Adaptive fault-tolerant tracking control for nonlinear systems with unknown control coefficient and input saturation

In this article, the tracking control problem is investigated for a class of nonlinear systems in the presence of unknown disturbance, input saturation, actuator fault, and unknown control coefficient. A novel disturbance observer-based adaptive fault-tolerant tracking control strategy is proposed with regard to nonlinear systems. Based on the Gaussian error function, the auxiliary dynamic system is designed to offset effects caused by the input saturation. Moreover, the Nussbaum-type function is employed to avert control singularity and deal with the unknown control coefficient. A theoretical analysis indicates that the boundedness of all signals in the closed-loop system can be guaranteed. Finally, two examples with one concerning the dynamic point-the-bit rotary steerable drilling tool system are given to confirm the validity of the method.     

Command-filtered-based neuroadaptive control for multi-input multi-output saturated nonstrict-feedback nonlinear systems with prescribed tracking performance

In this article, the prescribed performance control strategy is extended to multi-input multi-output nonstrict-feedback nonlinear systems with asymmetric input saturation, and not only each element in tracking error vector converges to a prescribed small region within preassigned finite time, but also the converging mode during the preset time is prespecifiable and controllable explicitly. By blending the barrier function with novel speed function, a prescribed performance controller using command-filtered-based vector-backstepping design framework is proposed to steer the tracking error vector for the first time, where the boundedness of filter errors is guaranteed by sufficiently small time constant and an error compensator is constructed to handle the effects of filter errors. To attenuate the adverse effects resulted from nondifferentiable input saturation, hyperbolic tangent function is utilized to estimate asymmetric saturation function such that the control input is designed as a new state variable with initial value of zero in augmented system. Nussbaum function is employed to overcome singularity problem caused by the differentiation of hyperbolic tangent function. At each step of backstepping design, the universal approximation property of neural network and the command filter system are utilized to approximate uncertain dynamics and to solve algebraic loop obstacle due to nonstrict-feedback structure, respectively. Moreover, only one parameter needs to be updated online to cope with the lumped uncertain dynamics by virtual parameter technology, rendering a control strategy with low complexity computation. The validity of the presented controller is verified by theoretical analysis and two-link robotic system.     

具有输入饱和的不正定关联系统分散控制

针对在实际控制系统中,如果不考虑输入饱和而设计控制器,闭环系统的稳定性无法保证,讨论了具有输入饱和的不确定非线性交联系统的分散控制问题。利用Riccati方程的方法、Lyapunov稳定理论和矩阵理论,研究了一类具有输入饱和的不确定非线性关联大系统的分散鲁棒镇定问题,给出了该类系统可分散鲁棒控制的一个充分条件,并提出了一种分散鲁棒控制器的设计方法。同时,考虑了一类具有输入饱和的不确定非线性相似关联大系统,由于相似系统的结构特点,给出了简洁的分散鲁棒控制条件。     

Mapping filtered forwarding‐based robust adaptive control for uncertain nonlinear systems with input constraint

This work develops a robust adaptive control algorithm for uncertain nonlinear systems with parametric uncertainties and external disturbances satisfying an extended matching condition. This control method is implemented in the framework of a mapping filtered forwarding‐based technique. As an attractive alternative of the adaptive backstepping method, this bottom‐up strategy forms a virtual controller and a parameter updated law at each step of the design, where Lyapunov functions and the prior knowledge of system parameters are not required. The boundedness of all signals is guaranteed by using Barbalat's lemma. According to immersion relationship, a compliant behavior of systems behaves accordingly to the lower‐order target dynamics. Furthermore, input constraints are handled by estimating a saturated scaling. A spring, mass, and damper system is used to demonstrate the controller performances via simulation results.     

Adaptive control of stochastic nonlinear systems with Markovian switching

This paper is concerned with the problem of adaptive control for a class of stochastic nonlinear systems with Markovian switching, where the upper bounds of nonlinearities of stochastic Markovian jump systems are assumed to be unknown. Firstly, an adaptation law is developed to estimate these unknown parameters. Then, a class of adaptive state feedback controller is proposed such that not only the estimated errors are bounded almost surely but also, the states of the resulting closed‐loop system are asymptotically stable almost surely. Finally, a numerical example is given to show the validity of the results.Copyright © 2012 John Wiley & Sons, Ltd.     

