体操机器人的模糊控制策略

提出了一种体操机器人模糊控制策略,它结合了无需模型和基于模型的模糊控制,无需模型的模糊控制器是为摇起体操机器人垢,它确保体操机器人的随着每次摆动而增加,基于模型的控制器是为平衡体操机器人设计的,它基于一个Ｔａｋａｇｉ－Ｓｕｇｅｎｏ模糊模型。     

LMI Consensus Condition for Discrete-time Multi-agent Systems

This paper examines a consensus problem in multi-agent discrete-time systems, where each agent can exchange information only from its neighbor agents. A decentralized protocol is designed for each agent to steer all agents to the same vector. The design condition is expressed in the form of a linear matrix inequality. Finally, a simulation example is presented and a comparison is made to demonstrate the effectiveness of the developed methodology.      

Stability analysis and guaranteed domain of attraction for a class of hybrid systems: an LMI approach

This paper presents sufficient conditions for the regional stability problem for switched piecewise affine systems, a special class of Hybrid Systems. This class of systems are described by an affine differential equation of the type x˙=A(δ)x+b(δ), where x denotes the continuous state vector and δ is a vector of logical variables that modifies the local model of the system in accordance with the continuous dynamics. Using a Lyapunov function of the type v(x)=x′P(x)x, we present LMI conditions that, when feasible, guarantee local stability of the origin of the switched system. Examples of switched affine systems are used to illustrate the results. Copyright © 2003 John Wiley & Sons, Ltd.     

Simple LMI based learning control design

In this note, a simple linear matrix inequality (LMI) design method is proposed for iterative learning control (ILC). The design can ensure a monotonic error decay in 2‐norm. Experimental results on a SCARA robot shows that the design can achieve nearly perfect tracking. Copyright © 2009 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

LMI based stability analysis and robust controller design for discrete linear repetitive processes

Discrete linear repetitive processes are a distinct class of 2D linear systems with applications in areas ranging from long‐wall coal cutting through to iterative learning control schemes. The main feature which makes them distinct from other classes of 2D linear systems is that information propagation in one of the two independent directions only occurs over a finite duration. This, in turn, means that a distinct systems theory must be developed for them. In this paper, the major new development is that an LMI based re‐formulation of the stability conditions can used to enable the design of a family of control laws which have a well defined physical basis. It is also noted that this setting can be used to investigate robustness aspects. Copyright © 2003 John Wiley & Sons, Ltd.     

Design improvements and control of a hybrid walking robot

In this paper design improvements and control algorithms are presented for a 2-DOF (Degree-Of-Freedom) hybrid leg-wheel walking machine. A prototype of a low-cost robot, which is capable of straight walking and steering with only two actuators, has been designed and built at LARM: Laboratory of Robotics and Mechatronics in Cassino. A control system has been developed in order to control the robot’s operation and to improve the prototype’s behavior. The designed control system and simulation results have been reported to show the operation of the prototype.     

An efficient LMI approach for the quadratic stabilisation of a class of linear,uncertain, time-varying systems

The purpose of this article is to provide a numerically efficient method for the quadratic stabilisation of a class of linear, discrete-time, uncertain, time-varying systems. The considered class of systems is characterised by an interval time-varying (ITV) matrix and constant sensor and actuator matrices. It is required to find a linear time-invariant (LTI) static output feedback controller yielding a quadratically stable closed-loop system independently of the parameter variation rate. The solvability conditions are stated in terms of linear matrix inequalities (LMIs). The set of LMIs includes the stability conditions for the feedback connection of a unique suitably defined extreme plant with an LTI output controller and the positivity of a closed-loop extremal matrix. A consequent noticeable feature of the article is that the total number of LMIs is independent of the number of uncertain parameters. This greatly enhances the numerical efficiency of the design procedure.     

LMI optimization approach to robust decentralized controller design

A new approach for design of robust decentralized controllers for continuous linear time‐invariant systems is proposed using linear matrix inequalities (LMIs). The proposed method is based on closed‐loop diagonal dominance. Sufficient conditions for closed‐loop stability and closed‐loop block‐diagonal dominance are obtained. Satisfying the obtained conditions is formulated as an optimization problem with a system of LMI constraints. By adding an extra LMI constraint to the system of LMI constraints in the optimization problem, the robust control is addressed as well. Accordingly, the decentralized robust control problem for a multivariable system is reduced to an optimization problem for a system of LMI constraints to be feasible. An example is given to show the effectiveness of the proposed method. Copyright © 2010 John Wiley & Sons, Ltd.     

A novel design approach for switched LPV controllers

A novel design procedure for switched linear parameter-varying (LPV) controller is proposed. The new procedure, based on the Youla parameterisation ideas, decomposes the controller design into two steps. One focuses on ensuring global stability and the other on fulfilling the local performance specifications. This scheme allows the design of each local controller independently of each other, which may achieve higher performance without compromising the global stability and also simplifies the synthesis and the implementation of the local controllers. Any standard LPV synthesis procedure can be used to design these controllers. On the other hand, the stability during switching is ensured with convex constraints and no restrictions are imposed on the switching among controllers. The use of the proposed procedure is illustrated with an active magnetic bearing example.     

