Semi-global stabilization of a class of uncertain nonlinear systems by linear output feedback

This brief deals with the problem of semi-global stabilization by output feedback for a class of uncertain nonlinear systems. Due to the presence of mismatched uncertainties and the lack of triangularity condition, the systems under consideration are not uniformly completely observable. In addition, the uncertain nonlinear dynamics of the systems are higher order, rather than linearly growing, in the unmeasurable states. All these make the systems not semi-globally stabilizable by the existing output feedback design schemes. In this brief, by extending the feedback domination design techniques proposed by Qian and Lin, a systematic design scheme is developed to construct linear output feedback controllers that semi-globally stabilize a general class of uncertain nonlinear systems under less restrictive conditions.     

Disturbance observer based control for nonlinear systems

This work presents a general framework for nonlinear systems subject to disturbances using disturbance observer based control (DOBC) techniques. A two-stage design procedure to improve disturbance attenuation ability of current linear/nonlinear controllers is proposed where the disturbance observer design is separated from the controller design. To facilitate this concept, a nonlinear disturbance observer is developed for disturbances generated by an exogenous system, and global exponential stability is established under certain condition. Furthermore, semiglobal stability condition of the composite controller consisting of a nonlinear controller and the nonlinear disturbance observer is established. The developed method is illustrated by the application to control of a two-link robotic manipulator.     

Observer-Based H ∞ Synchronization and Unknown Input Recovery for a Class of Digital Nonlinear Systems

This paper considers the synchronization and unknown input recovery problem for a class of digital nonlinear systems based on a nonlinear observer approach. A generalized Luenberger-like observer is introduced for a class of discrete-time Lipschitz nonlinear systems. Stability conditions for the existence of asymptotic observers are established in terms of some linear matrix inequalities. It is shown that the proposed conditions are less conservative than some existing ones in the recent literature. Moreover, an observer design method is used to address the problem of H _∞ synchronization and unknown input recovery for a class of Lipschitz nonlinear systems in the presence of disturbances in both the state and output equations. Finally, a numerical example is provided to illustrate the effectiveness of the proposed design.     

一类非线性不确定时滞系统鲁棒容错控制

研究一类不确定非线性时滞系统的鲁棒容错控制问题.针对不确定非线性时滞系统,基于执行器连续型增益故障模式,利用Lyapunov-Krasovskii泛函方法和线性矩阵不等式方法,推导了当一类非线性不确定系统满足一定范数有界条件时,闭环系统时滞无关鲁棒容错控制器存在的充分条件,并给出了状态反馈鲁棒容错控制器的设计方法.将所设计的状态反馈控制方法应用于某一非线性不确定时滞系统,仿真结果表明设计的控制器不仅使得该故障系统对于执行器故障具有完整性,并且能达到给定的H∞性能指标,从而验证了所提出方法的可行性和有效性.     

Recursive Parameter Estimation Algorithms and Convergence for a Class of Nonlinear Systems with Colored Noise

Parameter estimation is important for controller design of linear systems and nonlinear systems. The parameters of the systems can be estimated through some identification algorithms. This paper presents a recursive generalized extended least squares algorithm and a generalized extended stochastic gradient (GESG) algorithm for identifying the parameters of a class of nonlinear systems. Furthermore, a multi-innovation GESG algorithm is derived to improve the estimation accuracy. The simulation example is provided to test the effectiveness of the proposed algorithms.     

Design and performance of adaptive systems based on structured stochastic optimization strategies

The theory and design of linear adaptive filters based on FIR filter structures is well developed and widely applied in practice. However, the same is not true for more general classes of adaptive systems such as linear infinite impulse response adaptive filters (MR) and nonlinear adaptive systems. This situation results because both linear IIR structures and nonlinear structures tend to produce multi-modal error surfaces for which stochastic gradient optimization strategies may fail to reach the global minimum. After briefly discussing the state of the art in linear adaptive filtering, the attention of this paper is turned to MR and nonlinear adaptive systems for potential use in echo cancellation, channel equalization, acoustic channel modeling, nonlinear prediction, and nonlinear system identification. Structured stochastic optimization algorithms that are effective on multimodal error surfaces are then introduced, with particular attention to the particle swarm optimization (PSO) technique. The PSO algorithm is demonstrated on some representative IIR and nonlinear filter structures, and both performance and computational complexity are analyzed for these types of nonlinear systems.     

