Practical Finite-time Stability Research Articles

Practical finite-time command filtered backstepping control of MPCVD reactor systems with uncertainties

A practical finite-time command filtered backstepping control method is proposed in this paper for a microwave plasma chemical vapor deposition (MPCVD) reactor system. The MPCVD reactor system is modeled as a coupled nonlinear system with unknown control direction functions and unknown nonlinearities. To address the unknown nonlinearities, novel practical finite-time command filters are proposed to construct the estimations of such nonlinearities. On the other hand, an equivalent augmented system of the reactor system is proposed to address the design challenges that posed by the system unknown control direction functions. Additionally, it can be concluded that the proposed control method ensures practical finite-time stability of the reactor system tracking errors by using the practical finite-time Lyapunov stability criterion. Finally, the effectiveness of the approach is demonstrated through the simulation results.

Finite-Time Fuzzy Adaptive PPC for Nonstrict-Feedback Nonlinear MIMO Systems.

This article addresses the issue of the fuzzy adaptive prescribed performance control (PPC) design for nonstrict feedback multiple input multiple output (MIMO) nonlinear systems in finite time. Unknown nonlinear functions are handled via fuzzy-logic systems (FLSs). By combining the adaptive backstepping control algorithm and the nonlinear filters, a novel dynamic surface control (DSC) method is proposed, which can not only avoid the computational complexity issue but also improve the control performance in contrast to the traditional DSC control methods. Furthermore, to make the tracking errors have the prescribed performance in finite time, a new Lyapunov function is constructed by considering the transform error constraint. Based on the designed Lyapunov functions, it is proved that all the signals of the controlled systems are semiglobal practical finite-time stability (SGPFS). Finally, a simulation example is provided to illustrate the feasibility and validity of the put forward control scheme.

Event-triggered adaptive sliding mode control for steer-by-wire systems with actuator fault

The event-triggered tracking control is studied for the steer-by-wire (SbW) system with actuator fault, inaccurate dynamic model, and external disturbance. First, an adaptive sliding mode control based on event-triggering mechanism is proposed. The lumped nonlinearity, including friction torque and self-aligning torque of SbW systems, is approximated by an adaptive robust radial basis function neural network (RBFNN). Robust terms of sliding mode control attenuate the negative effects of the actuator fault, modeling error, external disturbance, and event-triggering error on control performance. More importantly, the sliding-mode high-frequency switching control appears in the high-order derivative of sliding variable without increasing the input–output relative degree, thereby eliminating chattering. Furthermore, the designed method can achieve the practical finite-time stability. The proposed event-triggering mechanism can strictly exclude Zeno behavior and economize the communication resources. Finally, simulations and experiments show the effectiveness of the proposed algorithm.

Adaptive Fuzzy Finite-Time Fault-Tolerant Consensus Tracking Control for High-Order Multiagent Systems With Directed Graphs.

This article investigates the distributed adaptive fuzzy finite-time fault-tolerant consensus tracking control for a class of unknown nonlinear high-order multiagent systems (MASs) with actuator faults and high powers (ratio of positive odd rational numbers). The fault models include both loss of effectiveness and bias fault. Compared with existing similar results, the MASs considered here are more general and complex, which include the special case when the powers are equal to 1. Besides, the functions in this article are completely unknown and do not need to satisfy any growth conditions. In the backstepping framework, an adaptive fuzzy fault-tolerant consensus tracking controller is designed via adding one power integrator technique and directed graph theory so that the controlled systems are semiglobal practical finite-time stability (SGPFTS). Finally, numerical simulation results further verify the effectiveness of the developed control scheme.

A dual-mode finite-time extremum seeking controller design technique

This manuscript proposes a finite-time extremum-seeking control system for a class of unknown nonlinear dynamical systems. A dual-mode approach is considered. The dual-mode control action combines a proportional feedback operating in the time-scale of the system and a slow perturbation-based extremum-seeking gradient descent. The resulting two time-scale extremum seeking control formulation is shown to achieve practical finite-time stability of the system to the optimum equilibrium conditions for the state variables and the input variables. A brief simulation study is presented to demonstrate the effectiveness of the proposed technique.

Event-triggered adaptive NN practical finite-time control with its application to MPCVD reactors

The practical finite-time control problem of uncertain nonlinear systems is investigated in this paper. To address the uncertain nonlinearities of the system, neural networks are introduced to approximate the lumped nonlinearities containing the system unknown functions. On the other hand, to alleviate the signal transmission pressure of the system, an improved event-triggered mechanism is presented to reduce the controller update frequency without degrading the control performance of the system. By using practical finite-time stability, it is obtained that the system tracking errors are practical finite-time stable without Zeno behavior. Finally, the effectiveness of the proposed method is verified by the simulation results of its application to a microwave plasma chemical vapor deposition (MPCVD) reactor system.

