Semi-global robust output regulation for a class of singular nonlinear systems via nonlinear internal model

Most of existing results on robust output regulation problem of singular nonlinear systems are limited to local solutions. In this paper, the semi-global robust output regulation problem for a class of singular nonlinear systems is investigated by using a nonlinear internal model. Attaching a nonlinear internal model to the singular nonlinear system yields an augmented singular nonlinear system whose semi-global robust stabilisation solution leads to the solution of the semi-global robust output regulation problem of the original singular nonlinear system. The solvability conditions of the semi-global output regulation problem are established by addressing the solvability of the robust stabilisation problem of augmented singular nonlinear system. Finally, a numerical simulation example is used to illustrate the design of the semi-global regulator for the singular nonlinear systems.     

Robust right coprime factorization and robust stabilization ofnonlinear feedback control systems

Robust right coprime factorization and robust stabilization of nonlinear feedback control systems are studied. The concept of robust right coprime factorization of nonlinear operators for feedback control systems is introduced. Some conditions for the robustness of a right coprime factorization of a nonlinear plant under unknown but bounded perturbations are derived. An example with a closed-form solution is included to illustrate the general theory and a step-by-step construction of the robust factorization and the robust stabilization     

一类非线性离散系统模糊控制器的分析和设计

针对一类非线性离散不确定系统,在系统状态不可测的情况下,以T-S模型描述不同状态空间的局部动态区域,并通过中心平均反模糊化、乘积推理、单点模糊化方法得到全局模糊系统模型.基于李亚普诺夫理论和线性矩阵不等式,设计了一种基于观测器的鲁棒控制器,并对离散状态下的此类系统进行了稳定分析.最后通过M ATLAB仿真,证明了该方法的有效性.     

Adaptive robust stabilisation for a class of uncertain nonlinear time-delay dynamical systems

The problem of adaptive robust stabilisation is considered for a class of uncertain nonlinear dynamical systems with multiple time-varying delays. It is assumed that the upper bounds of the nonlinear delayed state perturbations are unknown and that the time-varying delays are any non-negative continuous and bounded functions which do not require that their derivatives have to be less than one. In particular, it is only required that the nonlinear uncertainties, which can also include time-varying delays, are bounded in any non-negative nonlinear functions which are not required to be known for the system designer. For such a class of uncertain nonlinear time-delay systems, a new method is presented whereby a class of continuous memoryless adaptive robust state feedback controllers with a rather simpler structure is proposed. It is also shown that the solutions of uncertain nonlinear time-delay systems can be guaranteed to be uniformly exponentially convergent towards a ball which can be as small as desired. Finally, as an application, an uncertain nonlinear time-delay ecosystem with two competing species is given to demonstrate the validity of the results.     

一类非线性广义系统的时滞相关耗散控制

针对一类带有非线性摄动的广义时滞系统,研究了时滞相关的鲁棒耗散问题.讨论了此类非线性广义时滞系统的鲁棒耗散性.同时对此类非线性广义时滞系统的二次稳定性进行了研究,分别用线性矩阵不等式（LMI）的方法给出了充分条件,也给出了时滞相关的鲁棒耗散的时滞上界.并且,给出了时滞相关的鲁棒耗散的状态反馈控制器.最后,通过例子验证了定理的可行性.     

Semi‐Global Robust Output Regulation for A Class of Singular Nonlinear Systems with Unknown Algebraic Equations

This paper considers semi‐global robust output regulation problem for a class of singular nonlinear systems whose algebraic equations are not precisely known. Since the algebraic equations are not known, the output regulation problem of singular nonlinear systems cannot be solved by directly reducing the singular nonlinear system into a normal nonlinear system. Based on internal model principle, we convert the robust output regulation problem of singular nonlinear systems into a robust stabilization problem of an augmented singular nonlinear system. The augmented singular nonlinear system is also with unknown algebraic equations. However, without transforming the singular nonlinear system into a normal nonlinear system, it is shown that the augmented singular nonlinear system can be semi‐globally stabilized by a high gain output feedback control law under some reasonable assumptions. Moreover, the semi‐global stabilization control law of the augmented singular nonlinear systems also solves the semi‐global robust output regulation problem of the original singular nonlinear system.     

