonlinear System With Dead Zone.

Considering the uncertain nonstrict nonlinear system with dead-zone input, an adaptive neural network (NN)-based finite-time online optimal tracking control algorithm is proposed. By using the tracking errors and the Lipschitz linearized desired tracking function as the new state vector, an extended system is present. Then, a novel Hamilton-Jacobi-Bellman (HJB) function is defined to associate with the nonquadratic performance function. Further, the upper limit of integration is selected as the finite-time convergence time, in which the dead-zone input is considered. In addition, the Bellman error function can be obtained from the Hamiltonian function. Then, the adaptations of the critic and action NN are updated by using the gradient descent method on the Bellman error function. The semiglobal practical finite-time stability (SGPFS) is guaranteed, and the tracking errors convergence to a compact set by zero in a finite time.

Adaptive Robust Finite-Time Nonlinear Control of a Typical Autonomous Underwater Vehicle With Saturated Inputs and Uncertainties

The problem of finite-time path following control for a typical 6-DOF (degree of freedom) autonomous underwater vehicle (AUV) subjected to parametric and modeling uncertainties, disturbances and unknown saturation nonlinearities is studied and discussed in this article. For the mentioned AUV, finite-time control inputs are designed based on innovative terminal sliding surfaces and several finite-time adaptation laws. By means of the designed adaptation laws, the unknown physical parameters of AUVs, the unknown upper bound of uncertainties, and an unknown parameter of input saturation are estimated. By using the Lyapunov stability theorem, it is proven that designed control inputs are able to ensure and provide the practical finite-time stability for the closed-loop AUV system. Furthermore, it is mathematically demonstrated that the tracking errors (defined for the path following problem of the AUV) converge to the vicinity of zero within an adjustable finite time. Finally, the efficacy of the suggested control scheme is demonstrated by the hardware-in-the-loop OPAL real-time test.

Finite-Time Adaptive Fuzzy Decentralized Control for Nonstrict-Feedback Nonlinear Systems With Output-Constraint

This paper addresses the finite time adaptive fuzzy decentralized control problem for interconnected large scale nonlinear systems in nonstrict feedback forms with output-constraint. The fuzzy logic systems are used to approximate the unknown nonlinear functions and a state observer is constructed to estimate the immeasurable states. In order to deal with the output constraint problem, the barrier Lyapunov function is introduced. By combining backstepping recursion design with a command filter, a finite time fuzzy adaptive decentralized control method is presented. The stability analysis can be obtained based on the finite time Lyapunov stability theory, which demonstrates that the closed-loop system are semi-global practical finite-time stability, the system outputs can track the given reference signals and keep in the given constraint bounds in a finite time. Finally, two simulation examples are provided to elaborate the effectiveness of the presented control scheme.

Finite-time prescribed performance control of switched nonlinear systems with input quantisation

ABSTRACT This paper investigates the finite-time performance control of a class of switched nonlinear systems with input quantisation, where the control input is quantised by a class of sector-bounded quantizers. By introducing a barrier Lyapunov function and a hyperbolic tangent function, a control scheme is proposed to achieve the practical finite-time stability with prescribed performance, and a new compensation is constructed for the effects of quantisation error. Furthermore, the proposed result is extended to the case that the quantisation parameters are unknown, and adaptive laws are proposed which do not require the knowledge on the bounds of these unknown parameters. A simulation example is provided to show the effectiveness of the proposed method.

Adaptive Neural Networks Finite-Time Optimal Control for a Class of Nonlinear Systems

This article addresses the finite-time optimal control problem for a class of nonlinear systems whose powers are positive odd rational numbers. First of all, a finite-time controller, which is capable of ensuring the semiglobal practical finite-time stability for the closed-loop systems, is developed using the adaptive neural networks (NNs) control method, adding one power integrator technique and backstepping scheme. Second, the corresponding design parameters are optimized, and the finite-time optimal control property is obtained by means of minimizing the well-defined and designed cost function. Finally, a numerical simulation example is given to further validate the feasibility and effectiveness of the proposed optimal control strategy.

Adaptive finite-time sliding mode control design for finite-time fault-tolerant trajectory tracking of marine vehicles with input saturation

The increasing interest in marine mechatronic systems and their applications has promoted the development of advanced control algorithms for the trajectory control of marine vehicles including ships, surface vehicles, and underwater vehicles. In this paper, the finite-time fault-tolerant trajectory tracking of fully actuated marine vehicles is investigated in the presence of parametric uncertainties, external disturbances, actuator faults, and input saturation. A novel adaptive finite-time sliding mode control scheme is proposed by combining the homogeneous integral sliding mode manifold, the fast terminal sliding mode control, and the adaptation technique. Rigorous theoretical analysis for the practical finite-time stability of the whole closed-loop system is provided. The proposed control scheme can guarantee the position and velocity tracking errors converge to the small region about zero in finite time even in the presence of actuator faults. To the best of the authors’ knowledge, there are really limited existing controllers can achieve such excellent performance in the same conditions. In addition, the proposed control scheme is structurally simple, model-independent, and continuous with chattering free, which makes it affordable for practical applications. Numerical simulations illustrate the effectiveness and superiority of the proposed control scheme.

