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.     

Adaptive fuzzy dual-performance fault-tolerant control for interconnected nonlinear systems

This article focuses on the decentralized adaptive fuzzy fixed-time fault-tolerant control issue for the error-constrained interconnected nonlinear systems with unknown actuator faults possessing dead zone. The unknown nonlinear functions can be modeled via fuzzy logic systems. By utilizing the parameter estimation method, the effect of unknown actuator faults possessing dead zone can be compensated. To guarantee the predefined dynamic performance of state tracking errors, the barrier Lyapunov functions and prescribed performance functions are introduced. Then, a dual-performance fault-tolerant control method that can guarantee fast transient performance and predefined performance of state tracking errors is proposed via using the decentralized backstepping technique. In addition, on the basis of the Lyapunov stability theory and the fixed-time criterion, it is proved that the predefined performance of full-state errors and the stability of closed-loop systems can be guaranteed. Finally, two numerical examples are provided to illustrate the effectiveness of the proposed control scheme.     

一类不确定非线性系统的自适应模糊跟踪控制

针对一类不确定非线性连续系统，用模糊系统对未知函数进行逼近的基础上，利用Lyapunov稳定性理论，提出了一种新的自适应模糊跟踪控制算法，此算法的特点是，无论取多少条模糊系统的规则，自适应学习的参数只有一个，便于实现，而且还能确保闭环系统渐近稳定，并使系统的跟踪误差为零，仿真研究表明，所提出的算法是有效的。     

一类不确定非线性系统的自适应模糊滑模控制

针对一类不确定非线性系统自适应模糊控制中,为了保证系统稳定性而附加监督控制问题,根据滑模控制原理并利用模糊系统的逼近能力,提出了一种Ⅰ型间接自适应模糊滑模控制方法。该方法取消了监督控制,用滑模控制器增加了逼近误差的自适应补偿,李雅普诺夫稳定性理论分析证明,控制系统全局稳定且跟踪误差收敛到零。将这种控制器应用到过程控制的典型对象液位控制中,仿真结果表明了该控制器的有效性和可行性。     

Adaptive fuzzy finite-time fault-tolerant control of nonlinear systems with state constraints and input quantization

This article concentrates on an adaptive finite-time fault-tolerant fuzzy tracking control problem for nonstrict feedback nonlinear systems with input quantization and full-state constraints. By utilizing the fuzzy logic systems and less adjustable parameters method, the unknown nonlinear functions are addressed in each step process. In addition, a dynamic surface control technique combined with fuzzy control is introduced to tackle the variable separation problem. The problem for the effect of quantization and unlimited number of actuator faults is tackled by a damping term with smooth function in the intermediate control law. Finite-time stability is achieved by combining barrier Lyapunov functions and backstepping method. The finite-time controller is designed such that all the responses of the systems are semiglobal practical finite-time stable and ensured to remain in the predefined compact sets while tracking error converges to a small neighborhood of the origin in finite time. Finally, simulation examples are utilized to testify the validity of the investigated strategy.     

Adaptive fuzzy control for nontriangular form systems with time-varying full-state constraints

This article investigates an adaptive fuzzy tracking control problem for a class of nontriangular form systems with asymmetric time-varying full state constraints. Unknown functions are approximated by the fuzzy logic systems. A domination approach is employed to tackle the nontriangular form structure. Time-varying asymmetric barrier Lyapunov functions (ABLFs) are adopted to ensure full-state constraints satisfaction. Based on the backstepping technique and time-varying ABLFs, an adaptive controller is proposed and guarantees that all the signals in the closed-loop system are ultimately bounded and the time-varying full state constraints are met. Simulation examples are presented to further demonstrate the effectiveness of the proposed approach.     

