Fault-tolerant Tracking Control Problem Research Articles

Adaptive Fault-Tolerant Tracking Control for Discrete-Time Nonstrict-Feedback Nonlinear Systems With Stochastic Noises

This paper discusses the problem of fault-tolerant tracking control for discrete-time nonstrict-feedback nonlinear systems in the presence of stochastic noises and actuator faults. The system is characterized by a discrete-time nonstrict-feedback structure and multiplicative stochastic noise related to the states, which poses a challenge for the design and analysis of the fault-tolerant controller. Moreover, the considered actuator faults include multiplicative and additive faults without prior information. By integrating the properties of the backstepping framework and neural networks, and by introducing an adaptive fault compensation term, a novel fault-tolerant tracking control strategy is proposed. The effects of faults are compensated and the difficulties caused by the system structure are overcome, avoiding the algebraic loop problem and overcoming the causal contradiction. Given specific parameters, the designed fault-tolerant controller can ensure that the tracking error converges to an adjustable region regarding the origin and that all system signals are uniformly bounded concerning the mean-square sense. The simulation examples illustrate the effectiveness of the designed fault-tolerant control method. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —As system complexity has been increasing, practical systems are often affected by faults when performing tracking control. Fault-tolerant control can provide acceptable robustness and improve system safety. On the one hand, many practical systems are nonlinear, difficult to model mathematically and accurately, and affected by stochastic noises. On the other hand, with digital control, the object is a discrete-time system. In practical applications, the upper bounds of the faults and the noises are often unknown. In this paper, a novel adaptive fault-tolerant control method is proposed for the more general uncertain discrete-time nonlinear systems, i.e., nonstrict-feedback nonlinear systems, with stochastic noises and actuator faults. Neural networks and an adaptive fault compensation term are integrated into the fault-tolerant controller. By adjusting the controller parameters properly, it is ensured that the tracking error converges to a small neighborhood of zero in the event of a fault occurring. In future research, sensor faults, input constraints, optimal control design, and applications in multi-agent systems will be considered.

Adaptive fixed-time fault-tolerant tracking control for rotary steerable drilling tool systems

In this paper, the problem of adaptive fixed-time fault-tolerant tracking control is investigated for rotary steerable drilling tool systems (RSDTSs). Markov jump system (MJS) is used to describe the RSDTS with varying parameters which are induced by the changing environment. By employing the smooth projection operator technique, adaptive laws are established to estimate the faults. Based on the fault compensation strategy, a new adaptive fixed-time fault-tolerant tracking control scheme is proposed to ensure that the RSDTS is globally stochastically practically fixed-time stable. In addition, to reduce the computational burden in the backstepping framework, the derivatives of the virtual control are directly derived using command filters. Finally, the experiment performed on the rotary steerable drilling tool systems prototype is exploited to demonstrate the feasibility and effectiveness of the proposed method.

Prescribed-time fault-tolerant tracking control for Markov jump nonlinear systems based on saturation dynamics filters

This paper investigates the problem of prescribed-time fault-tolerant tracking control for a class of Markov jump nonlinear systems affected by actuator faults and input saturation. First, a new time-varying constraint function and an error transformation are invoked to transform the original prescribed-time tracking control problem into a tracking control problem with deferred constraint for tracking error. Furthermore, the parameter correction terms are designed, on which a novel Markov jump saturation dynamic filter is constructed to handle the unfavorable effect of input saturation. Meanwhile, the projection operator technique and the norm estimation methodology are integrated to devise adaptive laws to estimate the unknown actuator faults evolving in accordance with the Markov chain. A new prescribed-time fault-tolerant tracking control scheme is put forward that realizes the deferred constraint on the tracking error, which in turn ensures that the tracking error of the system converges to a prescribed accuracy within a prescribed-time. Finally, two simulation examples, one of which implements a prescribed-time fault-tolerant tracking control for rotary steerable drilling tool system, are presented to illustrate the effectiveness and practicality of the developed scheme.