Neural Network-Based Finite-Time Command Filtering Control for Switched Nonlinear Systems With Backlash-Like Hysteresis.

This brief is concerned with the finite-time tracking control problem for switched nonlinear systems with arbitrary switching and hysteresis input. The neural networks are utilized to cope with the unknown nonlinear functions. To present the finite-time adaptive neural control strategy, a new criterion of practical finite-time stability is first developed. Compared with the traditional command filter technique, the main advantage is that the improved error compensation signals are designed to remove the filtered error and the Levant differentiators are introduced to approximate the derivative of the virtual control signal. The finite-time adaptive neural controller is proposed via the new command filter backstepping technique, and the tracking error converges to a small neighborhood of the origin in finite time. Finally, the simulation results are provided to testify the validity of the proposed method.

Finite-Time Adaptive Fuzzy DSC for Uncertain Switched Systems

The finite-time adaptive fuzzy tracking control problem for a class of strict-feedback uncertain switched systems is investigated in this paper. Based on fuzzy approximation and adaptive dynamic surface control (DSC) technique, a finite-time adaptive state feedback fuzzy controller is developed via the common Lyapunov functions. Different from the existing works on uncertain switched systems, the DSC control scheme is developed based on a nonlinear filter to solve the “explosion of complexity” problem, and the structure of the proposed fuzzy controller is simple. Under the designed controller, all the signals of the closed-loop system remain semi-globally bounded, and within a finite-time interval, the system tracking error converges to an arbitrarily small region. That is, the semi-globally practical finite-time stability of the controlled system is guaranteed. To show the availability of the presented control scheme, a simulation example is given in this paper.

Command-Filter-Based Finite-Time Adaptive Control for Nonlinear Systems With Quantized Input

This article considers the finite-time adaptive control problem of nonlinear systems with quantized input signal. Compared with existing results, the quantized parameters are unknown and the bound of the disturbance is not required. By utilizing the command filter backstepping method, an adaptive switching-type controller is designed and a novel switching mechanism is also proposed. By regulating the controller parameters online, practical finite-time stability can be guaranteed for the closed-loop system. Finally, a simulation example is given to illustrate the effectiveness of the proposed method.

Adaptive finite-time fuzzy control for nonlinear systems with input quantization and unknown time delays

We investigate the finite-time adaptive control issue for a class of nonlinear systems with quantized input signals and unknown time delays in this paper. In the control design process, the nonlinear terms are approximated by the fuzzy logic systems. A hysteretic quantizer is introduced to avoid chattering in the quantized signals, and the fuzzy state observer is constructed to estimate the unmeasurable states of the system. In order to propose the finite-time control strategy, firstly, a semi-global practical finite-time stability criterion is given. On this basis, a fuzzy adaptive controller is designed by combining the dynamic surface control technology with backstepping method. The controller can not only ensure that the observer and tracking error converge to a small neighborhood of the origin in a finite time, but also keep all the signals in the closed-loop system bounded. Finally, the effectiveness and feasibility of the control method are verified by two simulation examples.

Finite-time adaptive switched gain control for non-strict feedback nonlinear systems via nonlinear command filter

This paper is aimed at developing a finite-time adaptive control for non-strict feedback nonlinear systems with unknown backlash-like hysteresis. First, the adaptive fuzzy systems are applied to identify the unknown functions which contain all the system states. Second, based on the practical finite-time stability criteria, a novel finite-time adaptive switched gain controller via nonlinear command filter is proposed. The stability analysis shows that the tracking error converges to a small region around the origin within a finite time. Meanwhile, all the resulting closed-loop system states are bounded. Finally, simulation examples verify the effectiveness of the designed control scheme.

Event‐triggered practical finite‐time output feedback stabilisation for switched non‐linear time‐delay systems

This study investigates the event-triggered practical finite-time output feedback control for a class of switched high-order non-linear time-delay systems with uncertain control coefficients. A reduced-order observer is first constructed to estimate the unmeasurable states. By adding a power integrator technique, an event-triggered output feedback controller is designed for the nominal system. Subsequently, the constructed observer and controller are scaled with a suitable gain by homogeneous domination approach, which, together with an appropriate Lyapunov–Krasoviskii functional, can render that the uncertain switched high-order non-linear system with time-varying delay is practical finite-time stability. Finally, two examples are provided to demonstrate the validity of the proposed scheme.