Adaptive fault compensation control for nonlinear uncertain fractional-order systems: Static and dynamic event generator approaches

The tracking problem of the fractional-order nonlinear systems is assessed by extending new event-triggered control designs. The considered dynamics are accompanied by the uncertain strict-feedback form, unknown actuator faults and unknown disturbances. By using the neural networks and the fault compensation method, two adaptive fault compensation event-triggered schemes are designed. Unlike the available control designs, two static and dynamic event-triggered strategies are proposed for the nonlinear fractional-order systems, in a sense that the minimum/average time-interval between two successive events can be prolonged in the dynamic event-triggered approach. Besides, it is proven that the Zeno phenomenon is strictly avoided. Finally, the simulation results prove the effectiveness of the presented control methods.     

Event-triggered sliding mode tracking control of autonomous surface vehicles

This paper is concerned with an event-triggered sliding mode control (SMC) scheme for trajectory tracking in autonomous surface vehicles (ASVs). First, an event-triggered variable that consists of tracking error, desired trajectory and exogenous input of the reference system is introduced to decrease the magnitude of the robust SMC term. Then, the reaching conditions of the designed event-triggered sliding mode are established. Moreover, the event-triggered induced errors that exist in the rotation matrix of the ASV are analyzed. In the presence of parameter uncertainties and external disturbances, the proposed event-triggered SMC scheme can ensure the control accuracy and low-frequency actuator updates. Then both actuator wear and energy consumption of the actuators can be reduced comparing with the traditional time-triggered controller. The proposed controller not only guarantees uniform ultimate boundedness of the tracking error but also ensures non-accumulation of inter-execution times. The results are illustrated through simulation examples.     

Online adaptive policy iteration based fault-tolerant control algorithm for continuous-time nonlinear tracking systems with actuator failures

In this paper, a novel tracking control scheme for continuous-time nonlinear affine systems with actuator faults is proposed by using a policy iteration (PI) based adaptive control algorithm. According to the controlled system and desired reference trajectory, a novel augmented tracking system is constructed and the tracking control problem is converted to the stabilizing issue of the corresponding error dynamic system. PI algorithm, generally used in optimal control and intelligence technique fields, is an important reinforcement learning method to solve the performance function by critic neural network (NN) approximation, which satisfies the Lyapunov equation. For the augmented tracking error system with actuator faults, an online PI based fault-tolerant control law is proposed, where a new tuning law of the adaptive parameter is designed to tolerate four common kinds of actuator faults. The stability of the tracking error dynamic with actuator faults is guaranteed by using Lyapunov theory, and the tracking errors satisfy uniformly bounded as the adaptive parameters get converged. Finally, the designed fault-tolerant feedback control algorithm for nonlinear tracking system with actuator faults is applied in two cases to track the desired reference trajectory, and the simulation results demonstrate the effectiveness and applicability of the proposed method.     

Event-triggered adaptive fault-tolerant control for nonlinear systems fusing static and dynamic information

In this paper, a novel event-triggered adaptive fault-tolerant control scheme is proposed for a class of nonlinear systems with unknown actuator faults. Multiplicative faults and additive faults are taken into account simultaneously, both of which may vary with time. Different from existing results, our controller fuses static reliability information and dynamic online information, which is helpful to enhance the fault-tolerant capability. With the aid of an event-triggering mechanism, an actuator switching strategy and a bound estimation approach, the communication burden is significantly reduced and the impacts of the actuator faults as well as the network-induced error are effectively compensated for. Moreover, by employing the prescribed performance control technique, the system tracking error can converge to a predefined arbitrarily small residual set with prescribed convergence rate and maximum overshoot, which implies that the proposed scheme is able to ensure rapid and accurate tracking. Simulation results are presented to illustrate the effectiveness of the proposed scheme.     

Distributed robust event-triggered adaptive control for a class of uncertain nonlinear multi-agent systems with actuator saturation

This paper studies the event-triggered consensus control problem for high-order uncertain nonlinear multi-agent systems with actuator saturation. By using a smooth Lipschitz function to approximate the saturation nonlinearity, an augment system and the Nussbaum function are adopted to deal with the residual terms of saturation nonlinearity based on adaptive backstepping method. Since excessive energy and communication resources will be consumed during the procedure to handle actuator saturation, two event-triggered mechanisms are proposed to save the communication resources and reduce the controllers’ update frequency. Whenever the triggered conditions are satisfied, the control signals transmitted to the actuators are updated and broadcasted to the neighboring area. A ’disturbance-like’ term is integrated so that the event-triggered control problem with actuator saturation can be transformed into a robust problem while the unknown disturbances are tackled by adaptive update laws. Moreover, the requirement for global communication topology known by all the agents is relaxed by introducing new estimators. All the signals in the closed-loop system are uniformly bounded and the consensus tracking errors are exponentially converged to a bounded set. Meanwhile, the Zeno behavior is excluded. Simulation results are employed to validate the advantages of our proposed methods.     