Adaptive controller design with prescribed performance for switched nonstrict feedback nonlinear systems with actuator failures

This article is concerned with the adaptive output-feedback control of switched nonstrict feedback nonlinear systems. By introducing a novel error surface, an adaptive control strategy is proposed for the general case where the nonlinear functions and the control gain functions are unknown, and the states are unmeasurable. The considered switched nonlinear system contains unknown actuator failures, which are modeled as both loss of effectiveness and lock-in-place. In order to improve the transient performance in the presence of unknown actuator failures, the prescribed performance approach is used. The “explosion of complexity” problem is avoided through using low-pass filters. The stability of the closed-loop system under arbitrary switching is shown using Lyapunov stability theory, based on which, the tracking error is shown to converge to a small residual set with the prescribed performance bounds. The advantages of the proposed technique are verified through simulations of two numerical and practical examples.     

Adaptive prescribed performance tracking control for uncertain strict-feedback Multiple Inputs and Multiple Outputs nonlinear systems based on generalized fuzzy hyperbolic model

This article proposes an adaptive prescribed performance tracking control methodology for a class of strict-feedback Multiple Inputs and Multiple Outputs nonlinear systems. A combination of backstepping technique and the generalized fuzzy hyperbolic model was used in recursive design of adaptive controller. A novel performance constraint function guarantees the tracking control performance. Lyapunov stability analysis proves that the designed controller can ensure the predefined transient and all signals within the closed-loop systems are semiglobally uniformly ultimately bounded. In the end, simulation results illustrate the validity of the proposed approach.     

Adaptive control for nonlinear uncertain systems with actuator amplitude and rate saturation constraints

A direct adaptive nonlinear tracking control framework for multivariable nonlinear uncertain systems with actuator amplitude and rate saturation constraints is developed. To guarantee asymptotic stability of the closed‐loop tracking error dynamics in the face of amplitude and rate saturation constraints, the control signal to a given reference (governor or supervisor) system is modified to effectively robustify the error dynamics to the saturation constraints. Illustrative numerical examples are provided to demonstrate the efficacy of the proposed approach. Copyright © 2008 John Wiley & Sons, Ltd.     

Asynchronous adaptive output feedback sliding mode control for Takagi-Sugeno fuzzy Markovian jump systems with actuator faults

In this article, the problem of asynchronous adaptive dynamic output feedback sliding mode control (SMC) for a class of Takagi-Sugeno (T-S) fuzzy Markovian jump systems (MJSs) with actuator faults is investigated. The asynchronous dynamic output feedback control strategy is employed, as the nonsynchronization phenomenon of jump modes exists between the plant and the controller. A novel asynchronous adaptive SMC approach is proposed to solve the synthesis problem for T-S fuzzy MJSs with actuator faults. Sufficient conditions for stochastic asymptotic stability of T-S fuzzy MJSs are given. Under the designed asynchronous adaptive SMC scheme, the effects of actuator faults and external disturbance can be completely compensated and the reachability of sliding surface is ensured. Finally, an example is provided to demonstrate the effectiveness of the proposed design techniques.     

Fuzzy adaptive two-bits-triggered control for nonlinear uncertain system with input saturation and output constraint

In this work, a fuzzy adaptive two-bits-triggered control is investigated for the nonlinear uncertain systems with input saturation and output constraint. The considered systems are more widespread. Without sufficient transmission resources, how to resolve the constraint issues while guarantee the control performance is difficult and challenging. Then, hyperbolic tangent function and barrier Lyapunov function are integrated with the designed auxiliary system to solve input saturation and output constraint. Meanwhile, faced with the transmission resources limitation, this work both considers the triggering condition and the control signal transmission bits. A two-bits-triggered control is proposed to economize the transmission resources. Furthermore, improved fuzzy logic systems are established to further promote the control performance. It combines with the time-varying approximation error for processing. The boundedness of all the system signals can be proved. Simulation results illustrate the validity of the proposed approach.     