Performance-Improved Design of N-PID Controlled Motion Systems With Applications to Wafer Stages

A nonlinear filter design is proposed to improve nanopositioning servo performances in high-speed (and generally linear) motion systems. The design offers a means to adapt fundamental control design tradeoffs-like disturbance suppression versus noise sensitivity-which are otherwise fixed. Typically performance-limiting oscillations in the feedback system that benefit from extra control are temporarily upscaled and subjected to nonlinear weighting. For sufficiently large amplitudes, this nonlinear filter operation induces extra controller gain. Oscillations that do not benefit from this extra control (typically because they represent noise contributions that should not be amplified) remain unscaled and, as such, do not induce extra controller gain. The combined usage of linear weighting filters with their exact inverses renders this part of the nonlinear filter design strictly performance based. The effective means to improve servo performance is demonstrated on a short-stroke wafer stage of an industrial wafer scanner. Since the nonlinear filter design is largely based on Lyapunov arguments, stability is guaranteed along the different design steps.     

一种基于神经网络的超稳定自适应控制算法

提出了一种用于控制复杂非线性系统的超稳定自适应控制算法。使用波波夫超稳定性原理设计控制器。用神经网络在线辨识系统的建模误差及不确定性因素，辨识结果作为补偿信号以实现系统的鲁棒控制。对一双输入双输出非线性系统的仿真结果表明，所提出的超稳定自适应控制算法具有较好的性能。     

Nonlinear filtering for state delayed systems with Markovian switching

This paper deals with the filtering problem for a general class of nonlinear time-delay systems with Markovian jumping parameters. The nonlinear time-delay stochastic systems may switch from one to the others according to the behavior of a Markov chain. The purpose of the problem addressed is to design a nonlinear full-order filter such that the dynamics of the estimation error is guaranteed to be stochastically exponentially stable in the mean square. Both filter analysis and synthesis problems are investigated. Sufficient conditions are established for the existence of the desired exponential filters, which are expressed in terms of the solutions to a set of linear matrix inequalities (LMIs). The explicit expression of the desired filters is also provided. A simulation example is given to illustrate the design procedures and performances of the proposed method.     

Performance benefits of hybrid control design for linear andnonlinear systems

This paper provides an overview of recent developments on design of hybrid controllers for continuous-time control systems that can be described by linear or nonlinear differential state equations. Hybrid controllers provide a generalization of classical feedback controllers for linear and nonlinear systems. The benefit of hybrid controllers, that they can be used to achieve closed-loop performance objectives that cannot be achieved using classical linear or nonlinear controllers, is emphasized. This paper introduces hybrid controllers in the form of a switching control architecture and provides a summary of recently developed control approaches that utilize this control architecture. We provide a conceptual framework for these results, identify limitations of the results, and discuss the current status of hybrid control design approaches     

混沌系统同步的抗干扰优化设计

本文研究混沌系统同步的抗信道噪声和参数失配干扰优化设计问题。以非线性反馈混沌同步方案为基础，推导出一种抗干扰优化设计方法。对蔡氏电路的仿真实验表明，用该方法设计的混沌同步系统具有较强的抗干扰能力。     

A self-organizing fuzzy sliding-mode controller design for a classof nonlinear servo systems

A self-organizing fuzzy controller to augment a sliding-mode control (SOFSMC) scheme for a class of nonlinear systems is proposed. The motivation behind this scheme is to combine the best features of self-organizing fuzzy control and sliding-mode control to achieve rapid and accurate tracking control of a class of nonlinear systems. The chatter encountered by most sliding-mode control schemes is greatly alleviated without sacrificing invariant properties. A stability analysis is presented; the design guidelines and the class of applicable systems are clearly identified. To verify the scheme, the authors performed experiments on its implementation in a magnetic levitation system. The results show that both alleviation of chatter and robust performance are achieved; the advantages of the scheme are indicated in comparison with the conventional sliding-mode design     

A Systematic Approach to Bi-Directionally Nonlinearly Coupled Systems Design for the Generation of Complex Dynamical Behaviours

In this paper, a procedure to design a class of coupled systems that exhibit complex behaviours is presented. The proposed method is rigorously and systematically applicable to any dynamic system with nonlinear polynomial elements. Starting from two identical nonlinear algebraic systems, the proposed approach determines a proper bidirectional coupling that is able to force the coupled systems to exhibit complex behaviours. The coupling strength permits to control bifurcations of the system, i.e., to move through different regions of the parameter space, characterized by different complex behaviours of the system. Among the analyzed complex phenomena (generalized synchronization, blowout bifurcation, on-off intermittency and hyperchaos) a particular relevance is given to hyperchaotic behaviour. Moreover the basic design principle is demonstrated by means of proper examples.     

