Event-driven NN adaptive fixed-time control for nonlinear systems with guaranteed performance

This article investigates the adaptive neural network fixed-time tracking control issue for a class of strict-feedback nonlinear systems with prescribed performance demands, in which the radial basis function neural networks (RBFNNs) are utilized to approximate the unknown items. First, an modified fractional-order command filtered backstepping (FOCFB) control technique is incorporated to address the issue of the iterative derivation and remove the impact of filtering errors, where a fractional-order filter is adopted to improve the filter performance. Furthermore, an event-driven-based fixed-time adaptive controller is constructed to reduce the communication burden while excluding the Zeno-behavior. Stability results prove that the designed controller not only guarantees all the signals of the closed-loop system (CLS) are practically fixed-time bounded, but also the tracking error can be regulated to the predefined boundary. Finally, the feasibility and superiority of the proposed control algorithm are verified by two simulation examples.     

Multilayer-neural-network observer with compensator and command-filter-based adaptive backstepping tracking control of switched nonlinear systems

This study presents an output backstepping control architecture based on command filter via Multilayer-Neural-Network Pre-Observer with compensator to realise the reference signal tracking of an arbitrarily switching nonlinear systems with nonseperated parameter. First, a multilayer neural network pre-observer is designed before backstepping procedures to servo reconstruct the system states which can not be obtained directly. The pre-observer has superior performance in neutralizing the states abrupt chattering caused by the arbitrarily switching parameter entered in the nonlinear structure. Next, observer error compensation mechanism is designed to compensate the state estimation and shrink the approximation error domain further. Then, the backstepping controller with compensation signal based on command filter is presented to realise the stable reference signal tracking. Last, the proposed control scheme guarantees the states of the closed-loop system bounded. This mechanism makes up the shortcoming of the traditional state observer and give more flexibility in reconstructing the systems states timely, then overcomes the obstacle of the arbitrarily switching parameterized system. Furthermore, compared with the existing traditional uniform robust uncertain controller, the developed backstepping control method combining with the pre-observer not only guarantees the states servo reconstruction and servo control of the switched system, but also improves the tracking performance. Finally, a low-velocity servo turnable switched system is extensively simulated to demonstrate the effectiveness of the developed controller.     

Neural network-based sensor fault estimation and active fault-tolerant control for uncertain nonlinear systems

In this work, we developed a novel active fault-tolerant control (FTC) design scheme for a class of nonlinear dynamic systems subjected simultaneously to modelling imperfections, parametric uncertainties and sensor faults. Modelling imperfections and parametric uncertainties are dealt with using an adaptive radial basis function neural network (RBFNN) that estimates the uncertain part of the system dynamics. For sensor fault estimation (FE), a nonlinear observer based on the estimated dynamics is designed. A scheme to estimate sensor faults in real-time using the nonlinear observer and an additional RBFNN is developed. The convergence properties of the RBFNN, used in the fault FE part, are improved by using a sliding surface function. For FTC design, a sliding surface is designed that incorporates the real-time sensor FE. The resulting sliding mode control (SMC) technique-based FTC law uses the estimated dynamics and real-time sensor FE. A double power-reaching law is adopted to design the switching part of the control law to improve the convergence and mitigate the chattering associated with the SMC. The FTC works well in the presence and absence of sensor faults without the requirement for controller reconfiguration. The stability of the proposed active FTC law is proved using the Lyapunov method. The developed scheme is implemented on a nonlinear simulation of an unmanned aerial vehicle (UAV). The results show good performance of the proposed unified FE and the FTC framework.     

Robust integral backstepping control for sensorless IPM synchronous motor controller

In this paper, a sensorless speed control for interior permanent magnet synchronous motors (IPMSM) is designed by combining a robust backstepping controller with integral actions and an adaptive interconnected observer. The IPMSM control design generally requires rotor position measurement. Then, to eliminate this sensor, an adaptive interconnected observer is designed to estimate the rotor position and the speed. Moreover, a robust nonlinear control based on the backstepping algorithm is designed where an integral action is introduced in order to improve the robust properties of the controller. The stability of the closed-loop system with the observer–controller scheme is analyzed and sufficient conditions are given to prove the practical stability. Simulation results are shown to illustrate the performance of the proposed scheme under parametric uncertainties and low speed. Furthermore, the proposed integral backstepping control is compared with the classical backstepping controller.     

