Fuzzy adaptive command filtered backstepping fault-tolerant control for a class of nonlinear systems with actuator fault

This paper investigates a class of nonlinear systems with actuator fault. In particular, fuzzy logic systems have been used to approximate the unknown nonlinear functions, backstepping procedure is adopted to design controller for the system with mismatched condition, command filter is utilized to eliminate the explosion of complexity of the backstepping and also to compensate the output of a filter subjected to the derivative of the virtual control. The stability of the closed-loop system and the convergence of the tracking error are proved via Lyapunov Theorem. In addition, two numerical simulation examples are illustrated the effectiveness of the proposed approach.     

High-order command filtered adaptive backstepping control for second- and high-order fully actuated strict-feedback systems

In this paper, a high-order command filtered adaptive backstepping (HOCFAB)-based approach is proposed in order to track a given reference signal for the second- and high-order strict-feedback systems (SFSs) with parametric uncertainties, where both their subsystems hold a common full-actuation structure, namely, high-order fully actuated (HOFA) SFSs. Unlike the prevailing traditional first-order state-space backstepping approach which suffers from the problem of “explosion of terms”, the proposed HOCFAB approach circumvents the complexity arising owing to differentiating the virtual controllers repeatedly, and does not need to convert the high-order systems into first-order forms which is easier to carry out and demands fewer steps. Meanwhile, an error-compensating mechanism is constructed to reduce filtering errors. A critical analysis is theoretically proven which indicates that in both cases the entire system states are uniformly ultimately bounded under the proposed high-order controller, and the tracking error could be made arbitrarily small with predesigned parameters. Finally, the effectiveness of the proposed scheme is verified by a benchmark application in the robotic manipulator.     

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.     

Reduced-order K-filters-based event-triggered adaptive command filtered tracking control for stochastic constrained nonlinear systems

To ensure better performance and simultaneously save resources, an event-triggered adaptive command filtered dynamic surface control (ACFDSC) method for uncertain stochastic nonstrict-feedback nonlinear systems with dynamic output constraints and prescribed performance is designed in this article. Firstly, with the help of reduced-order K-filters, linearly parameterized neural networks and specific coordinate transformation technique, the unmeasurable states, nonlinearities, two types of unmodeled dynamics and output constraints are dealt with respectively. Then, an event-triggered ACFDSC strategy is proposed to ensure that the tracking error reaches a specific bound within a finite time. By introducing the compensated signal into the complete Lyapunov function, and with the assistance of the compact set defined in the stability analysis, all signals are strictly demonstrated to be semi-globally uniformly ultimately bounded. The simulation results verify the effectiveness of the proposed method.     

Non-fragile finite-time sliding mode control for Markovian jump systems with randomly occurring uncertainties and controller gain variations

This paper considers the sliding mode control (SMC) problem of a class of uncertain Markovian jump systems, in which there exist randomly occurring parameter uncertainties and random gain variations in the controller. By introducing two independent random variables obeying Bernoulli distribution, the random characteristics of parameter uncertainties and controller gain variations are described. A mode-dependent sliding surface is constructed, and then, the non-fragile SMC scheme is synthesized such that the specified sliding surface is reached in finite time. Furthermore, the stochastic finite-time boundedness over both the reaching and sliding stages are ensured simultaneously under some sufficient conditions. Finally, the developed non-fragile SMC approach is verified by a practical example.     

Robust finite-time cooperative formation control of UGV-UAV with model uncertainties and actuator faults

This paper investigates the finite-time cooperative formation control problem for a heterogeneous system consisting of an unmanned ground vehicle (UGV) - the leader and an unmanned aerial vehicle (UAV) - the follower. The UAV system under consideration is subject to modeling uncertainties, external disturbance as well as actuator faults simultaneously, which is associated with aerodynamic and gyroscopic effects, payload mass, and other external forces. First, a backstepping controller is developed to stabilize the leader system to track the desired trajectory. Second, a robust nonsingular fast terminal sliding mode surface is designed for UAV and finite-time position control is achieved using terminal sliding mode technique, which ensures the formation error converges to zero in finite time in the presence of actuator faults and other uncertainties. Furthermore, by combining the radial basis function neural networks (NNs) with adaptive virtual parameter technology, a novel NN-based adaptive nonsingular fast terminal sliding formation controller (NN-ANFTSMFC) is developed. By means of the proposed adaptive control strategy, both uncertainties and actuator faults can be compensated without the prior knowledges of the uncertainty bounds and fault information. By using the proposed control schemes, larger actuator faults can be tolerated while eliminating control chattering. In order to realize fast coordinated formation, the expected position trajectory of UAV is composed of the leader position information and the desired relative distance with UGV, based on local distributed theory, in the three-dimensional space. The tracking and formation controllers are proved to be stable by the Lyapunov theory and the simulation results demonstrate the effectiveness of proposed algorithms.     