控制增益符号已知的MIMO非线性时滞系统自适应控制

针对一类具有死区模型并且控制增益符号已知的不确定多输入多输出非线性时滞系统,基于滑模控制原理提出了一种稳定的自适应神经网络控制方案。该方案通过使用Lyapunov-Krasovskii泛函抵消了因未知时变时滞带来的系统不确定性。通过利用积分型李亚普诺夫函数,并且构造逼近连续函数,闭环系统证明是半全局一致终结有界。仿真结果表明了该方法的有效性。     

T-S fuzzy controllers for nonlinear interconnected systems with multiple time delays

This paper investigates the effectiveness of a passive tuned mass damper (TMD) and fuzzy controller in reducing the structural responses subject to the external force. In general, TMD is good for linear systems. We proposed here an approach of Takagi-Sugeno (T-S) fuzzy controller to deal with the nonlinear system. To overcome the effect of modeling error between nonlinear multiple time-delay systems and T-S fuzzy models, a robustness design of fuzzy control via model-based approach is proposed in this paper. A stability criterion in terms of Lyapunov's direct method is derived to guarantee the stability of nonlinear multiple time-delay interconnected systems. Based on the decentralized control scheme and this criterion, a set of model-based fuzzy controllers is then synthesized via the technique of parallel distributed compensation (PDC) to stabilize the nonlinear multiple time-delay interconnected system and the H/sup /spl infin// control performance is achieved at the same time. Finally, the proposed methodology is illustrated by an example of a nonlinear TMD system.     

Synthesis of feedback systems with nonlinear time-varying uncertain plants to satisfy quantitative performance specifications

A synthesis procedure for systems with a nonlinear time-varying constrained part (plant) with uncertain parameters, subjected to a finite set of deterministic command and disturbance inputs I = {i^α} is presented. The design must guarantee that in response to i^α, the system output c^α∈ S^α, despite the plant uncertainty, where S^αis a prescribed set of acceptable responses, for that α value. The basic design philosophy is to convert the uncertain nonlinear plant set into an "equivalent" uncertain-linear time-invariant plant set. A synthesis procedure exists for the latter problem. Schauder's fixed-point theorem is used to prove that the resulting design satisfies the nonlinear problem. The final design emerges, in general, with linear and nonlinear time-varying compensation networks. Two design examples are included.     

MATLAB环境下非线性控制系统的建模与仿真

MATLAB软件在许多科学领域中成为计算机辅助设计、算法研究和应用开发的基本工具,在MATLAB/Simulink中对线性定常系统或者简单的非线性控制系统的建模与仿真比较简单方便,但对复杂非线性控制系统的建模与仿真实现困难。提出一种在MATLAB环境下利用m函数实现非线性控制系统的建模与仿真方法,该方法简单直观,维护性较好,具有可移植性。对复杂的非线性控制系统的建模与仿真,该方法可以明显提高仿真的效率。仿真实例验证了该方法的有效性和可行性。     

Nichtlineare Trajektorienfolgeregelung für einen Laborhelikopter

This contribution is devoted to the nonlinear tracking control problem of the laboratory experiment helicopter 3DOF distributed by Quanser. The laboratory experiment belongs to the class of mechanical systems with three degrees-of-freedom and two control inputs. It is well known that the systematic design of nonlinear controllers for underactuated mechanical systems is a challenge compared to fully actuated systems. On certain simplifying assumptions, which very well apply to the operating range of practical interest, we can show that the mathematical model is configuration flat. Thereby, a mechanical system is said to be configuration flat if it is differential flat and the flat outputs solely depend on the generalized coordinates of the mechanical system. The controller design is based on a formulation of the mechanical system on a Riemannian manifold where the kinetic energy serves as a natural Riemannian metric. In a first step a nonlinear tracking controller including an integral part in the linear error system is designed by means of a quasi-static state feedback. In a second step the design of the tracking controller is based on the theory of exact linearization utilizing the so-called dynamic extension algorithm. The experimental results of both controllers are compared and discussed in detail. In particular, the quasi-static state feedback controller shows an excellent tracking behavior. The performance as being obtained by the nonlinear controlled cannot be achieved by conventional linear control strategies.     

Determination of proper output variables for the decoupling of nonlinear systems

The letter deals with the design of nonlinear time-variant systems by decoupling. A method is presented to determine proper output variables in order to generate maximum differential order. As a conclusion equivalence turns out between this procedure and the transformation to nonlinear phase-variable canonical form.