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.     

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.     

Compound conditions event-triggered tracking control for nonlinear multiagent systems with nonlinear output faults

This article is devoted to investigating the compound conditions event-triggered prescribed performance tracking problem for strict-feedback nonlinear multiagent systems with nonlinear output faults and unknown disturbances. A simplified event-triggered sampling condition is designed to successfully reduce the number of state triggered design parameters. Besides, a compound conditions event-triggered mechanism is constructed, which integrates state triggered and controller triggered simultaneously to reduce communication burden. Furthermore, by using disturbance observers and prescribed performance functions, unknown external disturbances are compensated and the tracking errors can converge into the prescribed boundary, respectively. Moreover, all the signals of the closed-loop system are semiglobally uniformly ultimately bounded. Finally, the availability of the proposed control strategy is testified via simulation results.     

Decentralized prescribed performance adaptive tracking control for Markovian jump uncertain nonlinear systems with input saturation

A decentralized prescribed performance adaptive tracking control problem is investigated for Markovian jump uncertain nonlinear interconnected large‐scale systems. The considered interconnected large‐scale systems contain unknown nonlinear uncertainties, unknown control gains, actuator saturation, and Markovian jump signals, and the Markovian jump subsystems are in the form of triangular structure. First, by defining a novel state transformation with the performance function, the prescribed performance control problem is transformed to stabilization problem. Then, introducing an intermediate control signal into the control design, employing neural network to approximate the unknown composite nonlinear function, and based on the framework of the backstepping control design and adaptive estimation method, a corresponding decentralized prescribed performance adaptive tracking controller is designed. It is proved that all the signals in the closed‐loop system are bounded, and the prescribed tracking performances are guaranteed. A numerical example is provided to illustrate the effectiveness of the proposed control strategy. Copyright © 2016 John Wiley & Sons, Ltd.     

Adaptive multi-dimensional Taylor network funnel control of a class of nonlinear systems with asymmetric input saturation

In view of the result and performance of control are affected by the existence of input constraints and requirements, adaptive multi-dimensional Taylor network (MTN) funnel control problem is studied for a class of nonlinear systems with asymmetric input saturation in this paper. Firstly, the effect of asymmetric input saturation can overcome by introducing the Gaussian error function, namely, the asymmetric saturation model is represented as a simple linear model with a bounded disturbance. Secondly, MTNs are employed to approximate the unknown functions in the controller design. Then, an adaptive MTN tracking controller is developed by blends the idea of funnel control into backstepping, which can guarantee that the tracking error always meets the given prescribed performance regarding the transient and steady state responses as well as the output of system tracks the give continuous reference signal. Finally, the effectiveness of the proposed control is demonstrated using two examples.     

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。     

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.     

Extended-state-observer-based dynamic surface control of flexible-joint robot systems with input saturation

This article presents an extended-state-observer-based dynamic surface control approach for flexible-joint robot systems with asymmetric input saturation and large unknown dynamic knowledge. Traditional controllers for flexible-joint robot systems usually use approximation technology to deal with unknown dynamics knowledge. Unlike the traditional control algorithm, this article utilizes an extended state observer to estimate the unknown dynamics. For the closed-loop system, the delay strategy handles the time-scale separation issue, the filtering system overcomes the “explosion of differentiation” caused by the repeated differentiation of auxiliary control signals, and the mean-value-theorem solves the input saturation problem of the actuator. The stability analysis implies that estimation errors of extended state observers (ESOs) and other state variables are semiglobally uniformly ultimately bounded. Compared with fuzzy control algorithms, the novel ESO-based dynamic surface control approach not only omits online learning time but also uses only a few control parameters to obtain satisfactory tracking performance. Finally, a comparison simulation experiment is provided to illustrate the effectiveness of the gained conclusions.     

Observer‐based fuzzy adaptive quantized control for uncertain nonlinear multiagent systems

This paper focuses on consensus quantized control design problem for uncertain nonlinear multiagent systems with unmeasured states. Every follower can be denoted through a system with unmeasurable states, hysteretic quantized input, and unknown nonlinearities. Fuzzy state observer and Fuzzy logic systems are employed to estimate unmeasured states and approximate unknown nonlinear functions, respectively. The hysteretic quantized input can be split into two bounded nonlinear functions to avoid chattering problem. By combining adaptive backstepping and first‐order filter signals, an observer‐based fuzzy adaptive quantized control scheme is designed for each follower. All signals exist in closed‐loop systems are semiglobally uniformly ultimately bounded, and all followers can accomplish a desired consensus results. Finally, a numerical example is employed to elaborate the effectiveness of proposed control strategy.     

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.     

Distributed adaptive iterative learning control for nonlinear multiagent systems with state constraints

This paper addresses the consensus problem of nonlinear multiagent system with state constraints. A novel γ‐type barrier Lyapunov function is adopted to handle with the bounded constraints. The iterative learning control strategy is introduced to estimate the unknown parameter and basic control signal. Five control schemes are designed, in turn, to address the consensus problem comprehensively from both theoretical and practical viewpoints. These schemes include the original adaptive scheme, projection‐based scheme, smooth function‐based scheme and its alternative, and dead‐zone–like scheme. The consensus convergence and constraints guarantee are strictly proved for each control scheme by using the barrier composite energy function approach. Illustrative simulations verify the theoretical analysis.     