Adaptive fuzzy finite-time output feedback fault-tolerant control for MIMO stochastic nonlinear systems with non-affine nonlinear faults

This paper investigates adaptive fuzzy finite-time output feedback fault-tolerant tracking control problem for multiple-input multiple-output (MIMO) stochastic non-strict feedback nonlinear systems with non-affine nonlinear faults and states unmeasured. Firstly, high-gain fuzzy state observers are constructed to overcome the state unmeasured problem in the system. Secondly, the mean-value theorem and input compensation techniques are employed to decouple non-affine nonlinear faults, and the resulting unknown control coefficients problem is handled using Nussbaum functions. In addition, dynamic surface control techniques and error compensation mechanisms are considered in the controller design, which effectively decreases the computational complexity of the control scheme. By combining the adaptive backstepping technique with finite-time control, a novel adaptive fuzzy dynamic surface finite-time output feedback fault-tolerant tracking control algorithm is proposed. The designed controller guarantees that all signals in the stochastic systems are semi-global finite-time stable in probability (SGFSP) as well as the tracking errors can converge to a small neighborhood within the origin in finite-time. Finally, two simulation examples are introduced to verify the effectiveness of the suggested control strategy.

Two-dimensional model-free Q-learning-based output feedback fault-tolerant control for batch processes

For batch processes with partial actuator failures and unknown system dynamics, an innovative two-dimensional (2D) model-free Q-learning algorithm is proposed to obtain the optimal controller's gains, achieving output feedback fault-tolerant control. First, a 2D linear model is constructed to describe batch processes with partial actuator failures. Then, the state increments in the batch direction and the output errors in the time direction are used as novel state variables to construct a multi-degree-of-freedom model. Second, a 2D Bellman equation is proposed through a connection between a 2D value and a 2D Q functions. Next, a 2D off-policy model-free Q-learning algorithm is highlighted, which incorporates target policies into a multi-degree-of-freedom model and focuses on using policy iteration to solve the fault-tolerant tracking control problem. The robustness analysis rigorously proves the stability of the closed-loop system. Lastly, the simulation results of the holding stage prove the feasibility and effectiveness of the presented algorithm.

Pseudo-partial-derivative information-driven adaptive fault-tolerant tracking control for discrete-time systems

The fault-tolerant tracking control problem is studied for the discrete-time systems with actuator faults. To lessen adverse impacts of actuator fault, a PPD information-driven fault estimation algorithm is established to adaptively estimate actuator fault information online, which avoids the additional construction and training process of neural network. With the aid of the adaptive fault compensation, a model-free adaptive fault-tolerant tracking control algorithm is constructed to ensure that the expected output reference trajectory can be tracked by system output. Moreover, only input and output data are employed throughout the design process, system dynamics are not demanded. Ultimately, the availability of developed strategy is proved through a simulation.

Fault-tolerant tracking control for nonlinear systems with multiplicative actuator faults in view of zero-sum differential games

In view of zero-sum differential games, this paper addresses the fault-tolerant tracking control (FTTC) problem for nonlinear systems with multiplicative actuator faults. By augmenting the nominal system, the trajectory tracking problem is transformed into an optimal regulation problem. A fault observer is designed to estimate the multiplicative actuator fault factor. In order to better reflect system performance, a comprehensive performance index function including the trajectory tracking error, the control input, and the multiplicative actuator fault is constructed. By considering the control input and the multiplicative actuator fault as two players in the zero-sum differential game (ZSDG), the FTTC problem is thus transformed into a ZSDG problem. Then, a fault-tolerant control based on ZSDG is designed by solving the Hamilton–Jacobi-Isaacs (HJI) equation. Since the HJI equation is difficult to solve, a critic neural network is constructed to obtain its approximation, which constitutes the Nash equilibrium of the ZSDG. The closed-loop faulty system is guaranteed to be uniformly ultimately bounded via the Lyapunov’s direct method. The effectiveness of the developed FTTC method is demonstrated by two simulation examples.