Finite time fractional order ISMC with time delay estimation for re-entry phase of RLV with enhanced chattering suppression

This paper investigates the attitude controller design for the reusable launch vehicle (RLV) in its re-entry phase under the influence of model uncertainties and external disturbances. The navigation of RLV along a predefined safe trajectory is a challenging task since the RLV system dynamics has a complex nonlinear behaviour with uncertain environmental conditions. Therefore, this paper proposes a time-delay estimation technique with fractional order integral sliding mode control abbreviated as FOISMC-TDC, for efficient tracking of a pre-designed reference trajectory that ensures safe landing of the RLV. The time delay estimation method in the proposed research employs the input–output information of the immediate past instant to estimate any uncertainties and un-modelled dynamics. The estimated value is then fed to the composite control for disturbance compensation without primarily relying on the switching control of FOISMC approach. This in turn, eliminates the problem of high-frequency chattering in the control input. In addition, by using FOISMC philosophy finite time convergence of system states is achieved with desired error response. Furthermore, Lyapunov and homogeneity theories have been utilized to establish practical finite-time stability of the overall closed loop system. Numerical analysis with state-of-the-art techniques have also been presented to demonstrate effectiveness of the proposed methodology.

Prescribed Performance Fuzzy Adaptive Output Feedback Control for Nonlinear MIMO Systems in a Finite Time

This article studies the fuzzy adaptive output feedback control design problem for nonstrict feedback multi-input–multi-output nonlinear systems with full-states prescribed performance in finite time. Fuzzy logic systems are introduced to solve the problem of unknown nonlinear dynamics. And on this basis, a fuzzy-based state observer is designed to observe the unmeasurable state. Further, by combining the adaptive back-stepping control algorithm and the nonlinear filters, a novel dynamic surface control (DSC) method is proposed, which not only solves the computational complexity explosion problem inherent in the back-stepping control algorithm, but also improves the control performance, in contrast to the traditional DSC methods with linear filters. Besides, to further improve the tracking performance under the structure of full-states prescribed performance, a new Lyapunov function is designed considering the transform error constraint. Based on the Lyapunov theory, the stability of the closed-loop system is analyzed to ensure that all signals of the closed-loop system are semiglobal practical finite-time stability. Finally, to elaborate on the feasibility and effectiveness of the proposed control method, a simulation example is provided.

Distributed Cooperative Compound Tracking Control for a Platoon of Vehicles With Adaptive NN.

This article focuses on the distributed cooperative compound tracking issue of the vehicular platoon. First, a definition, called compound tracking control, is proposed, which means that the practical finite-time stability and asymptotical convergence can be simultaneously satisfied. Then, a modified performance function, named finite-time performance function, is designed, which possesses the faster convergence rate compared to the existing ones. Moreover, the adaptive neural network (NN), prescribed performance technique, and backstepping method are utilized to design a distributed cooperative regulation protocol. It is worth noting that the convergence time of the proposed algorithm does not depend on the initial values and design parameters. Finally, simulation experiments are given to further verify the effectiveness of the presented theoretical findings.

Practical adaptive finite-time stabilization for a class of second-order systems

This paper considers the practical adaptive finite-time stabilization problem for a class of second-order systems. Based on the adding a power integrator technique and the adaptive method, a novel adaptive control strategy is presented to assure the trajectories of the closed-loop systems converge to a small neighborhood of the origin in a finite time. Under the adaptive control strategy, the dynamical change of control gain is dependent on the cases whether the state trajectories enter or leave a pre-designed domain or not. In addition, the practical finite-time stability (PFTS) of systems is testified via utilizing the Lyapunov method and adaptive mechanism. Last of all, the validity of the obtained practical adaptive finite-time algorithm is verified via simulation results.