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.     

Nonfragile control design for consensus of semi-Markov jumping multiagent systems with disturbances

The consensus problem for multiagent systems (MASs) with semi-Markov jumping parameters under the influence of disturbances is investigated in this article. In the first part of this article, an extended dissipative approach is used for the consensus of MASs with semi-Markovian jumping parameters and external disturbances via nonfragile controller with randomly occurring gain fluctuations. Besides, in the second part of the article, the consensus of stochastic semi-Markovian jumping MASs via nonfragile controller subject to probabilistic time-varying delay is discussed. The primary motive of this article is to develop a robust controller such that the considered MASs with semi-Markov jumping parameters achieve consensus in the presence of external disturbances. For this, the chosen problems are first converted to stabilization problems then by using Lyapunov stability theory and linear matrix inequality approach, the stabilization criterion have been established. At last, two numerical examples are worked out to illustrate the efficiency of the proposed control methodologies.     

受扰非线性时滞系统近似最优跟踪控制

为了研究一类参考输入和扰动由外系统描述的非线性时滞系统最优输出跟踪问题,利用逐次逼近法将原最优跟踪问题转化为一族不含时滞项和超前项的非齐次线性两点边值问题序列,通过迭代求解该问题序列,提出了一个伴随向量解序列近似求解过程。最优输出跟踪控制律由解析的前馈-反馈项和以伴随向量的极限形式给出的非线性时滞补偿项组成,通过截取伴随向量序列的有限步迭代值,得到了问题的次优控制律。利用构造扰动和参考输入降维观测器,解决了前馈控制律的物理可实现问题;仿真结果表明,该方法计算量较小,容易工程实施,能有效地解决非线性时滞系统的最优跟踪控制问题。     

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.     

Adaptive cooperative tracking control of uncertain nonlinear multiagent systems with uncertain Markov switching communication graphs

This paper deals with the cooperative tracking problem of nonlinear multiagent systems. Compared with the existing works, both the uncertainties in model and switching topology are considered. Two control laws, the adaptive distributed controller based on state information and the adaptive distributed controller based on output information, are proposed using the neural networks. The advantage of the proposed controller is that we no longer require the exact knowledge of follower agents' parameters and the precise switching signal of communication topology by taking advantages of neural networks approximation and the property of transition probabilities. It is proved that all followers can track the leader with permitted bounded errors under the proposed controller. An illustration is given to testify the efficacy of the proposed approach.     

非线性系统的模糊输入多采样率数字控制

针对非线性系统的模糊多采样率数字控制问题,基于T-s模糊模型和离散模糊基函数值,建立了被控对象的输入多采样率数字控制系统模型.采用PDC控制原理,提出了一种新的模糊多采样率数字控制方法,给出了控制器设计算法,并通过求解带有线性矩阵不等式(LMI)约束的凸优化问题来获得控制器的参数.倒立摆控制器设计实例证明了设计方法是有效、可行的.     

Immersion and invariance adaptive control for discrete‐time systems in strict‐feedback form with input delay and disturbances

This work presents a new adaptive control algorithm for a class of discrete‐time systems in strict‐feedback form with input delay and disturbances. The immersion and invariance formulation is used to estimate the disturbances and to compensate the effect of the input delay, resulting in a recursive control law. The stability of the closed‐loop system is studied using Lyapunov functions, and guidelines for tuning the controller parameters are presented. An explicit expression of the control law in the case of multiple simultaneous disturbances is provided for the tracking problem of a pneumatic drive. The effectiveness of the control algorithm is demonstrated with numerical simulations considering disturbances and input‐delay representative of the application.     

Tracking control for first-order multi-agent systems

In this paper, the conventional tracking control problem is expanded to first-order multi-agent systems, which can be solved by directly guiding any agent in the group. The following three kinds of desired motions are considered for all agents to track: 1) stillness in space, 2) variable motion with known acceleration, 3) variable motion with partly unknown acceleration. Specifically, fixed networks with time delays and switching networks without delays are both considered in case 1). Switching networks with and without time delays are both studied in case 2), while for 3), switching networks without delays are mainly investigated. A numerical simulation example is included to illustrate the results. __________ Translated from Progress of Artificial Intelligence in China, 2007, 505–510 [译自: 中国人工智能进展]     

Adaptive finite‐time actuator fault‐tolerant coordinated attitude control of multispacecraft with input saturation

In this study, for nonrigid spacecraft formation, a distributed adaptive finite‐time actuator fault‐tolerant (FTAFT) coordinated attitude tracking control (CATC) issue is addressed. Aiming at stabilizing the spacecraft formation flying system during a limited time, two distributed adaptive FTAFT CATC strategies are presented. Initially, on basis of distributed finite‐time observer (DFTO), adaptive control, consensus approach, graph theory, and finite‐time theory, we develop a distributed adaptive FTAFT coordinated attitude tracking controller to repress the impact of the external state‐dependent and state‐independent disturbance, unknown time‐varying inertia uncertainty, and actuator fading or fault. Then, combining with the proposed controller, a distributed adaptive FTAFT control law with input saturation subjected to physical limitations of actuator is further designed. In addition, a self‐adjusting matrix (SAM) is proposed to improve the actuators' performance. With the two proposed CATC strategies, the followers can synchronize with the leader. Simulations demonstrated the validity of the designed control laws.