一类非线性激励器系统的鲁棒自适应跟踪

考虑一类具有非线性激励器不确定系统的鲁棒跟踪问题，其不确定性是部分已知的。所构造的鲁棒自适应控制方案能确保系统的跟踪误差终极一致有界．与已有文献结果相比．未知参数估计的自适应律和控制器是连续的，从而使得所提出的设计方案在实际控制问题中易实现。且与具有线性激励器的系统一样具有较强的鲁棒性．最后通过数值算例进一步说明了该设计方案是有效的。     

不确定非线性系统的鲁棒H∞控制分析与综合

讨论一类仿射非线性系统的鲁棒H_∞ 控制问题. 针对自由系统, 外部干扰输入矩阵和控制输入矩阵都具有加法不确定性的系统, 将鲁棒性能的分析和综合归结为求解一组Hamilton_Jacobi不等式, 给出了确保非线性控制系统满足鲁棒干扰抑制性能的充分条件, 获得了非线性鲁棒控制器的一种形式. 一个仿真例子验证了所得结论的正确性.     

Robust stability analysis of systems with real parametric uncertainty: A global optimization approach

This paper presents an optimization framework for the robustness analysis of linear and nonlinear systems with real parameter uncertainty. For linear systems, a nonlinear programming formulation for the exact calculation of the stability margin is presented. The potential of decomposition-based global optimization methods for the solution of this nonconvex problem is discussed. Next the concept of the stability margin is extended to a class of nonlinear systems. A nonlinear stability margin and a uniqueness margin are defined to address the effect of parametric uncertainty on the stability of a particular steady state, as well as on the number of steady states of the system. This analysis allows for the derivation of necessary and sufficient conditions for robust stability and robust uniqueness of the steady state of the system in the presence of parametric uncertainty.     

在闭环极点约束条件下研究控制系统最大鲁棒稳定界

不仅研究了一类扰动控制系统鲁棒稳定界的定义、优化等问题, 而且通过研究控制系统鲁棒稳定界与Riccati矩阵方程解的关系, 提出了在闭环极点约束条件下研究鲁棒稳定界的方法, 并给出了基于LQ逆问题参数化解的极大化鲁棒稳定界的优化算法.     

Operator-based nonlinear feedback control design using robust right coprime factorization

In this note, robust stabilization and tracking performance of operator based nonlinear feedback control systems are studied by using robust right coprime factorization. Specifically, a new condition of robust right coprime factorization of nonlinear systems with unknown bounded perturbations is derived. Using the new condition, a broader class of nonlinear plants can be controlled robustly. When the spaces of the nonlinear plant output and the reference input are different, a space change filter is designed, and in this case this note considers tracking controller design using the exponential iteration theorem.     

基于状态观测器的一类非线性系统的模糊鲁棒控制

利用T－S模型对一类非线性不确定系统进行模糊建模,在此基础上研究模糊鲁棒观测器及模糊状态鲁棒控制器的设计,并证明所设计的模糊鲁棒观测器和模糊状态鲁棒控制器具有全局渐近稳定性质。     

Robust switching adaptive control of multi-input nonlinear systems

During the last decade a considerable progress has been made in the design of stabilizing controllers for nonlinear systems with known and unknown constant parameters. New design tools such as adaptive feedback linearization, adaptive back-stepping, control Lyapunov functions (CLFs) and robust control Lyapunov functions (RCLFs), nonlinear damping and switching adaptive control have been introduced. Most of the results developed are applicable to single-input feedback-linearizable systems and parametric-strict-feedback systems. These results, however, cannot be applied to multi-input feedback-linearizable systems, parametric-pure-feedback systems and systems that admit a linear-in-the-parameters CLF. In this paper, we develop a general procedure for designing robust adaptive controllers for a large class of multi-input nonlinear systems. This class of nonlinear systems includes as a special case multi-input feedback-linearizable systems, parametric-pure-feedback systems and systems that admit a linear-in-the-parameters CLF. The proposed approach uses tools from the theory of RCLF and the switching adaptive controllers proposed by the authors for overcoming the problem of computing the feedback control law when the estimation model becomes uncontrollable. The proposed control approach has also been shown to be robust with respect to exogenous bounded input disturbances     