Formula omitted]output feedback fault-tolerant control of industrial processes based on zero-sum games and off-policy Q-learning

Traditional model-based control methods are often not applicable in industrial processes given the typical situation that model parameters are unknown, coefficient matrices are difficult to obtain, and system states are unpredictable. Accordingly, an output feedback fault-tolerant control method based on zero-sum game theory and off-policy Q-learning is presented in this study, with the aim of achieving smooth operation and good tracking performance for industrial processes that often contain sensor faults and disturbances. The specific steps are as follows. First, a system tracking error is introduced into the system to realize a novel extended model. Second, by establishing a performance index function and combining it with minimax theory, the fault-tolerant tracking control problem is converted into a zero-sum game problem. The Bellman and Riccati equations can be established after analyzing the relationship between the performance index and value functions. Then, the Q-function is introduced, and an off-policy Q-learning algorithm is combined with the Kronecker product without knowledge of system model parameters to design an optimal controller unbiased to detection noise. Finally, the effectiveness of the algorithm is verified by considering the injection molding process as an example. The experimental results validate that the designed controller demonstrates good control and extends the range of tolerable faults while maintaining good tracking performance.

Improved finite-time prescribed performance based adaptive neural control for nonlinear systems with sensor faults

In this article, based on a novel finite-time prescribed performance function, we consider the issue of the adaptive neural fault-tolerant tracking control problem for a type of nonlinear system with sensor faults. The control performance of the system may be affected when sensor faults occur. For the controlled system with sensor faults, an improved finite-time performance function is proposed so that its initial conditions do not need to be set in advance. Compared with existing performance functions, the performance functions in this paper can ensure that the system is always controllable, even if the sensor faults occur suddenly during the steady operation. Moreover, Radial basis function (RBF) neural networks (NNs) are employed to estimate the uncertain smooth nonlinear functions. With the help of the adaptive backstepping control technique, an improved adaptive prescribed performance control technique is developed, which can realize the boundedness of every signal in the closed-loop system, and the tracking error can be limited within the neighborhood near the origin. Simulation results demonstrate the effectiveness of the proposed control scheme.

Adaptive Fuzzy Fixed-Time Control for High-Order Nonlinear Systems With Sensor and Actuator Faults

The adaptive fuzzy fixed-time fault-tolerant tracking control problem for high-order nonlinear systems (HONS) with sensor and actuator faults is considered in this paper. The fuzzy logic systems is introduced to approximate the unknown nonlinear functions of the HONS. In addition, on the basis of backstepping technology and fixed-time theory, an adaptive fuzzy fixed-time fault-tolerant controller is developed to ensure all signals of the closed-loop HONS to be bounded. Eventually, the numerical example can be shown to prove rationality of developed method.

Adaptive Fault-Tolerant Tracking Control for Uncertain Nonlinear Systems With Unknown Control Directions and Limited Resolution

This article addresses the adaptive fault-tolerant tracking control (FTTC) problem for a family of strict-feedback uncertain nonlinear systems subject to limited sensor resolution and unknown control directions. Both partial loss-of-effectiveness (LOE) and lock-in-place (LIP) faults of actuators are investigated. An adaptive control strategy based on a Nussbaum-type function and neural networks is presented by introducing a backstepping approach to make the system output track a desired reference output signal with bounded tracking error in the case of faulty actuators. The effect of the limited resolution is decoupled from the nonlinear system and is approximated using a neural network. The impact of disturbances is effectively compensated by utilizing adaptive parameter estimation terms in the backstepping procedure. It is proven that the proposed FTTC strategy can ensure the boundedness of all signals and guarantee that the output tracking error can converge into a small neighborhood of the origin. Two simulation examples are given to illustrate the effectiveness of the proposed FTTC strategy.

