Robust output tracking of uncertain nonlinear time‐delay systems with unknown dead‐zone inputs via control schemes with a simple structure

The adaptive robust output tracking control problem is considered for a class of uncertain nonlinear time‐delay systems with completely unknown dead‐zone inputs. A new design method is proposed so that some adaptive robust output tracking control schemes with a rather simple structure can be constructed. It is not necessary to know the nonlinear upper bound functions of uncertain nonlinearities. In fact, the constructed output tracking control schemes are structurally linear in the state and have a self‐tuning control gain function that is updated by an adaptation law. In this paper, the dead‐zone input is nonsymmetric, and its information is assumed to be completely unknown. In addition, a numerical example is given to describe the design procedure of the presented method, and the simulations of this numerical example are implemented to demonstrate the validity of the theoretical results.     

Robust control with pole assignment in a specified region for systems under parameter perturbations; application to a nonlinear system

This paper deals with the problem of determination of feedback gains in order to achieve required performances under linear time invariant perturbations. Based upon the Lagrange multiplier method, the proposed method determines feedback gains that ensure both robust stability and robust performance for a linear uncertain system. It is applied to a nonlinear crane system control design. The nonlinear system is first partitioned into some uncertain linear systems. Then the proposed method is applied to each uncertain linear system. Application is easily demonstrated and, consequently, a nonlinear crane control system can be easily designed. Finally, it is shown in a numerical example that the proposed method is effective.     

多时滞离散不确定系统的模糊输出反馈保性能控制

针对一类用T-S模糊模型描述的多时滞离散不确定系统,研究了其输出反馈保性能鲁棒控制问题.基于线性矩阵不等式方法,给出了系统模糊输出反馈保性能控制律存在的一个充分条件和性能上界,并证明了该条件等价于一组线性矩阵不等式的可行性问题.通过建立和求解一个凸优化问题,给出了系统设计次优保性能模糊输出反馈控制律的方法.最后通过算例验证了结果的有效性.     

Adaptive robust control of a class of nonlinear systems in semi‐strict feedback form with non‐uniformly detectable unmeasured internal states

This paper proposes a novel control method for a special class of nonlinear systems in semi‐strict feedback form. The main characteristic of this class of systems is that the unmeasured internal states are non‐uniformly detectable, which means that no observer for these states can be designed to make the observation error exponentially converge to zero. In view of this, a projection‐based adaptive robust control law is developed in this paper for this kind of system. This method uses a projection‐type adaptation algorithm for the estimation of both the unknown parameters and the internal states. Robust feedback term is synthesized to make the system robust to uncertain nonlinearities and disturbances. Although the estimation error for both the unknown parameters and the internal states may not converge to zero, the tracking error of the closed‐loop system is proved to converge to zero asymptotically if the system has only parametric uncertainties. Furthermore, it is theoretically proved that all the signals are bounded, and the control algorithm is robust to bounded disturbances and uncertain nonlinearities with guaranteed output tracking transient performance and steady‐state accuracy in general. The class of system considered here has wide engineering applications, and a practical example—control of mechanical systems with dynamic friction—is used as a case study. Simulation results are obtained to demonstrate the applicability of the proposed control methodology. Copyright © 2010 John Wiley & Sons, Ltd.     

利用降维状态观测器离散系统的鲁棒容错控制

研究了线性离散不确定系统的鲁棒容错控制问题。针对线性离散控制系统存在不确定性和传感器失效的情况，利用降维观测器估计系统的状态，并基于估计的状态构成鲁棒容错控制律。给出了闭环系统具有鲁棒容错特性的充分条件。数值算例表明了算法的有效性。     

Adaptive robust H∞ state feedback control for linear uncertain systems with time‐varying delay

This paper considers the problem of adaptive robust H_∞ state feedback control for linear uncertain systems with time‐varying delay. The uncertainties are assumed to be time varying, unknown, but bounded. A new adaptive robust H_∞ controller is presented, whose gains are updating automatically according to the online estimates of uncertain parameters. By combining an indirect adaptive control method and a linear matrix inequality method, sufficient conditions with less conservativeness than those of the corresponding controller with fixed gains are given to guarantee robust asymptotic stability and H_∞ performance of the closed‐loop systems. A numerical example and its simulation results are given to demonstrate the effectiveness and the benefits of the proposed method. Copyright © 2008 John Wiley & Sons, Ltd.     