Practical finite-time adaptive sliding mode control for 5-link biped robot in the presence of uncertainty

ABSTRACT In this paper, novel practical finite-time robust adaptive controllers are investigated for a 5-link single support phase (SSP) lower limb biped robot subjected to unknown physical and dynamical parameters, disturbances, and unknown input saturation. The developed adaptive approaches are based on a terminal sliding surface and a finite-time stability analysis to design controller and adaptation laws. The adaptive mechanisms deal with estimating unknown terms, the upper bound of the unknown term vector, or estimating the unknown limits of input saturation. Consequently, the proposed approach is applicable when the physical and dynamical parameters of the robot and the saturation input parameters are not known. In addition, the Lyapunov stability approach warranties that the tracking errors are robust finite-time uniformly ultimately bounded and provides the practical finite-time stability of the closed-loop system. Finally, numerical simulations are provided to show the feasibility, effectiveness, and performance enhancement of the proposed methods over state-of-the-art methods.

Novel finite-time adaptive sliding mode tracking control for disturbed mechanical systems

In this paper, the finite-time tracking control problem of mechanical systems subject to model uncertainties and external disturbances is investigated. A new type of finite-time adaptive sliding mode control approach is proposed based on a novel integral sliding mode surface and a novel parametric adaptation mechanism. The integral sliding mode surface is originally designed by utilizing the adding a power integrator technique. The parametric adaptation mechanism is developed by using a single adaptive updating law to estimate the square of the upper bound of the lumped uncertain term. As compared with the most existing studies, the distinctive features of the proposed controller are threefold. (1) Benefiting from the novel integral sliding mode surface, the proposed controller has no singularity problem inherently existing in the terminal sliding mode control. (2) Owing to the use of novel parametric adaptation mechanism, the proposed controller is smooth and the unexpected chattering phenomenon is significantly attenuated. Moreover, the proposed controller is structurally simple and requires relatively few online calculations, which makes it affordable for practical applications. (3) The practical finite-time stability of the overall closed-loop system is strictly proved. The proposed controller can ensure the position and velocity tracking errors stabilize to the adjustable small neighborhoods around the origin in finite time. Lastly, the effectiveness and advantages of the proposed control approach are illustrated through simulations and comparisons.

Finite-Time Leader-Following Consensus of Multiagent Systems With Actuator Faults and Input Saturation

This article studies the fault-tolerant leader-following consensus problem for multiagent systems with input saturation. The main contribution is to present a modified low-and-high gain feedback approach to deal with multiple actuator faults, including partial loss of effectiveness, outage, and stuck simultaneously. First, without consideration of saturation, a distributed fault-tolerant control scheme is put forward by the adaptive technique, and a practical finite-time stability result is established. Second, by employing the fault-tolerant theory and introducing a novel form of parametric algebraic Riccati equation, a modified low-and-high gain feedback approach is developed for the saturated control strategy. It is proven that the practical finite-time stability can be achieved, and both the steady-state consensus error and the settling time can be well estimated. Finally, numerical simulations are provided to validate the effectiveness of the theoretical results.

Adaptive Finite-Time Neural Constrained Control for Nonlinear Active Suspension Systems Based on the Command Filter

This article focuses on the adaptive finite-time command filter control problem for nonlinear quarter active suspension systems with actuator failure. In the previous designs of active suspension systems, a second-order system for the vehicle body movement is employed to achieve the controller design and a zero-dynamic analysis is needed, thus the designed controller only contains a part of system variables and there is a difficulty in selecting a proper Lyapunov function in the zero-dynamic analysis. In order to overcome the aforementioned problems, a novel active suspension system is shown based on the Butterworth low-pass filter. The neural networks (NNs) are used to identify the unknown functions of active suspension systems. Meanwhile, the command filter is proposed to handle the “explosion of complexity” problem caused by the adaptive backstepping technique. Then, the adaptive practical finite-time control scheme combined with the command filter and neural identify technique is constructed in a unified framework, which can handle the “singularity” problem. Through the practical finite-time stability analysis, it is easily to obtain that all signals of closed-loop systems are bounded in a finite time. Finally, simulation results for the nonlinear quarter active suspension systems are provided to verify the effectiveness of the NN control scheme.

Adaptive neural finite-time control of nonlinear systems subject to sensor hysteresis

In this paper, an adaptive neural control scheme is proposed for a class of unknown nonlinear systems with unknown sensor hysteresis. The radial basis function neural networks are employed to approximate the unknown nonlinearities and the backstepping technique is implemented to construct controllers. The difficulty of the control design lies in that the genuine states of the system are not available for feedback, which is caused by sensor hysteresis. The proposed control scheme eventually ensures the practical finite-time stability of the closed-loop system, which is proved by the Lyapunov theory. A numerical simulation example is included to verify the effectiveness of the developed approach.