Robust reliable dissipative filtering for Markovian jump nonlinear systems with uncertainties

This paper investigates the problem of robust reliable dissipative filtering for a class of Markovian jump nonlinear systems with uncertainties and time‐varying transition probability matrix described by a polytope. Our main attention is focused on the design of a reliable dissipative filter performance for the filtering error system such that the resulting error system is stochastically stable and strictly dissipative. By introducing a novel augmented Lyapunov–Krasovskii functional, a new set of sufficient conditions is obtained for the existence of reliable dissipative filter design in terms of linear matrix inequalities (LMIs). More precisely, a sufficient LMI condition is derived for reliable dissipative filtering that unifies the conditions for filtering with passivity and H_∞ performances. Moreover, the filter gains are characterized in terms of solution to a set of linear matrix inequalities. Finally, two numerical examples are provided to demonstrate the effectiveness and potential of the proposed design technique. Copyright © 2016 John Wiley & Sons, Ltd.     

Adaptive event-triggered consensus control of multi-agent systems with prescribed performance and input quantization

This paper focuses on the adaptive fuzzy event-triggered consensus control problem for multi-agent systems (MAS) with prescribed performance and input quantization. Based on a prescribed performance function and an input quantization decomposition method, a new adaptive fuzzy event-triggered consensus protocol is presented. The instances in the event-triggered mechanism are triggered only when the event-triggered error exceeds a specified threshold, which can save limited communication resources. It is demonstrated that the event-triggered control protocol ensures that all signals in the MAS are semi-globally uniformly ultimately bounded. As a result, the consensus tracking errors converge to prescribed limits. Finally, simulation examples are provided to validate effectiveness of the proposed event-triggered control methods.     

Tracking control for nonlinear time-delay multiagent systems with input saturation

In this paper, the tracking control problem for a class of nonlinear time-delay multiagent systems with input saturation is considered. The nonlinear dynamics are dominated by strict-feedback form and satisfy Lipschitz conditions with constant gains. First, it indicated that the tracking control problem is equivalent to a general bound problem of high-dimensional multivariable systems. Second, an ingenious state transformation is utilized to change the bound problem into the parameter design problem. Third, by the static gain control technique and the hyperbolic tangent function, both state feedback and output feedback controllers are built such that all signals of the closed-loop systems are globally bounded, and the tracking errors between the followers and the leader can converge to a small neighborhood around the origin by appropriately selecting parameters. Finally, an example is shown to verify the feasibility of our results.     

Finite‐time prescribed performance adaptive fuzzy fault‐tolerant control for nonstrict‐feedback nonlinear systems

This paper focuses on a finite‐time adaptive fuzzy control problem for nonstrict‐feedback nonlinear systems with actuator faults and prescribed performance. Compared with existing results, the finite‐time prescribed performance adaptive fuzzy output feedback control is under study for the first time. By designing performance function, the transient performance of the corresponding controlled variable is maintained in a prescribed area. Combining the finite‐time stability criterion with backstepping technique, a feasible adaptive fault‐tolerant control scheme is proposed to guarantee that the system output converges to a small neighborhood of the origin in finite time, and the closed‐loop signals are bounded. Finally, simulation results are shown to illustrate the effectiveness of the presented control method.     

Adaptive prescribed performance control of nonlinear systems with unknown dead zone

An alternative adaptive control with prescribed performance is proposed to address the output tracking of nonlinear systems with a nonlinear dead zone input. An appropriate function that characterizes the convergence rate, maximum overshoot, and steady‐state error is adopted and incorporated into an output error transformation, and thus the stabilization of the transformed system is sufficient to achieve original tracking control with prescribed performance. The nonlinear dead zone is represented as a time‐varying system and Nussbaum‐type functions are utilized to deal with the unknown control gain dynamics. A novel high‐order neural network with a scalar adaptive weight is developed to approximate unknown nonlinearities, thus the computational costs can be diminished dramatically. Some restrictive assumptions on the system dynamics and the dead‐zone are circumvented. Simulations are included to validate the effectiveness of the proposed scheme. Copyright © 2012 John Wiley & Sons, Ltd.     