Adaptive fuzzy control for high-order nonlinear systems with time-varying full-state constraints and input saturation

The adaptive control for a class of high-order nonlinear systems with time-varying full-state constraints and input saturation is investigated in this paper. To deal with time-varying constraints, a type of high-order barrier Lyapunov functions(BLFs) are constructed. Its performance can be guaranteed with the disappearance of constraints. By building fuzzy systems, unknown functions can be approximated. Together with adding a power integrator technique and the gain-update law, an adaptive controller is designed. As a result, all the constraints are not breached, and the tracking error converges to an arbitrarily small zone around the origin. Finally, a practical example and a numerical example illustrate the effectiveness of the proposed method.     

Adaptive finite-time tracking control for parameterized nonlinear systems with full state constraints

In this article, the issue of adaptive finite-time dynamic surface control (DSC) is discussed for a class of parameterized nonlinear systems with full state constraints. Using the property of logarithmic function, a one-to-one nonlinear mapping is constructed to transform a constrained system into an unconstrained system with the same structure. The nonlinear filter is constructed to replace the first-order linear filter in the traditional DSC, and the demand on the filter time constant is reduced. Based on finite-time stable theory and using modified DSC, the finite-time controller is designed via DSC. Theoretical analysis shows that all the signals in the closed-loop system are semiglobal practical finite-time stable. Furthermore, none of the states are outside the defined open set. In the end, simulation results are presented to demonstrate the effectiveness of the proposed control schemes with both linear filters and nonlinear filters.     

Adaptive fuzzy FTC design of nonlinear stochastic systems with actuator faults and unmodeled dynamics

This paper investigates an adaptive fuzzy control method for accommodating actuator faults in a class of uncertain stochastic nonlinear systems with both immeasurable states and unmodeled dynamics. The considered faults are modeled as both loss of effectiveness and lock‐in‐place. To deal with the immeasurable states, a novel state observer containing the actuator faults is designed. Combining with the backstepping technique and stochastic small‐gain theorem, an adaptive fuzzy output feedback control method is developed. The presented design scheme can guarantee that the closed‐loop system is input‐to‐state practically stable in probability. Finally, a simulation example is shown to verify the effectiveness of the proposed control method.     

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.     

一类非仿射非线性系统的自适应模糊控制

为了讨论一类非仿射非线性系统自适应模糊控制问题,利用有关隐函数定理和泰勒公式,将系统由非仿射型转变为仿射型,基于滑模控制原理,并运用模糊逻辑系统对未知函数进行在线逼近,提出了一种具有监督器的自适应模糊控制方法。该方法在考虑到外界干扰的情况下,通过监督控制器保证闭环系统所有信号有界,通过引入最优逼近误差的自适应补偿项来消除建模误差的影响。通过Lyapunov方法,证明了跟踪误差收敛到零,仿真结果表明了该方法的有效性。     

Adaptive control of feedforward nonlinear systems with uncertain time-varying parameters and an unknown time-varying delay in the input

In this paper, we consider a global regulation problem for a class of feedforward nonlinear systems. The key features of our considered system are identified by the presence of uncertain time-varying parameters associated with main diagonal states and input and an unknown time-varying delay in the input. Moreover, the growth rates of nonlinearity and the input-delay are only known to be finite. To solve our considered problem, we give a process to obtain a compact set that contains the allowed time-varying parameters. Then, we propose an adaptive controller which handles both unknown growth rate of nonlinearity and input-delay for system regulation. We carry out the rigorous system analysis and show the effectiveness of our proposed control scheme via an application example.     

Nonlinear control for uncertain nonlinear systems with unknown control directions using less or no parameter estimates

For the parametric strict‐feedback nonlinear systems with unknown virtual control coefficients and unknown control directions, the control schemes presented in the existing literature have the disadvantage of overparametrization. In this paper, a novel systematic design procedure is developed to solve the overparametrization problem. Two nonlinear controllers are designed by combining the backstepping technique and the Nussbaum gain approach. A main advantage of the proposed controllers is that they contain less or no parameter estimates that need to be updated online. In the first scheme, the number of the estimated parameters is equal to the dimension of the controlled system. In the second scheme, no parameter estimates are required. In both of the control schemes, the boundedness of all the closed‐loop signal is guaranteed, and the asymptotic convergence of the system states is achieved. An example is provided to demonstrate the effectiveness of the proposed design approaches. Copyright © 2014 John Wiley & Sons, Ltd.     