Cerebellar Model Articulation Neural Network-Based Distributed Fault Tolerant Tracking Control with Obstacle Avoidance for Fixed-Wing UAVs

In this paper, the distributed fault-tolerant tracking control (FTTC) and obstacle avoidance problem is investigated for multiple unmanned aerial vehicles (UAVs) considering lumped disturbances and communication link faults. Firstly, a cerebellar model articulation neural network (CMANN) is introduced to esti-mate the lumped disturbances. Meanwhile, the distributed virtual leader state observers are used to address unknown communication faults. Then, a distributed nonsingular fast terminal sliding mode formation controller is implemented to track desired trajectory, and an virtual-agent artificial potential function (VAAPF) is designed to accomplish obstacle avoidance. Furthermore, the stability of the closed loop formation control systems with obstacle avoidance is proved using graph theory and Lyapunov theory. Finally, simulation results of three fixed-wing UAVs are given to show the effectiveness and good performance of the proposed scheme.

Off-policy reinforcement learning-based novel model-free minmax fault-tolerant tracking control for industrial processes

For industrial processes with external disturbance and actuator failure, off-policy reinforcement learning-based novel model-free minmax fault-tolerant control is proposed in this paper to solve H∞ fault-tolerant tracking control problem. An augmented model equivalent to the original system is constructed, and the state of the new augmented model is composed of state increment and tracking error of the original system. The original H∞ fault-tolerant tracking problem was transformed into the linear quadratic zero-sum game problem by establishing performance index function, and the Game Algebraic Riccati Equation (GARE) was established. Then Q function was introduced and the Off-policy reinforcement learning algorithm was designed. Different from the traditional model-based fault-tolerant control method, the proposed algorithm does not need the knowledge of system dynamics, and it can learn from the measured data of the system trajectory to solve the GARE. In addition, it is proved that the probing noise added to satisfy the persistent excitation condition does not cause bias. A simulation example of injection molding process is used to verify the effectiveness of the proposed algorithm.

Single critic network based fault-tolerant tracking control for underactuated AUV with actuator fault

This work investigates the fault-tolerant control problem for underactuated autonomous underwater vehicle (AUV), in which the actuator fault is addressed, that is the sophisticated and challenging problem. A single critic network based adaptive dynamic programming (ADP) is employed to construct a novel fault-tolerant control scheme combined with the backstepping method. Firstly, a virtual velocity control vector is designed based on the kinematic model of underactuated AUV using backstepping approach. The virtual velocity control vector is taken as the virtual velocity of the dynamic model of underactuated AUV. Secondly, an error tracking system is constructed to transform the fault-tolerant tracking control problem into the optimal control problem. Then an online policy iteration algorithm is designed based on the estimated system states. Based on Lyapunov approach, the stability of the error tracking system is guaranteed by the proposed controller. Finally, the simulation results are shown to verify the effectiveness of the proposed method in this work.

Adaptive cooperative fault-tolerance tracking control for multi-agent system with hybrid actuator faults and multiple unknown control directions

This paper investigates the cooperative fault-tolerant control for the nonlinear multi-agent system with hybrid actuator faults and multiple unknown control directions based on robust adaptive fuzzy sliding mode technology (RAFSMT). Firstly, a piecewise Nussbaum function is proposed to solve the multiple unknown control directions, and the robust adaptive fuzzy technique is designed to handle the nonlinear uncertainty in the system. Meanwhile, a first-order sliding mode differentiator is introduced, and it is combined with the adaptive backstepping technique to obtain the first-order derivative of the virtual control law. Moreover, a robust bounded method is used to improve the convergence speed and tracking accuracy of the designed adaptive cooperative controller. Then, the designed controller can effectively solve the fault-tolerant tracking control problem of multi-agent systems with hybrid actuator faults and unknown control directions. Compared with the methods in other references, the proposed method can make the system still maintain a good tracking effect with small steady-state error, short response time, and good fault tolerance. Finally, the effectiveness of the proposed method is verified by the comparison of simulation examples.