Discrete-time command filtered adaptive fuzzy fault-tolerant control for induction motors with unknown load disturbances

In this paper, a command filtered fault-tolerant control (CFFTC) approach is investigated for induction motors (IMs) discrete-time system in the presence of actuator faults and unknown load disturbances. Firstly, the IMs system discrete-time model is obtained by Euler method. Then, the fuzzy logic systems (FLSs) is utilized to compensate for unknown actuator faults. Besides, introducing the error compensation mechanism into discrete-time systems via command filters, “complexity of computation” and noncausal problem can be conquered, and the filtering error is avoided concurrently. Finally, simulation results demonstrate the validity of the presented fault-tolerant method for IMs system.     

Adaptive finite-time tracking control of robot manipulators with multiple uncertainties based on a low-cost neural approximator

Benefiting from a newly designed switching function in terminal sliding manifold and novel uncertainty handling solutions, this article presents a low-cost neuroadaptive control scheme that can not only achieve the finite time tracking control of robot system with multiple uncertainties also circumvent the possible singularity. Specifically, for the kinematics parameter uncertainties involved, the proposed terminal sliding mode observer can ensure the actual position of end-effector be accurately estimated within a finite time. And then, a neural approximator is designed to handle the non-parameterizable lumped dynamics uncertainty, and a new low-cost neural adaptive mechanism is constructed to reduce the computational burden. Furthermore, it is proved that all closed-loop signals are bounded and the tracking error converges to an arbitrarily small adjustable neighborhood of the origin within a finite time. The comparison simulation example also confirms the effectiveness and superiority of the proposed control scheme.     

Adaptive control of bi-directionally coupled Lorenz systems with uncertainties

The bi-directionally coupled Lorenz systems are linked to the modeling of a coupled double loop thermosyphon system where the mass momentum and heat exchange are both considered. As the key parameters of the system, known as Rayleigh numbers, increase, the system of differential equations predicts typical flow dynamics in a thermosyphon from heat conduction to time-dependent chaos. In many applications including the thermosyphon systems, there are uncertainties associated with mathematical models such as unmodeled dynamics and parameter variations. Also, under the high heat environment for a thermosyphon, there exist external disturbances quantitatively linked to the Rayleigh numbers. All these sources constitute uncertainties to the dynamical system. Our objective is to design adaptive controllers to stabilize the chaotic flow in each thermosyphon loop with unknown system parameters and existence of uncertainties. The controllers consist of a proportional controller with an adaptive gain and a wavelet network that reconstructs the unknown functions representing the uncertainties. Explicit stability bounds and adaptive laws for the control parameters are obtained so that the coupled Lorenz systems are globally stabilized.     

Input-output finite-time stability for networked control systems with memory event-triggered scheme

This paper has investigated the input-output finite time stability (IO-FTS) for a class of networked control systems (NCSs) with network-induced delay. To reduce the frequents of packets transmission, a novel memory event-triggered scheme (METS) has been proposed. Different from existing event-triggered schemes, the proposed METS can make use of certain released packets to generate new event. By this way, the event generator can do more precise decision and better control performance can be expected. By using a Lyapunov functional method, sufficient condition for the IO-FTS of NCSs has been derived. Then a co-design method is proposed to obtain the memory feedback gains and parameters of the METS. Finally, a simulation example is carried out and the effectiveness of the designed METS is validated. The IO-FTS of NCSs with solved memory feedback gains is also confirmed.     

IBLF-based adaptive finite-time control and modeling for continuous stirred tank reactor with output constraint

This paper studies a finite-time adaptive fuzzy control approach for a continuous stirred tank reactor (CSTR) with percent conversion constraint and uncertainties. This system is seen as a class of non-affine systems, and the system is resolved by the mean value theorem. Integral barrier Lyapunov functions (iBLFs) are used to handle output constraint in the design process of the finite-time adaptive controller. In order to calculate the time derivative of the virtual controller, a finite-time convergent differentiator (FTCD) is proposed, which can avert the issue of “explosion of complexity” in the backstepping design. Based on the finite time stability theory, the proposed approach not only ensures the closed-loop stability, but also guarantees tracking performance in a finite time. Finally, the simulation results on CSTR are showed to reveal the availability of the developed control scheme.     

Full-order terminal sliding-mode control of MIMO systems with unmatched uncertainties

To control MIMO systems with unmatched uncertainties, two sliding-mode controllers are presented in this paper. Firstly, a terminal sliding-mode controller is presented to force the output of an MIMO system to a region near zero in finite-time. With the analysis on the effect of the unmatched uncertainties, a full-order terminal sliding-mode control is further proposed to force the output of the MIMO system to converge to zero rather than a region. The virtual control is utilized to establish the reference for the part of the system states, which can reject unmatched uncertainties completely. To generate continuous virtual control signals, the proposed full-order terminal sliding-mode controller makes the ideal sliding motion as the full-order dynamics rather than the reduced-order dynamics in traditional sliding-mode control systems. Finally, the simulations on the control of an L-1011 fixed wing aircraft at cruise flight conditions validate the effectiveness of the proposed method.     