Robust fuzzy control and evolutionary fuzzy identification of singularly perturbed nonlinear systems with parameter uncertainty

This paper presents an H _∞ robust fuzzy control strategy which stabilizes singularly perturbed (SP) nonlinear systems with bounded uncertainties and guarantees disturbance attenuation bounds for all admissible uncertainties. The modified Takagi–Sugeno (T–S) fuzzy linear models are used to describe the SP nonlinear systems. By the proposed fuzzy control strategy, the number and type of membership functions in the fuzzy control rules are not necessarily the same as those in the fuzzy models. A sufficient condition for the existence of the H _∞ robust fuzzy controllers is then presented in terms of a novel linear matrix inequalities (LMIs) form which takes full consideration of modeling error and uncertainties in system parameters. This condition provides extra design parameters with more flexibility in control gain selection. Furthermore, we propose a compound search strategy composed of island genetic algorithms concatenated with the simplex method to identify the uncertain SP nonlinear systems for the fuzzy control design, and to solve the LMI problem. Finally, design example of the proposed H _∞ robust fuzzy controller for an uncertain SP nonlinear system is presented.     

Decentralized guaranteed cost control for uncertain large‐scale systems using additive control gain

This paper investigates an application of additive control gain to the guaranteed cost control (GCC) problem of decentralized robust control for a class of discrete‐time uncertain large‐scale systems. Based on the Linear Matrix Inequality (LMI) design approach, a class of decentralized local fixed state feedback controllers with additive control gain is established. The novel contribution of this paper is that multiobjective control is attained by using the additive control gain. Although the additive control gain is included in the uncertain large‐scale systems, the closed‐loop system is asymptotically stable. In order to demonstrate the efficiency of our proposed controller, using the fuzzy logic control as the additive control gain, the simple numerical example is given. © 2009 Wiley Periodicals, Inc. Electr Eng Jpn, 169(3): 18–32, 2009; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/eej.20726     

Passivity‐based adaptive output tracking control for switched nonlinear systems with uncertain parameters

This paper addresses the issue of the adaptive output tracking control for switched nonlinear systems with uncertain parameters. The solvability of the tracking control problem for each subsystem is not necessary to hold. Individual update laws corresponding to different unknown parameters are adopted to reduce the conservativeness produced from the adoption of a common undated law. By means of the dual design of the adaptive controllers and a state‐dependent switching law using multiple storage functions technique, several conditions are obtained under which the adaptive output tracking control problem for switched nonlinear systems is solvable. Finally, an example shows the effectiveness of the proposed method.     

基于自适应迭代学习的多智能体系统编队控制

针对带未知时变参数的非线性多智能体系统的编队问题,提出一种分布式自适应迭代学习控制策略。首先,通过傅里叶级数对系统的不确定参数进行展开,采用一个收敛级数序列处理傅里叶级数展开产生的截断误差,结合多智能体运行过程中的编队误差推导自适应迭代学习控制律和参数更新律;其次,针对领导者动态对大部分智能体都是未知的情况,设计新的辅助控制来补偿未知动态和避免未知有界干扰;然后,基于李亚普诺夫能量函数证明了在所设计控制律作用下多智能体系统编队误差随着迭代次数的增加在有限时间内趋于0;最后,将该控制策略运用到多无人机编队系统中,并通过搭建半物理实验平台,验证了控制方法的有效性。实验结果表明该控制方法可以确保多智能体快速形成所需编队,并且每个智能体在有限时间内可以精确跟踪期望轨迹。所提方法充分考虑了多智能体系统的参数不确定性以及抗干扰的能力,为实际应用中复杂多智能体系统的精确控制提供了有效的方法。     

离散非线性大系统的非脆弱H_∞保性能控制

针对一类用T-S模糊模型描述的不确定离散非线性大系统,研究了其鲁棒非脆弱H_∞保性能模糊控制问题.基于Lyapunov稳定理论,得到一种通过状态反馈实现的非脆弱H_∞保性能模糊控制器.该模糊控制器能保证闭环系统稳定和一定的二次型性能指标上界,同时具有H_∞下的干扰抑制作用.数值例子仿真表明了该设计方法的有效性.     