Fraction dynamic-surface-based adaptive neural finite-time control for stochastic nonlinear systems subject to unknown control directions,time-varying input delay and state delay

In this paper, an adaptive neural finite-time tracking control is studied for a category of stochastic nonlinearly parameterized systems with multiple unknown control directions, time-varying input delay, and time-varying state delay. To this end, a novel criterion of semi-globally finite-time stability in probability (SGFSP) is proposed, in the sense of Lyapunov, for stochastic nonlinear systems with multiple unknown control directions. Secondly, a novel auxiliary system with finite-time convergence is presented to cope with the time-varying input delay, the appropriate Lyapunov Krasovskii functionals are utilized to compensate for the time-varying state delay, Nussbaum functions are exploited to identify multiple unknown control directions, and the neural networks (NNs) are applied to approximate the unknown functions of nonlinear parameters. Thirdly, the fraction dynamic surface control (FDSC) technique is embedded in the process of designing the controller, which not only the “explosion of complexity” problems are successfully avoided in traditional backstepping methods but also the command filter convergence can be obtained within a finite time to lead greatly improved for the response speed of command filter. Meanwhile, the error compensation mechanism is established to eliminate the errors of the command filter. Then, based on the proposed novel criterion, all closed-loop signals of the considered systems are SGPFS under the designed controller, and the tracking error can drive to a small neighborhood of the origin in a finite time. In the end, three simulation examples are applied to demonstrate the validity of the control method.     

Command filter-based adaptive fault-tolerant tracking control for uncertain non-strict feedback multi-agent systems with or without state constraints

This paper considers the topic of adaptive leader-following fault-tolerant tracking control for a class of non-strict feedback nonlinear multi-agent systems with or without state constraints in a unified solution. Through the use of certain transformation techniques, the original constraint system is recast as a new completely unconstrained system. Compared with the existing results, the limitation that the constraint functions need upper bound is relaxed. By employing radial basis function neural networks (RBFNNs) to approximate the unknown functions. A novel adaptive fault-tolerant consensus tracking control (CTC) manner is raised with command filtered backstepping design. Then, through the Lyapunov stability analysis, the proposed scheme can ensure all signals in the closed-loop system are cooperative semi-globally uniformly ultimately bounded (SGUUB). Finally, simulation example confirms the efficiency of the proposed method.     

Command filtered robust adaptive NN control for a class of uncertain strict-feedback nonlinear systems under input saturation

This paper develops a robust adaptive neural network (NN) tracking control scheme for a class of strict-feedback nonlinear systems with unknown nonlinearities and unknown external disturbances under input saturation. The radial basis function NNs with minimal learning parameter (MLP) are employed to online approximate the uncertain system dynamics. The adaptive laws are designed to online update the upper bound of the norm of ideal NN weight vectors, and the sum of the bounds of NN approximation errors and external disturbances, respectively. An auxiliary dynamic system is constructed to generate the augmented error signals which are used to modify the adaptive laws for preventing the destructive action due to the input saturation. Moreover, the command filtering backstepping control method is utilized to overcome the shortcoming of dynamic surface control method, the tracking-differentiator-based control method, etc. Our proposed scheme is qualified for simultaneously dealing with the input saturation effect, the heavy computational burden and the “explosion of complexity” problems. Theoretical analysis illuminates that our scheme ensures the boundedness of all signals in the closed-loop systems. Simulation results on two examples verify the effectiveness of our developed control scheme.     

Anti-oscillation and chaos control of the fractional-order brushless DC motor system via adaptive echo state networks

This paper proposes anti-oscillation and chaos control scheme for the fractional-order brushless DC motor system wherein there exist unknown dynamics, immeasurable states and chaotic oscillation. Aimed at immeasurable states, the high-gain observers with fast convergence are presented to obtain the information of system states. To compensate uncertainties existing in the dynamic system, a finite-time echo state network with a weight is proposed to approximate uncertain dynamics while its weight is tuned by a fractional-order adaptive law online. Meanwhile a fractional-order filter is introduced to deal with the repeated derivative of the backstepping. Based on the fractional-order Lyapunov stability criterion, the anti-oscillation and chaos control scheme integrated with a high-gain observer, an echo state network and a filter are proposed by using recursive steps of backstepping. The proposed scheme guarantees the boundedness of all signals of the closed-loop system in the sense of global asymptotic stability, and also suppresses chaotic oscillation. Finally, the effectiveness of our scheme is demonstrated by simulation results.     

Semi-globally/globally stable adaptive NN backstepping control for uncertain MIMO systems with tracking accuracy known a priori

