具有多线性相关系数扰动的有理函数的严格正实不变性判据及其应用

传递函数的严格正实不变性分析,由于它在绝对稳定性分析中的重要作用,引起了人们的 重视.该文考虑在多线性相关系数摄动下,有理函数族的严格正实不变性的判别问题.利用 严格正实函数所具有的相位条件和映射定理.证明了在参数空间中判别该有理函数族保持严 格正实不变性的顶点检验条件,并将这一结果应用于带参数不确定性的鲁里叶系统的绝对稳 定性分析中.     

带有时滞状态的不确定Lur''e-Postnikov系统的鲁棒镇定

由Lyapunov和一种Razumikhin型的方法, 讨论了带有时滞状态的不确定Lur’e_Postnikov系统的鲁棒镇定. 证明对带有状态时滞和范数有界扰动的不确定Lur’e_Postnikov系统, 若其系统矩阵满足某个代数Riccati不等式, 则可通过某 (静态 )线性状态反馈或 (动态 )状态反馈使其闭环系统是二次稳定的. 同样, 应用一Razumikhin型方法, 对带有时变时滞的一类不确定非线性系统的能稳定性问题, 也给出一个充分条件.     

Multi‐parametric extremum seeking‐based iterative feedback gains tuning for nonlinear control

We study in this paper the problem of iterative feedback gains auto‐tuning for a class of nonlinear systems. For the class of input–output linearizable nonlinear systems with bounded additive uncertainties, we first design a nominal input–output linearization‐based robust controller that ensures global uniform boundedness of the output tracking error dynamics. Then, we complement the robust controller with a model‐free multi‐parametric extremum seeking control to iteratively auto‐tune the feedback gains. We analyze the stability of the whole controller, that is, the robust nonlinear controller combined with the multi‐parametric extremum seeking model‐free learning algorithm. We use numerical tests to demonstrate the performance of this method on a mechatronics example. Copyright © 2016 John Wiley & Sons, Ltd.     

A Multi-step Output Feedback Robust MPC Approach for LPV Systems with Bounded Parameter Changes and Disturbance

This paper considers a multi-step output feedback robust model predictive control (OFRMPC) approach for the linear parameter varying (LPV) systems with bounded changes of scheduling parameters and bounded disturbance. Less conservative bounds of future estimation error sets and system parametric uncertain sets are predicted by considering bounded changes of scheduling parameters in LPV systems. In the multi-step OFRMPC approach, an optimization problem is solved to obtain a sequence of controller gains, which considers predictions of future bounds of estimation error sets and system parametric uncertain sets. The optimized sequence of controller gains corresponding to a sequence of Lyaponov matrices have less constraint conditions and also introduce more degree of freedom for the optimization. The proposed multi-step OFRMPC guarantees robust uniform ultimately bounded of the estimation error and robust stability of the observer system. A numerical example is given to demonstrate the effectiveness of the approach.     

有结构摄动非线性系统的鲁棒绝对稳定性

考虑非线性闭环系统的鲁棒绝对稳定性,系统的线性部分受结构摄动以区间传递函数表示,而其非线性(不确定)反馈函数在一个扇区内.将鲁棒性分析的现代结果与经典的圆判据相结合,给出检验上述系统鲁棒绝对稳定性的方法.这个方法只用到16个特别选出的传递函数的奈氏曲线.这个数目不随系统的线性部分的阶次增高而加大,在某些特别情况下却可能更小.于是,将原问题的计算复杂性降到了一个非常低的水平.     

Adaptive stabilizing state feedback controllers of uncertaindynamical systems with multiple time delays

The problem of robust stabilization for a class of uncertain dynamical systems with multiple delayed state perturbations is considered. In this paper, it is assumed that each perturbation is bounded by a linear function of delayed state with unknown gains, and an adaptation law is proposed to estimate these unknown gains. Moreover, by making use of the updated values of these unknown bounds we propose a memoryless state feedback controller for such a class of uncertain time-delay systems. Based on Lyapunov stability theory and Lyapunov-Krasovskii functional, it is shown that the closed-loop dynamical system resulting from the proposed adaptive robust control schemes is globally stable in the sense of uniform ultimate boundedness. Finally, a numerical example is given to demonstrate the validity of the results     

Robust adaptive control for interval time-delay systems

1 Introduction The problem of time-delay is commonly encountered in various engineering systems, such as electric, pneumatic and hydraulic networks, long transmission lines, etc., and it is also a great source of systems instability and poor perfor- mance. During the last decades, we have seen an increasing interest for the control of this class of systems and many results have reported in the literature [1～5]. On the other hand, it has been recognized that nonlinear uncertainties are unavoid…     

鲁里叶系统鲁棒输入输出稳定性的H∞范数摄动界

讨论了一般鲁里叶系统的鲁棒输入、输出稳定性问题.利用H∞范数与互质因子摄动两种度量方法给出了鲁里叶系统在线性部分与非线性部分同时有摄动时,系统仍能保持输入、输出稳定性的摄动量上界估计式,并用两个例子说明了该摄动界的有效性.     