Adaptive fault-tolerant control for high-order fully actuated system with full-state constraints

This paper studies the adaptive tracking control problem for a class of uncertain high-order fully actuated (HOFA) systems with actuator faults and full-state constraints. Firstly, we design a novel nonlinear transformation function (NTF) only related to state and constraint boundaries and capable of handling asymmetric time-varying constraints. With the designed function, we obtain an equivalent totally unconstrained HOFA model which is generally simpler to design controllers than first-order state-space model. Then, the adaptive fault-tolerant controller is constructed with the help of the HOFA approach. By applying the Lyapunov stability theory, it is rigorously proved that the output tracking error converges to zero asymptotically, other signals of the resulting closed-loop systems are bounded, and full-state constraints are not violated for all time. Finally, the simulation results verify the efficiency of the proposed control design method.     

Adaptive fuzzy fault-tolerant decentralized control for uncertain nonlinear large-scale systems based on dynamic surface control technique

In this paper, an adaptive fuzzy decentralized control method is proposed for accommodating actuator faults for a class of uncertain nonlinear large-scale systems. The considered faults are modeled as both loss of effectiveness and lock-in-place. With the help of fuzzy logic systems to approximate the unknown nonlinear functions, the novel adaptive fuzzy faults-tolerant decentralized controllers are constructed by combining the backstepping technique and the dynamic surface control (DSC) approach. It is proved that the proposed control approach can guarantee that all the signals of the resulting closed-loop systems are bounded and the tracking errors converge to a small neighborhood of zero. Simulation results are provided to show the effectiveness of the control approach.     

Leader-following consensus for multi-agent systems with actuator faults via adaptive event-triggered control

In this paper, the leader-following consensus problem is investigated by event-triggered control for multi-agent systems subject to time-varying actuator faults. Firstly, for a case of the leader without control input, a distributed event-triggered fault-tolerant protocol is proposed with the help of adaptive gains. Secondly, the proposed protocol is developed by an auxiliary nonlinear function to compensate the effect of the leader’s unknown bounded input. It is shown that under the both obtained protocols the tracking errors converge to an adjustable neighborhood around the origin, meanwhile the Zeno behavior is avoided. Moreover, the protocols are fully distributed in sense that any global information associated with the network is no longer utilized. Finally, numerical examples are presented to show the validity of the obtained protocols.     

Dual-Condition event-Triggered distributed adaptive neural control for multi-Agent systems with nonlinear fault

This paper studies the cooperative adaptive dual-condition event-triggered tracking control problem for the uncertain nonlinear nonstrict feedback multi-agent systems with nonlinear faults and unknown disturbances. Under the framework of backstepping technology, a new threshold update method is designed for the state event-triggered mechanism. At the same time, we develop a novel distributed dual-condition event-triggered strategy that combined the fixed threshold triggered mechanism acted on the controller with the new event-triggered mechanism, which can better reduce the waste of communication bandwidth. To deal with the algebraic loop problem caused by the non-affine nonlinear fault, the Butterworth low-pass filter is introduced. At the same time, the unknown function problems are solved by the neural network technology. All signals of the system are semiglobally uniformly ultimately bounded and the tracking performance is achieved, which proved by the Lyapunov stability theorem. Finally, the results of the simulation test the efficiency of the proposed control scheme.     

Integrated event-triggered fault estimation and fault-tolerant control for discrete-time fuzzy systems with input quantization and incomplete measurements

This paper addresses the problem of robust integrated fault estimation (FE) and fault-tolerant control (FTC) for a class of discrete-time networked Takagi–Sugeno (T–S) fuzzy systems with two-channel event-triggered schemes, input quantization and incomplete measurements. The incomplete information under consideration includes randomly occurring sensor saturation and randomly occurring quantization. In order to save the limited networked resources, this paper firstly proposed a novel dynamic event-triggered scheme on the sensor side and a static one on the controller side. Secondly, an event-triggered FE observer for the T–S fuzzy model is designed to estimate actuator faults and system states, simultaneously. Then, a specified discrete sliding surface in the state-estimation space is constructed. By using time-delay analysis technique and considering the effects of event-triggered scheme, quantization, networked conditions, actuator fault and external disturbance, the sliding mode dynamics and error dynamics are unified into a new networked time-delay model. Based on this model, sufficient conditions are established such that the resulting augmented fuzzy system is stochastically stable with a prescribed H_∞ performance level with a single-step linear matrix inequality (LMI) formulation. Furthermore, an observer-based sliding mode controller for reaching motion is synthesized to guarantee the reachability of the sliding surface. Finally, a single-link flexible manipulator example is present to illustrate the effectiveness of the proposed method.     