Command filter-based finite-time adaptive fuzzy control for nonlinear systems with uncertain disturbance

In this paper, a command filter-based adaptive fuzzy controller is constructed for a class of nonlinear systems with uncertain disturbance. By using the error compensation signals and fuzzy logic system, a command filter-based control strategy is presented to make that the tracking error converge to an any small neighborhood of zero and all closed-loop signals are bounded. In the design procedure, fuzzy logic system is employed to estimate unknown package nonlinear functions, which avoids excessive and burdensome computations. The control scheme not only resolves the explosion of complexity problem but also eliminates the filtering error in finite-time. An example has evaluated the validity of the control method.     

Observer-based discrete-time sliding mode control for systems with unmatched uncertainties

This paper addresses an observer-based sliding mode control (SMC) approach for discrete-time systems with unmatched uncertainties. A modified sliding surface based on disturbance estimation and a sliding mode controller are designed to counteract with the unmatched disturbance. The proposed method exhibits the following three features. First, the hyperplane matrix is designed in a simple way based on the discrete-time Riccati equation. Second, a chattering-free SMC method is utilized. Third, the proposed approach retains the nominal performance of the system. The stability of the overall system is achieved and simulation results are presented to verify the effectiveness of the proposed method.     

Distributed adaptive observer-based prescribed finite-time control of constrained multi-agent systems

This work considers a distributed adaptive output feedback control problem for nonlinear constrained multi-agent systems (MAS) in the prescribed finite time. To begin with, a state observer is constructed to estimate the unmeasurable state. Then, we develop a novel observer based distributed adaptive prescribed finite time output feedback control algorithm by incorporating the prescribed finite-time control technique into the backstepping design method. Through Lyapunov stability theory, it can be shown that all signals of MASs are bounded, the tracking errors converge to the adjustable regions around the origin within the pre-given error accuracy and settling time, and all states keep in the prescribed constraint regions. Finally, a simulation example verifies the efficacy of the obtained theoretical results.     

Disturbance and state observer-based adaptive finite-time control for quantized nonlinear systems with unknown control directions

This paper concentrates on proposing a novel finite-time tracking control algorithm for a kind of nonlinear systems with input quantization and unknown control directions. The nonlinear functions in the system are approximated by the means of strong approximation capability of the fuzzy logic systems. Firstly, the nonlinear system with unknown control directions is transformed into an equivalent system with known control gains by coordinate transformation. Secondly, the unknown system states are estimated by a designed fuzzy state observer, and the disturbance observer is constructed to track the external disturbances. The command filtering method is proposed to approach the problem of “explosion of complexity” existed in the conventional backstepping design process. In this system, the difficulties caused by unknown control directions are solved via the Nussbaum gain approach. Finally, based on the fuzzy state observer, the controller of the original system is obtained via using the transformed system by the backstepping method. The boundedness of all signals and the convergence of tracking and observer errors at the origin are ensured for the closed-loop system, and demonstrated by the simulation result in this paper.     

Distributed event-triggered adaptive finite-time consensus control for second-order multi-agent systems with connectivity preservation

In this paper, we consider the robust finite-time consensus problem for second-order multi-agent systems (MASs) with limited sensing range and weak communication ability. As a stepping stone, a novel distributed finite-time sliding mode manifold is developed for MASs. Then, by combining artificial potential function technique with the presented sliding mode manifold, a robust distributed control scheme is proposed to enable the finite-time consensus of MASs while preserving the prescribed communication connectivity. Furthermore, the sampling frequency and implementation burden of the proposed controller can be reduced with resort to the event-triggered methodology. Finally, numerical examples are given to show the effectiveness of the proposed method.     

Observer-based finite-time asynchronous sliding mode control for Markov jump systems with time-varying delay

The issue of finite-time sliding mode control (SMC) is studied for a class of Markov jump systems, in which parameter uncertainties, external disturbances and time-varying delay are considered. Firstly, a suitable observer-based SMC law is devised so that state trajectory of the system can reach the designed sliding mode surface in finite-time, the gain of the controller is asynchronous to the mode of original system. Meanwhile, the sufficient conditions of finite-time boundedness in the sliding phase and reaching phase are derived by the time partition strategy. Moreover, the gains of the observer and the observer-based controller will be acquired by using the linear matrix inequalities tool. In fine, emulation products are used to confirm the merits of the SMC strategy.     

Stochastic model predictive control for linear systems with unbounded additive uncertainties

This paper presents two stochastic model predictive control methods for linear time-invariant systems subject to unbounded additive uncertainties. The new methods are developed by formulating the chance constraints into deterministic form, which are treated in analogy with robust constraints, by using the probabilistic reachable set. The first one is the time-varying tube-based stochastic model predictive control algorithm, which is designed by employing the time-varying probabilistic reachable sets as tubes. The second one is the constant tube-based stochastic model predictive control algorithm, which is developed by enforcing a constant tightened constraint in the entire prediction horizon. In addition, the soft constraints are proposed to associate with the state initialization in the algorithms to enhance the feasibility. The algorithm feasibility and closed-loop stability results are provided. The efficacy of the approaches is demonstrated by means of numerical simulations.