Analytical synthesis of robust controllers of the given accuracy under external perturbations

An approach that allows finding a set of robust statistic feedback controllers that ensure the given control accuracy for the controlled parameters in a multiconnected control system under bounded parametric and external perturbations of various classes is proposed. To describe the set of controllers of the given accuracy, the results of analytically solving the matrix equations based on matrix canonization and parametrization of the Lyapunov equation are used. The solvability conditions of the synthesis problem ensure the robustness and optimal suppression of the perturbations. They are homogeneously represented as linear matrix inequalities obtained based on the Lyapunov functions. A methodological example is given.     

A parametric Lyapunov equation approach to low gain feedback design for discrete-time systems

Low gain feedback, a parameterized family of stabilizing state feedback gains whose magnitudes approach zero as the parameter decreases to zero, has found several applications in constrained control systems, robust control and nonlinear control. In the continuous-time setting, there are currently three ways of constructing low gain feedback laws: the eigenstructure assignment approach, the parametric ARE based approach and the parametric Lyapunov equation based approach. The eigenstructure assignment approach leads to feedback gains explicitly parameterized in the low gain parameter. The parametric ARE based approach results in a Lyapunov function along with the feedback gain, but requires the solution of an ARE for each value of the parameter. The parametric Lyapunov equation based approach possesses the advantages of the first two approaches and results in both an explicitly parameterized feedback gains and a Lyapunov function. The first two approaches have been extended to discrete-time setting. This paper develops the parametric Lyapunov equation based approach to low gain feedback design for discrete-time systems.     

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     

Robust controller design of a class of nonlinear time delay systems via backstepping method

The robust control problem is investigated for nonlinear time delay systems with triangular structure. The uncertain delay disturbances are bounded by nonlinear functions with unknown coefficients. Via the backstepping method, we construct a state feedback controller with the help of Razumikhin lemma. Based on Lyapunov stability theory, we show that the resulting closed-loop system is UUB stable.     

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.     

混合不确定系统的鲁棒稳定性

研究兼有参数不确定性和非结构不确定性的混合不确定系统的鲁棒稳定性,该问题可以转化为具有参数摄动的传递函数族的最大H∞范数的计算问题,针对区间对象的加权H∞范数的最大值问题,给出了精确的计算公式并讨论了顶点检验成立的条件.     

Robustness margin calculation with dynamic and real parametricuncertainty

The problem of robust stability in feedback control systems with real uncertain parameters and unmodeled dynamics is considered. A robust margin r_m is defined, and an algorithm to calculate r_m and the closely related multivariable stability margin k_m is developed. How robust performance for real parametric uncertainty can be handled in this framework is also shown. The result essentially provides a method to check whether or not the infinity norm of a closed-loop transfer matrix is less than a specified level over a bounded set of real parametric variations     

复杂电力网络的鲁棒性控制研究

复杂电力网络中存在的一些随机扰动可能带来大规模停电,给国民经济造成巨大损失。为此,根据复杂电力网络的非线性特性,设计一种新的非线性控制器,达到复杂电力网络的稳定控制目的。应用复杂网络控制理论,对电力网络的鲁棒控制进行研究,使用符号函数和绝对值函数设计一种新型的非线性反馈控制器,根据Lyapunov稳定性理论,证明该控制器能够有效地保证带有随机扰动的复杂电力网络的鲁棒控制。仿真实验采用Lorenz系统,结果表明,该网络结构满足无标度特性,在非线性控制器下能够有效地实现鲁棒同步。     

Smooth stabilization implies coprime factorization

It is shown that coprime right factorizations exist for the input-to-state mapping of a continuous-time nonlinear system provided that the smooth feedback stabilization problem is solvable for this system. It follows that feedback linearizable systems admit such fabrications. In order to establish the result, a Lyapunov-theoretic definition is proposed for bounded-input-bounded-output stability. The notion of stability studied in the state-space nonlinear control literature is related to a notion of stability under bounded control perturbations analogous to those studied in operator-theoretic approaches to systems; in particular it is proved that smooth stabilization implies smooth input-to-state stabilization     

Lyapunov-based switching supervisory control of nonlinear uncertainsystems

The problem of controlling nonlinear noisy systems affected by parametric uncertainties is approached via the introduction of a supervisor which switches on, in feedback to the plant, one controller selected from a finite set of predesigned controllers. A Lyapunov-based falsification criterion allows one to ensure robust stability in the presence of uncertain constant parameters and exogenous bounded disturbances