Adaptive guaranteed cost control of a class of uncertain nonlinear systems

This paper proposes an adaptive guaranteed cost control (GCC) method for a class of nonlinear systems with uncertainties, which guarantees the system cost to be bounded by some specified values while adaptively compensating for the effects of uncertainties and nonlinearities in the system dynamics. By Lyapunov's theory and linear matrix inequality techniques, a parameter adaptation law and a sufficient condition for GCC design are derived for a class of uncertain nonlinear systems. Simulation results on a mechanical system with hard nonlinearity show the effectiveness of the proposed method.     

不确定中立型时滞系统的鲁棒控制--LMI方法

研究一类不确定中立型时滞系统的状态反馈鲁棒控制问题。系统包含状态时滞和参数不确定性。主要目的是利用Lyapunov稳定性方法及LMI方法设计线性无记忆状态反馈控制器,使得对于任意容许的不确定性,相应的闭环系统渐近稳定。控制器的设计依赖于一个LMI解的存在性,计算简单,易于实现。最后给出一个数值例子验证了本文结果的有效性。     

Global adaptive regulation control for a class of nonlinear systems with unknown control coefficients

This paper is concerned with the global asymptotic regulation control problem for a class of nonlinear uncertain systems with unknown control coefficients. The allowed class of uncertainties include unmeasured input‐to‐state stable (ISS) and/or weaker integral ISS (iISS) inverse dynamics, parametric uncertainties, and uncertain nonlinearities. By using the Nussbaum‐type gain technique and changing the ISS/integral ISS inverse dynamics supply rates, we design a dynamic output feedback controller which could guarantee that the system states are asymptotically regulated to the origin from any initial conditions, and the other signals are bounded in closed‐loop systems. The numerical example of a simple pendulum with all unknown parameters and without velocity measurement illustrates our theoretical results. The simulation results demonstrate its efficacy. Copyright © 2015 John Wiley & Sons, Ltd.     

不确定线性系统鲁棒容错控制器的设计

研究了范数有界参数摄动情况下的不确定线性系统的鲁棒容错控制问题。采用代数的方法给出了在不确定线性系统同时存在执行器失效的情况下，闭环系统具有鲁棒性和完整性的一个充分条件。同时应用线性矩阵不等式方法给出了线性不确定系统对执行器失效具有完整性的设计方法。数值算例表明文中给出的两种算法具有简单有效的特点。     

线性时滞系统的鲁棒广义H2弹性控制

研究了系统被控对象存在不确定性,同时控制器也存在摄动的控制问题,采用Lyapunov稳定性理论和线性矩阵不等式(LMI)方法,以一组LMI形式给出了控制器存在的充分条件,并给出了弹性控制器的设计方法。仿真实例表明,该方法提高了时滞系统的广义H2控制的鲁棒性,验证了所提出方法的有效性。     

一类不确定时滞系统的输出反馈镇定

对于控制通道中存在时滞的不确定时滞系统，讨论了时滞独立的输出反馈镇定律的设计问题，利用线性矩阵不等式方法给出了鲁棒镇定律的存在条件及镇定律存在时相应的镇定律设计方法，研究结果表明，针对控制通道中存在时滞的一类不确定系统，在一定条件下可以利用线性矩阵不等式方法设计输出反馈镇定律。文中给出了算例以说明方法的应用。     

基于LMI的奇异不确定时滞系统鲁棒保成本控制

针对一类奇异不确定时滞系统的鲁棒保成本控制,假定其中的不确定性是范数有界,采用基于线性矩阵不等式（LMI）和构造适当的Lyapunov泛函相结合的方法,给出了系统的鲁棒保成本状态反馈控制器存在的条件。通过求解相应的线性矩阵不等式就可得到鲁棒保成本控制,所设计的保成本控制器对所有容许的不确定性不仅使得相应的闭环系统达到二次稳定,也能保证闭环成本函数不超过一个确定的界。通过数值算例及仿真验证了所给方法的有效性。     

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.     

具有饱和执行器的不确定时滞系统鲁棒控制

针对一类具有饱和执行器的不确定时滞系统鲁棒镇定问题,且不确定项满足范数有界条件.基于一个适当的Lyapunov泛函,通过引入奇异系统变换,得到了闭环系统渐近稳定的充分条件,给出了一种时滞相关的控制器设计方法,并以矩阵不等式形式表示.若事先选定参数,则该矩阵不等式可以转化为线性矩阵不等式.数例表明了该方法的有效性.