Adaptive fuzzy output feedback fault-tolerant tracking control of switched uncertain nonlinear systems with sensor faults

This paper investigates the adaptive fuzzy output feedback fault-tolerant tracking control problem for a class of switched uncertain nonlinear systems with unknown sensor faults. In this paper, since the sensor may suffer from an unknown constant loss scaling failure, only actual output can be used for feedback design. A failure factor is employed to represent the loss of effectiveness faults. Then, an adaptive estimation coefficient is introduced to estimate the failure factor, and a state observer based on the actual output is constructed to estimate the system states. Fuzzy logic systems are used to approximate the unknown nonlinear functions. Based on the Lyapunov function method and the backstepping technique, the proposed control scheme with average dwell time constraints can guarantee that all states of the closed-loop system are bounded and the tracking error can converge to a small neighborhood of zero. Finally, two simulation examples are given to illustrate the effectiveness of the proposed scheme.

Fault-Tolerant Control of Pneumatic Continuum Manipulators Under Actuator Faults

This article is concerned with the fault-tolerant tracking control problem for pneumatic continuum manipulator (PCM) systems with actuator faults. Conventional control strategies applied to PCMs have difficulty addressing the tracking control issue for systems subject to actuator faults. In this article, we provide a robust fault-tolerant control strategy for solving this issue. We first present an error transformation approach that possesses potential robustness against model uncertainties and unknown actuator faults. To relax certain restrictions in the error transformation approach, we then adopt a tuning function to adjust the error variables. By doing so, global stability of the closed-loop system is ensured. Finally, the effectiveness of this control strategy is validated through experiments on a PCM.

Adaptive Fault-Tolerant Tracking Control for Discrete-Time Multiagent Systems via Reinforcement Learning Algorithm

This article investigates the adaptive fault-tolerant tracking control problem for a class of discrete-time multiagent systems via a reinforcement learning algorithm. The action neural networks (NNs) are used to approximate unknown and desired control input signals, and the critic NNs are employed to estimate the cost function in the design procedure. Furthermore, the direct adaptive optimal controllers are designed by combining the backstepping technique with the reinforcement learning algorithm. Comparing the existing reinforcement learning algorithm, the computational burden can be effectively reduced by using the method of less learning parameters. The adaptive auxiliary signals are established to compensate for the influence of the dead zones and actuator faults on the control performance. Based on the Lyapunov stability theory, it is proved that all signals of the closed-loop system are semiglobally uniformly ultimately bounded. Finally, some simulation results are presented to illustrate the effectiveness of the proposed approach.

Adaptive Fuzzy Output Feedback Fault-Tolerant Compensation for Uncertain Nonlinear Systems With Infinite Number of Time-Varying Actuator Failures and Full-State Constraints.

This paper focuses on the observer-based fuzzy adaptive fault-tolerant tracking control problem for uncertain nonlinear systems subject to unmeasured states and unmatched external disturbances. By designing a high gain state observer and a disturbance observer, unmeasured states and unmatched external disturbances are estimated and robust tracking performance is improved. Moreover, the barrier-type functions are introduced to the backstepping design procedure to address the problem that all states do not violate their constraint bounds. Finally, a novel fault-tolerant control scheme for output feedback is proposed by combining with the projection technique. By designing appropriate Lyapunov functions, it is concluded that all signals of the plant are bounded and the desired tracking error can be regulated to a small neighborhood around the origin. The simulation results show the effectiveness of the designed control scheme.

Fuzzy Adaptive Quantized Fault-Tolerant Control of Strict-Feedback Nonlinear Systems With Mismatched External Disturbances

In this paper, the problem of adaptive fault-tolerant tracking control for strict-feedback nonlinear systems is investigated. By using the Nussbaum function technique, the difficulty caused by input quantization and infinite number of time-varying actuator faults is handled and a novel fuzzy adaptive control scheme is designed without estimating a lower bound on the quantizer parameter and the time-varying effectiveness factor. Based on the Lyapunov stability theory, it is proven that all the signals in the resulting closed-loop system are bounded and the tracking error satisfies the desired performance all the time. Simulation results are presented to verify the effectiveness of the proposed controller.