不确定非线性环链系统的分散鲁棒控制

提出了环链系统和一类不确定非线性环链系统,利用线性代数理论,给出了实现环链系统的充要条件,运用李雅普诺夫稳定理论和矩阵理论研究了不确定非线性环链系统的鲁棒镇定,并给出了一种非线性鲁棒镇定控制器的设计,还考虑了一类非线性环链相似组合大系统,给出了分散鲁棒镇定条件,最后给出数值例子说明设计方法的有效性。     

On-line fault detection in uncertain nonlinear systems using diagnostic observers: a survey

The paper discusses the principles of model-based fault detection and isolation (FDI) in nonlinear and time-varying uncertain dynamic systems. Such systems are typical for such complex plants as, for example, in the chemical process industries or in advanced transportation technology. For a model-based fault diagnosis in such situations, robust or even adaptive strategies are needed. In this paper the theory of robust linear observer-based residual generation for FDI is reviewed from a general point of view. The structural equivalence between the parity space approach and observer-based approach is shown in a new simple graphical way by showing that the observer-based FDI concept can easily be transformed into an equivalent extended parity space configuration, without claiming, however, equivalence of the underlying design techniques. The unknown input observer approach known as a most powerful and comprehensive framework for robust residual generation for FDI in uncertain linear systems is extended to classes of nonlinear and time-varying systems. For such plants an adaptive nonlinear unknown input observer scheme is proposed. Finally, appropriate residual evaluation techniques are outlined and suggestions are made to increase the robustness, for instance by using adaptive thresholds.     

Robust Stability Analysis of Nonlinear Hybrid Systems

We present a methodology for robust stability analysis of nonlinear hybrid systems, through the algorithmic construction of polynomial and piecewise polynomial Lyapunov-like functions using convex optimization and in particular the sum of squares decomposition of multivariate polynomials. Several improvements compared to previous approaches are discussed, such as treating in a unified way polynomial switching surfaces and robust stability analysis for nonlinear hybrid systems.      

运用区间算法的约束非线性系统鲁棒模型预测控制

针对一类具有输入和状态约束的干扰有界非线性系统,提出了基于区间分析的约束非线性鲁棒模型预测控制,以降低计算量并扩大系统吸引域.首先,在集合运算的基础上,利用区间运算和函数区间扩展,给出了一种计算效能更好、保守性更低的非线性系统鲁棒一步集计算方法;其次,构造重叠的多面体控制不变集序列并以此计算约束非线性系统的鲁棒多步集,并通过设计基于集合的在线优化策略,提出了基于鲁棒一步集的单步优化非线性模型预测控制,有效降低了非线性优化的在线计算量;最后,仿真实例验证了算法的有效性.     

Adaptive robust control of uncertain nonlinear systems with nonlinear delayed state perturbations

The problem of robust stabilization of uncertain nonlinear dynamical systems with multiple time delays is considered. In the paper, the upper bound of the nonlinearity and uncertainty, including delayed states, is assumed to be a linear function of some parameters which are still assumed to be unknown. Here, we do not require that the nonlinear terms including delayed states are linear norm-bounded in the states. An improved adaptation law with σ-modification is employed to estimate the unknown parameters, and a class of memoryless adaptive robust state feedback controllers is proposed. It is also shown that the proposed adaptive robust controllers can guarantee the uniform asymptotic stability of uncertain nonlinear time-delay systems. Finally, as a numerical example, an uncertain time-delay ecosystem with two competing species is given to demonstrate the validity of the results.     

Set membership inversion and robust control from data of nonlinear systems

A set membership method for right inversion of nonlinear systems from data is proposed in the paper. Both the cases where the system to invert is known or unknown and therefore identified from data are addressed. The method does not require the invertibility of the regression function describing the system and ensures tight bounds on the inversion error. In the case of unknown system, the method allows the derivation of a robust right‐inverse, guaranteeing the inversion error bound for all the systems belonging to the uncertainty set which can be defined from the available prior and experimental information. Based on such a set membership inversion, two methods for robust control of nonlinear systems from data are introduced: nonlinear feed‐forward control (NFFC) and nonlinear internal model control (NIMC). Both the design methods ensure robust stability and bounded tracking errors for all the systems belonging to the involved uncertainty set. Two applicative examples of robust control from data are presented: NFFC control of semi‐active suspension systems and NIMC control of vehicle lateral dynamics.Copyright © 2013 John Wiley & Sons, Ltd.