Event-triggered adaptive fault-tolerant control of uncertain non-affine systems with predefined performance

This paper is concerned with an event-triggered adaptive fault-tolerant problem for an uncertain non-affine system. The implicit function theorem and mean value theorem are utilized to transform a non-affine system into an affine one, and an extended state observer and a tracking differentiator are used to estimate unknown dynamics and the derivative of virtual control laws, respectively. Adaptive laws are designed for unknown faults, and an event-triggered control scheme with a time-varying threshold, based on a tracking error and adaptive parameters, is developed. The tracking error is steered to converge to a bounded set with the help of a predefined performance function, and its transient performance is improved despite of faults. The stability of the closed-loop system is analyzed by the theorem of the input-to-state practically stability, and the Zeno behavior is excluded. Finally, two examples are given to illustrate the effectiveness of the proposed scheme.     

An improved design strategy for approximation-based adaptive event-triggered tracking of a class of uncertain nonlinear systems

This paper presents an improved adaptive design strategy for neural-network-based event-triggered tracking of uncertain strict-feedback nonlinear systems. An adaptive tracking scheme based on state variables transmitted from the sensor-to-controller channel is designed via only single neural network function approximator, regardless of unknown nonlinearities unmatched in the control input. Contrary to the existing multiple-function-approximators-based event-triggered backstepping control results with multiple triggering conditions dependent on all error surfaces, the proposed scheme only requires one triggering condition using a tracking error and thus can overcome the problem of the existing results that all virtual controllers with multiple function approximators should be computed in the sensor part. This leads to achieve the structural simplicity of the proposed event-triggered tracker in the presence of unmatched and unknown nonlinearities. Using the impulsive system approach and the error transformation technique, it is shown that all the signals of the closed-loop system are bounded and the tracking error is bounded within pre-designable time-varying bounds in the Lyapunov sense.     

Composite learning adaptive sliding mode control of fractional-order nonlinear systems with actuator faults

This paper considers the tracking control of fractional-order nonlinear systems (FONSs) in triangular form with actuator faults by means of sliding mode control (SMC) and composite learning SMC (CLSMC). In SMC design, a fractional sliding surface is introduced, and an adaptation law is designed to update the estimation of the mismatched parametric uncertainty in the actuator faults. The proposed SMC can guarantee the convergence of the tracking error where a persistent excitation (PE) condition should be satisfied. To overcome this limitation, by using the online recorded data and the instantaneous data, a prediction error of the parametric uncertainty is defined. Both the tracking error and the prediction error are utilized to generate a composite learning law. A composite learning law is designed by using the prediction error and the tracking error. The proposed CLSMC can guarantee not only the stability of system but also the accurate estimation of the parametric uncertainties in the actuator faults. In CLSMC, only an interval-excitation (IE) condition that is weaker than the PE one should be satisfied. Finally, simulation example is presented to show the control performance of the proposed methods.     

Distributed adaptive fault-tolerant formation control for heterogeneous multiagent systems under switching directed topologies

This paper studies the cooperative fault-tolerant formation control problem of tracking a dynamic leader for heterogeneous multiagent systems consisting of multipile unmanned aerial vehicles (UAVs) and unmanned ground vehicles (UGVs) with actuator faults under switching directed interaction topologies. Based on local neighborhood formation information, the distributed fault-tolerant formation controllers are constructed to ensure that all follower UAVs and UGVs can accomplish the demanding formation configuration in the state space and track the dynamic leader’s trajectory. By incorporating the sliding mode control and adaptive control technique, the actuator faults and unknown parameters of follower agents can be compensated. Through the theoretical analysis, it is proved that the cooperatively semiglobally uniformly ultimately boundedness of the closed-loop system is guaranteed, and the formation tracking errors converge to a small adjustable neighborhood of the origin. A simulation example is introduced to show the validity of the proposed distributed fault-tolerant formation control algorithm.     