Evaluation and design of actuator fault diagnosability for nonlinear affine uncertain systems with unknown indeterminate inputs

In this paper, the evaluation and design scheme of fault diagnosability are investigated by differential geometry theories for a class of nonlinear affine uncertain systems with unknown indeterminate inputs. Considering two coupling relationships of outputs with uncertainties and faults, the sufficient and necessary conditions of fault detectability and isolability are established. For the problem that uncertainties influence the system outputs and make the faults undetectable, a design scheme of fault diagnosability is proposed. For nonlinear affine uncertain systems, a relatively complete theoretical system of the evaluation and design of fault diagnosability comes into being. An illustrative example is given to demonstrate the effectiveness of the proposed evaluation and design scheme of fault diagnosability. Copyright © 2016 John Wiley & Sons, Ltd.     

Adaptive finite-time consensus tracking control for nonlinear multiagent systems in nonstrict feedback form with full-state constraints

In this article, the fuzzy adaptive finite-time consensus tracking control problem for nonstrict feedback nonlinear multiagent systems with full-state constraints is studied. The finite-time control based on command filtered backstepping is proposed to guarantee the finite-time convergence and eliminate the explosion of complexity problem caused by backstepping process, and the errors in the filtering process are compensated by using error compensation mechanism. Furthermore, based on the fuzzy logic systems, the uncertain nonlinear dynamics are approximated and the problem of state variables in nonstrict feedback form is solved by using the property of basis functions. The barrier Lyapunov functions are introduced to guarantee that all system states and compensated tracking error signals are constrained in the designed regions. A simulation example is given to verify the superiority of the proposed algorithm.     

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.     

不确定欠驱动非线性系统的模糊滑模控制

针对一类不确定欠驱动非线性系统，提出了一种模糊滑模控制新方案．该方案在T-S型模糊控制的基础上引入滑模控制，有效避免了T-S型模糊控制可能出现的不稳定情况，同时改善了系统的动态性能。采用吊车系统进行系统仿真，结果表明了该控制方案的有效性。     

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 fixed-time tracking control for stochastic pure-feedback nonlinear systems

The article discusses the adaptive fixed-time control problems for the stochastic pure-feedback nonlinear systems. Different from the existing results, the priori information of unknown virtual control coefficients (UVCC) is no longer needed in this article, which is realized by emplying the bound estimation method and well-defined smooth functions. A novel semi-global practical fixed-time stability criterion for the stochastic nonlinear systems is presented. Correspondingly, a new construction of Lyapunov function is proposed for the nonlinear stochastic system by adding the lower bounds of the UVCC. Based on the fuzzy logical system and fixed time stability theorem, a novel adaptive fuzzy fixed-time tracking control algorithm for stochastic nonlinear system is raised firstly. By theoretical analysis, we can conclude that the whole variables of the controlled system are bounded almost surely and the output can track the desired reference signal to a very small compact set within a predefined fixed-time interval. Finally, the raised method is illustrated by two simulation examples.     

Adaptive fuzzy finite-time consensus tracking for multiple Euler-Lagrange systems with unknown control directions

In this paper, the problem of adaptive fuzzy finite-time consensus tracking control for multiple Euler-Lagrange systems (ELSs) with uncertain dynamics and unknown control directions (UCDs) is investigated. The computational complexity problem in conventional backstepping is avoided by using finite-time command filter (FTCF), and the error in the filtering process is eliminated through error compensation signals. The fuzzy logic system combined with the adaptive control technique is applied to approximate and estimate the unknown nonlinear dynamics of ELS. The Nussbaum function-based continuous and nonsmooth input control torque is established to eliminate the influence of UCDs, and the proposed control scheme can guarantee the consensus tracking errors converge to the desired neighborhood of the origin within a finite time. Numerical simulation is used to test the effectiveness of the given algorithm.