This paper focuses on the problem of direct adaptive neural network (NN) tracking control for a class of uncertain nonlinear multi-input/multi-output (MIMO) systems by employing backstepping technique. Compared with the existing results, the outstanding features of the two proposed control schemes are presented as follows. Firstly, a semi-globally stable adaptive neural control scheme is developed to guarantee that the ultimate tracking errors satisfy the accuracy given a priori, which cannot be carried out by using all existing adaptive NN control schemes. Secondly, we propose a novel adaptive neural control approach such that the closed-loop system is globally stable, and in the meantime the ultimate tracking errors also achieve the tracking accuracy known a priori, which is different from all existing adaptive NN backstepping control methods where the closed-loop systems can just be ensured to be semi-globally stable and the ultimate tracking accuracy cannot be determined a priori by the designers before the controllers are implemented. Thirdly, the main technical novelty is to construct three new nth-order continuously differentiable switching functions such that multiswitching-based adaptive neural backstepping controllers are designed successfully. Fourthly, in contrast to the classic adaptive NN control schemes, this paper adopts Barbalat׳s lemma to analyze the convergence of tracking errors rather than Lyapunov stability theory. Consequently, the accuracy of ultimate tracking errors can be determined and adjusted accurately a priori according to the real-world requirements, and all signals in the closed-loop systems are also ensured to be uniformly ultimately bounded. Finally, a simulation example is provided to illustrate the effectiveness and merits of the two proposed adaptive NN control schemes.     

L’ Hopital’S rule-Based adaptive dynamic surface control for a class of strict-Feedback systems with unknown parameters

In this paper, a L’ Hopital’s rule-based adaptive dynamic surface control (L-ADSC) scheme is developed for a class of strict-feedback systems with unknown parameters using backstepping technique. The L-ADSC-derived backstepping technique is deployed to remove differentiation of complex virtual controller, thereby efficiently avoiding ”exlosion of complexity”. The L’ Hopital’s Rule is resorted to tackle singularity problem within controller synthesis. As a consequence, the proposed L-ADSC scheme guarantees that all signals of the closed-loop control system are semi-globally uniformly ultimately bounded. Simulation results show remarkable effectiveness.     

Event-triggered secure control of nonlinear multi-agent systems under sensor attacks

In this paper, a security consistent tracking control scheme with event-triggered strategy and sensor attacks is developed for a class of nonlinear multi-agent systems. For the sensor attacks on the system, a security measurement preselector and a state observer are introduced to combat the impact of the attacks and achieve secure state estimation. In addition, command filtering technology is introduced to overcome the “complexity explosion” caused by the use of the backstepping approach. Subsequently, a new dynamic event-triggered strategy is proposed, in which the triggering conditions are no longer constants but can be adjusted in real time according to the adaptive variables, so that the designed event-triggered mechanism has stronger online update ability. The measurement states are only transmitted through the network based on event-triggered conditions. The proposed adaptive backstepping algorithm not only ensures the security of the system under sensor attacks but also saves network resources and ensures the consistent tracking performance of multi-agent systems. The boundedness of all closed-loop signals is proved by Lyapunov stability analysis. Simulation examples show the effectiveness of the control scheme.     

Adaptive consensus control for output-constrained nonlinear multi-agent systems with actuator faults

This paper addresses the problem of leader-follower consensus fault-tolerant control for a class of nonlinear multi-agent systems with output constraints. Specifically, a new nonlinear state transformation function is proposed to deal with the asymmetric constraint on output. Moreover, by integrating backstepping and radial basis function neural network approaches, an adaptive consensus control framework is developed with a single parameter estimator, which mitigates the computation of control algorithm in comparison with conventional adaptive approximation based control techniques. Then an adaptive compensation method is proposed to eliminate the effect of actuator failure. Under the proposed control scheme, all the closed-loop signals of the systems are bounded and the consensus tracking error converges to an adjustable small neighborhood of zero. To evaluate the developed control algorithm, a group of four networked two-stage chemical reactors is used to illustrate the effectiveness of the theoretic results obtained.     

Adaptive fault-tolerant control with prescribed performance for switched nonlinear pure-feedback systems

In this paper, the problem of adaptive fuzzy fault-tolerant control is investigated for a class of switched uncertain pure-feedback nonlinear systems under arbitrary switching. The considered actuator failures are modeled as both lock-in-place and loss of effectiveness. By utilizing mean value theorem, the considered pure-feedback systems are transformed into a class of switched nonlinear strict-feedback systems. Under the framework of backstepping design technique and common Lyapunov function (CLF), an adaptive fuzzy fault-tolerant control (FTC) method with predefined performance bounds is developed. It is proved that under the proposed controller, all the signals of the close-loop systems are bounded and the state tracking error for each step remains within the prescribed performance bound (PPB) regardless of actuator faults and the system switchings. In addition, the tracking errors and magnitudes of control inputs can be reduced by adjusting the PPB parameters of errors in the first and last steps. The simulation results are provided to show the effectiveness of the proposed control scheme.     

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.     