Finite‐time attitude stabilization of rigid spacecrafts based on control Lyapunov functions

In this paper, the control Lyapunov function (CLF) approach is adopted to investigate the finite-time attitude control of rigid spacecraft subject to parameter uncertainty and external disturbance. By using an extended state observer to estimate the parameter uncertainty and external disturbance, a finite-time CLF controller is proposed for attitude stabilization of the spacecraft system. The designed finite-time CLF controller includes two parts. The first part is a classical CLF based attitude controller, which is proposed to ensure the globally asymptotical stability of the nominal spacecraft system. The second one is a sliding mode controller, which is used to ensure the finite-time convergence performance of the spacecraft control system. The advantage of the designed controller is that the states of the system can converge into a small neighourhood of zero in finite time, and simultaneously the given performance index can be minimized. The practical finite-time stability of the resulted closed-loop system is proven via Lyapunov stability theory. Finally, simulation results illustrate the effectiveness of the developed finite-time controller.

Observer-based finite-time adaptive fuzzy back-stepping control for MIMO coupled nonlinear systems.

An attempt is made in this paper to devise a finite-time adaptive fuzzy back-stepping control scheme for a class of multi-input and multi-output (MIMO) coupled nonlinear systems with immeasurable states. In view of the uncertainty of the system, adaptive fuzzy logic systems (AFLSs) are used to approach the uncertainty of the system, and the unmeasured states of the system are estimated by the finite-time extend state observers (FT-ESOs), where the state of the observer is a sphere around the state of the system. The accuracy and efficiency of the control effect are ensured by combining the back-stepping and finite-time theory. It is proved that all the states of the closed-loop adaptive control system are semi-global practical finite-time stability (SGPFS) by the finite-time Lyapunov stability theorem, and the tracking errors of the system states converge to a tiny neighborhood of the origin in a finite time. The validity of this scheme is demonstrated by a simulation.

Event-triggered type-2 fuzzy-based sliding mode control for steer-by-wire systems

This paper proposes an event-triggered higher-order sliding mode control for steer-by-wire (SbW) systems subject to limited communication resources and uncertain nonlinearity. First, an interval type-2 fuzzy logic system (IT2 FLS) is adopted to approximate the uncertain nonlinearities. A fuzzy-based state observer is developed to estimate unavailable states of the extended SbW system. Then, to save communication resources and eliminate chattering, an event-triggered higher-order 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. After that, the practical finite-time stability of the closed-loop SbW system is proved in the framework of the Lyapunov theory. Finally, numerical simulations and vehicle experiments are given to evaluate the effectiveness and superiority of the proposed scheme.

Reinforcement learning-based finite-time tracking control of an unknown unmanned surface vehicle with input constraints

In this paper, subject to completely unknown system dynamics and input constraints, a reinforcement learning-based finite-time trajectory tracking control (RLFTC) scheme is innovatively created for an unmanned surface vehicle (USV) by combining actor-critic reinforcement learning (RL) mechanism with finite-time control technique. Unlike previous RL-based tracking which requires infinite-time convergence thereby rather sensitive to complex unknowns, an actor-critic finite-time control structure is created by employing adaptive neural network identifiers to recursively update actor and critic, such that learning-based robustness can be sufficiently enhanced. Moreover, deduced from the Bellman error formulation, the proposed RLFTC is directly optimized in a finite-time manner. Theoretical analysis eventually shows that the proposed RLFTC scheme can ensure semi-global practical finite-time stability (SGPFS) for a closed-loop USV system and tracking errors converge to an arbitrarily small neighborhood of the origin in a finite time, subject to optimal cost. Both mathematical simulation and virtual-reality experiments demonstrate remarkable effectiveness and superiority of the proposed RLFTC scheme.

Adaptive control and disturbance compensation for gear transmission servo systems with large-range inertia variation

In gear transmission servo systems, backlash effect and inertia variation often generate low precision, oscillations or even affect the stability. Focusing on this issue, an adaptive terminal integral sliding mode control (ATISMC) strategy and a discrete linear extended state observer (DLESO) are proposed in this article. First, different from using traditional dynamic model, a characteristic model is established with online parameter identification to describe inertia variation. Then, a DLESO is proposed to observe and compensate the modeling error caused by parameter identification and backlash effect. An ATISMC is newly designed based on the characteristic model to suppress the uncertainties and stabilize the whole closed-loop system. Both the uniform ultimate boundedness of observation error and the practical finite-time stability of the system is proved. Finally, simulation and experimental results demonstrate that the proposed strategy can adapt to large-range inertia variation and suppress the backlash effect.