Adaptive control for switched uncertain nonlinear systems with time‐varying output constraint and input saturation

This paper is concerned with adaptive tracking control for switched uncertain nonlinear systems, which contain the time‐varying output constraint (TVOC) and input asymmetric saturation characteristic. In response to the unknown functions, the fuzzy logic systems are adopted. The controller is constructed by the backstepping technique. Based on the Tangent Barrier Lyapunov Function (BLF‐Tan), an adaptive switched control scheme is designed. It is demonstrated that all signals in the resulted system are semiglobally uniformly ultimately bounded with TVOC under arbitrary switchings. Furthermore, the effectiveness of presented control method is validated via the simulation example.     

Robust adaptive steering control for unmanned surface vehicle with unknown control direction and input saturation

A robust adaptive steering control method is proposed to solve the control problem of the unmanned surface vehicle (USV) with uncertainties, unknown control direction, and input saturation. In the controller design process, the adaptive fuzzy system is incorporated into dynamic surface control (DSC) to approximate the uncertainty term induced by external environmental disturbances and model parameters. Then, the Nussbaum function is used to eliminate the requirement for a priori knowledge of the control direction. Besides, to handle the input saturation, the adaptive fuzzy DSC is extended by a second‐order nonlinear filter and antisaturation auxiliary function to compensate for the magnitude and rate saturation of the rudder. All signals of the closed‐loop system are proven to be uniformly ultimately bounded (UUB) by Lyapunov theorem and the Lemma of Nussbaum gain, and the course error can converge to a small neighborhood of zero through choosing design parameters appropriately. Finally, simulation results and comprehensive comparisons are shown for the USV course system, which is demonstrative of the proposed controller's effectiveness and robustness.     

基于复合自适应的Buck变换器预设性能控制

针对Buck型变换器在复杂环境下发生负载波动时输出电压受扰的问题,提出了一种复合自适应预设性能控制方案以提升其控制效果。首先,利用自适应律对模型中包含负载项的非线性函数进行预测估计,同时通过在自适应律更新过程中构建并行估计模型获取预测误差,并将预测误差和跟踪误差融合以设计自适应参数更新律。然后,采用广义比例积分观测器来对剩余不确定性和外部扰动进行估计,并在控制律中进行补偿。最后,结合指令滤波反步控制和指定时间预设性能控制技术,提出了Buck型变换器复合自适应预设性能控制方案。所提出的方案保证了对负载波动的高精度预测,避免了在突发情况下输出电压超出预设函数范围,此外还证明了闭环控制系统中的信号收敛性。实验结果表明,复合自适应预设性能控制在负载突然减小的情况下系统最大偏离电压为0.376 V,相比于传统自适应反步控制的1.773 V减少了78.7%,验证了所提方案的有效性以及优越性。     

Robust adaptive tracking control for nontriangular time-delay nonlinear systems with input dead-zone and multiple uncertainties

This article studies the robust adaptive tracking control problem of nontriangular nonlinear systems that are affected by multiple state delays rather than the input-delay. Different from the related studies, the considered systems involve input dead-zone and various uncertainties arising in the control coefficients, structure parameters, time delays, and disturbances. A new adaptive control strategy is presented by introducing a dynamic-gain-based Lyapunov-Krasovskii functional and by generalizing the tuning function method in the framework of time-delay system theory. All the states of the closed-loop system are bounded and the tracking error can be adjusted sufficiently small. In the simulation, the delayed chemical system is studied to demonstrate the validity of the strategy.     

Accelerated neuroadaptive tracking control of strict‐feedback nonlinear systems without precise knowledge of target trajectory

The problem of tracking control under uncertain desired trajectory is interesting but nontrivial. The problem is even more challenging if the system under consideration involves modeling uncertainties. This paper investigates such problem for strict‐feedback nonlinear systems. By combining Fourier series with radial basis function neural networks (NNs), an analytical model is developed to reconstruct the unknown desired trajectory. Based on which, 2 neural adaptive control schemes are developed to maintain target tracking closely. The first control strategy is based on direct tuning of the NN weights, and the second strategy is built upon the concept of a virtual parameter related to NN weights, which substantially reduces the number of parameters to be online updated, rendering the strategy structurally simpler and computationally less expensive. The effectiveness of the proposed control strategy is confirmed by systematic stability analysis and numerical simulation.