Backstepping-based adaptive dynamic programming for missile-target guidance systems with state and input constraints

In this paper, a novel backstepping-based adaptive dynamic programming (ADP) method is developed to solve the problem of intercepting a maneuver target in the presence of full-state and input constraints. To address state constraints, a barrier Lyapunov function is introduced to every backstepping procedure. An auxiliary design system is employed to compensate the input constraints. Then, an adaptive backstepping feedforward control strategy is designed, by which the tracking problem for strict-feedback systems can be reduced to an equivalence optimal regulation problem for affine nonlinear systems. Secondly, an adaptive optimal controller is developed by using ADP technique, in which a critic network is constructed to approximate the solution of the associated Hamilton–Jacobi–Bellman (HJB) equation. Therefore, the whole control scheme consists of an adaptive feedforward controller and an optimal feedback controller. By utilizing Lyapunov's direct method, all signals in the closed-loop system are guaranteed to be uniformly ultimately bounded (UUB). Finally, the effectiveness of the proposed strategy is demonstrated by using a simple nonlinear system and a nonlinear two-dimensional missile-target interception system.     

Approximation-based decentralized output-feedback control for uncertain stochastic interconnected nonlinear time-delay systems with input delay and asymmetric input saturation

This paper proposes an adaptive observer-based neural controller for a class of uncertain large-scale stochastic nonlinear systems with actuator delay and time-delay nonlinear interactions, where drift and diffusion terms contain all state variables of their own subsystem. First, a state observer is established for estimating the unmeasured states, and a predictor-like term is utilized to transform the input delayed system into the delay-free system. Second, novel appropriate Lyapunov–Krasovskii functionals are used to compensate the time-delay terms, and neural networks are employed to approximate unknown nonlinear functions. At last, an output-feedback adaptive neural control scheme is constructed by using Lyapunov stability theory and backstepping technique. It is shown that the designed neural controller can ensure that all the signals in the closed-loop system are semi-globally uniformly ultimately bounded (SGUUB) and the tracking error is driven to a small neighborhood of the origin. The simulation results are presented to further show the effectiveness of the proposed approach.     

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.     

Adaptive dynamic programing design for the neural control of hypersonic flight vehicles

An adaptive dynamic programming controller based on backstepping method is designed for the optimal tracking control of hypersonic flight vehicles. The control input is divided into two parts namely stable control and optimal control. First, the back-stepping method is exploited via neural networks (NNs) to estimate unknown functions. Then, the computational load is reduced by the minimal-learning-parameter (MLP) scheme. To avoid the problem of “explosion of terms”, a first-order filter is adopted. Next, the optimal controller is designed based on the adaptive dynamic programming. In order to solve the Hamiltonian equation, NNs estimators are introduced to approximate performance indicators, achieving the approximate optimal control of hypersonic flight vehicles. Finally, the effectiveness and advantages of the control method are verified by simulation results.     

Robust tracking control for quadrotor with unknown nonlinear dynamics using adaptive neural network based fractional-order backstepping control

This work aims to design a neural network-based fractional-order backstepping controller (NNFOBC) to control a multiple-input multiple-output (MIMO) quadrotor unmanned aerial vehicle (QUAV) system under uncertainties and disturbances and unknown dynamics. First, we investigated the dynamic of QUAV composed of six inter-connected nonlinear subsystems. Then, to increase the convergence speed and control precision of the classical backstepping controller (BC), we design a fractional-order BC (FOBC) that provides further degrees of freedom in the control parameters for every subsystem. Besides, designing control is a challenge as the FOBC requires knowledge of accurate mathematical model and the physical parameters of QUAV system. To address this problem, we propose an adaptive approximator that is a radial basis function neural network (RBFNN) included in FOBC to fix the unknown dynamics problem which results in the new approach NNFOBC. Furthermore, a robust control term is introduced to increase the tracking performance of a reference signal as parametric uncertainties and disturbances occur. We have used Lyapunov's theorem to derive adaptive laws of control parameters. Finally, the outcoming results confirm that the performance of the proposed NNFOBC controller outperforms both the classical BC , FOBC and a neural network-based classical BC controller (NNBC) and under parametric uncertainties and disturbances.     

Adaptive neural network control for flexible telerobotic systems with communication constraints

This paper investigates the synchronous control problem for a class of flexible telerobotic systems subject to system uncertainties and communication constraints. In view of the asymmetric time-varying communication delays, an adaptive time-delay estimator is designed to reduce the impacts of delays on the system. Moreover, by combining the neural networks and parameter adaptive method, the uncertainties of system dynamics are estimated and compensated. Based on these efforts, a new adaptive compensation control protocol is proposed. Additionally, input quantization in network control induced chattering phenomenon and unknown parameters is also dealt with by the adaptive compensation method. A useful characteristic of this paper is that the “complexity explosion” problem caused by the backstepping technique is circumvented effectively. Finally, sufficient conditions are derived for the synchronous control of the master-slave flexible telerobotic system under Lyapunov stability theory. A numerical example of flexible-joint robotic system is provided to illustrate the effectiveness of the proposed control schemes.