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.     

Event-triggered adaptive tracking control of uncertain nonlinear systems with prescribed performance and actuator failures

This article studies adaptive prescribed performance tracking control problem for a class of strict-feedback nonlinear systems with parametric uncertainties and actuator failures. Firstly, in order to compensate the multiple uncertainties and eliminate the influence of actuator failure, a new adaptive tracking controller based on first-order filter technology will be proposed, which simplifies the algorithm design process. Then, by introducing an asymmetric state transition function, the transient and steady performances of the output tracking error are both constrained such that the predetermined performance control goal is achieved. Moreover, to reduce the communication burden from the controller to the actuator, the event-triggered mechanism is designed, and there will be no Zeno phenomenon. Based on Lyapunov stability theory, it is strictly proved that output signal can track the reference signal and all the signals of the closed-loop system are bounded. Finally, a simulation example is performed and the results demonstrate effectiveness of the proposed strategy.     

Event-triggered fault estimation and sliding mode fault-tolerant control for a class of nonlinear networked control systems

This paper is concerned with integrated event-triggered fault estimation (FE) and sliding mode fault-tolerant control (FTC) for a class of discrete-time Lipschtiz nonlinear networked control systems (NCSs) subject to actuator fault and disturbance. First, an event-triggered fault/state observer is designed to estimate the system state and actuator fault simultaneously. And then, a discrete-time sliding surface is constructed in state-estimation space. By the use of a reformulated Lipschitz property and delay system analysis method, the sliding mode dynamics and state/fault error dynamics are converted into a unified linear parameter varying (LPV) networked system model by taking into account the event-triggered scheme, actuator fault, external disturbance and network-induced delay. Based on this model and with the aid of Lyapunov–Krasovskii functional method, a delay-dependent sufficient condition is derived to guarantee the stability of the resulting closed-loop system with prescribed H_∞ performance. Furthermore, an observed-based sliding mode FTC law is synthesized to make sure the reachability of the sliding surface. Finally, simulation results are conducted to verify the effectiveness of the proposed method.     

Leader-following consensus control for semi-Markov jump multi-agent systems: An adaptive event-triggered scheme

The problem of event-triggered leader-following consensus control for semi-Markov multi-agent systems is investigated in this paper. A semi-Markov process is used to describe the sudden parameter changes between every agent. An adaptive event-triggered control strategy is proposed to make a balance between reducing unnecessary communication and meeting the required performance. A control protocol which can resist actuator faults is used to ensure the reliable leader-following consensus. By employing the Lyapunov–Krasovskii functional method, some sufficient conditions are provided to guarantee that the leader-following consensus can be achieved in mean-square sense. The consensus controller and the event-triggered parameter can be co-designed. Finally, the effectiveness of the proposed method is verified by a F-404 aircraft engine system.     

Fault-tolerant control for commercial aircraft with actuator faults and constraints

In this paper, a constrained control scheme based on model reference adaptive control is investigated for the longitudinal motion of a commercial aircraft with actuator faults and saturation nonlinearities. Actuator faults and constraints are both important factors adversely affecting the stability and performance of flight control systems. An adaptive adjustment law based on Lyapunov function is utilized to adjust the fault-tolerant control law. Both additive and multiplicative faults are considered in the designed controller to deal with the three types of actuator faults: locked in place, loss of effectiveness, and bias. Moreover, different techniques are implemented in the basic and fault-tolerant controller to anti-windup. Proofs for the stability of the two modified controllers which improve the performance of control system operating in the presence of actuator faults and saturations are proposed. Finally, a numerical example of the anti-windup fault-tolerant controller for a commercial aircraft is demonstrated. The stability and performance improvements can be accrued with the presented fault-tolerant control scheme.     

Adaptive sliding mode control for uncertain Euler–Lagrange systems with input saturation

In this paper, the tracking control problem of uncertain Euler–Lagrange systems under control input saturation is studied. To handle system uncertainties, a leakage-type (LT) adaptive law is introduced to update the control gains to approach the disturbance variations without knowing the uncertainty upper bound a priori. In addition, an auxiliary dynamics is designed to deal with the saturation nonlinearity by introducing the auxiliary variables in the controller design. Lyapunov analysis verifies that based on the proposed method, the tracking error will be asymptotically bounded by a neighborhood around the origin. To demonstrate the proposed method, simulations are finally carried out on a two-link robot manipulator. Simulation results show that in the presence of actuator saturation, the proposed method induces less chattering signal in the control input compared to conventional sliding mode controllers.