Characterizing the solution set of polynomial systems in terms of homogeneous forms: an LMI approach

This paper considers the problem of determining the solution set of polynomial systems, a well‐known problem in control system analysis and design. A novel approach is developed as a viable alternative to the commonly employed algebraic geometry and homotopy methods. The first result of the paper shows that the solution set of the polynomial system belongs to the kernel of a suitable symmetric matrix. Such a matrix is obtained via the solution of a linear matrix inequality (LMI) involving the maximization of the minimum eigenvalue of an affine family of symmetric matrices. The second result concerns the computation of the solution set from the kernel of the obtained matrix. For polynomial systems of degree m in n variables, a basic procedure is available if the kernel dimension does not exceed m+1, while an extended procedure can be applied if the kernel dimension is less than n(m?1)+2. Finally, some application examples are illustrated to show the features of the approach and to make a brief comparison with polynomial resultant techniques. Copyright © 2003 John Wiley & Sons, Ltd.     

PWL and PWA ℋ ∞ controller synthesis for uncertain PWA slab systems: LMI approach

This article presents new piecewise-affine (PWA) and piecewise-linear (PWL) ?_∞ controller synthesis methods for uncertain PWA slab systems. The synthesis problems are formulated as convex programs subject to a set of Linear Matrix Inequalities (LMIs), which can then be solved efficiently using available software. No other synthesis methods available in the literature can design a PWA controller for an uncertain PWA system using convex optimisation without constraining the controller gain matrix. Therefore this is the main contribution of the article. The proposed controller synthesis methodologies are applied to a circuit example.     

基于LMI和IMC的动态反馈抗饱和补偿设计

提出了一种基于线性矩阵不等式(LMI)和内模控制(IMC)的动态反馈抗饱和补偿器的设计方法,为此首先简要地介绍了基于统一框架的抗饱和补偿器设计方法,然后针对原框架计算量庞大的问题,利用模型精确的IMC结构中对象和控制器同时稳定就能保证系统闭环稳定的特性对框架进行改造,并进一步选取了具有(?)2范数形式的性能优化指标,通过整定控制器的方法来优化闭环系统的工作性能,给出了LMI形式的结果．最后给出了运用此方法设计补偿器的一个仿真实例．     

基于LMI的随动系统满意PID调节器设计

PID控制器在实际工程中应用广泛,而且工程上对随动系统的性能要求往往是多方面的．该文应用满意控制思想,研究了期望指标：扇形区域极点,稳态输出方差和动态误差系数约束下随动系统的PID控制设计问题．首先将PID控制参数设计转化为局部状态反馈问题,导出了3项指标约束的双线性矩阵不等式(BMI)描述．然后给出改进的迭代线性矩阵不等式(LMI)算法求解BMI可行解,得到使闭环系统满足3项期望指标的PID参数．最后给出了应用该方法数值算例．     

An LMI approach to robust fault estimation for a class of nonlinear systems

The paper presents a robust fault estimation approach for a class of nonlinear discrete‐time systems. In particular, two sources of uncertainty are present in the considered class of systems, that is, an unknown input and an exogenous external disturbance. Thus, apart from simultaneous state and fault estimation, the objective is to decouple the effect of an unknown input while minimizing the influence of the exogenous external disturbance within the framework. The resulting design procedure guarantees that a prescribed disturbance attenuation level is achieved with respect to the state and fault estimation error while assuring the convergence of the observer. The core advantage of the proposed approach is its simplicity by reducing the fault estimation problem to matrix inequalities formulation. In addition, the design conditions ensure the convergence of the observer with guaranteed performance. The effectiveness of the proposed approach is demonstrated by its application to a twin rotor multiple‐input multiple‐output system. Copyright © 2015 John Wiley & Sons, Ltd.     

Dilated LMI characterisations for linear time-invariant singular systems

This article explores, based on projection lemma, dilated linear matrix inequality (LMI) characterisations for linear time-invariant singular systems. The deduced formulations cover not only the existing results reported in the literature, but also complete some missing LMI conditions. This article also lightens the mutual relations of these characterisations and clarifies the relation between the dilated LMIs for the conventional state-space systems and those for singular systems. The well-known results for the state-space setting reported in the literature can be reviewed as special cases.     

A dilated LMI approach to robust performance analysis of linear time-invariant uncertain systems

This paper studies robust performance analysis problems of linear time-invariant systems affected by real parametric uncertainties. In the case where the state-space matrices of the system depend affinely on the uncertain parameters, it is know that recently developed extended or dilated linear matrix inequalities (LMIs) are effective to assess the robust performance in a less conservative fashion. This paper further extends those preceding results and propose a unified way to obtain numerically verifiable dilated LMI conditions even in the case of rational parameter dependence. In particular, it turns out that the proposed dilated LMIs enable us to assess the robust performance via multiaffine parameter-dependent Lyapunov variables so that less conservative analysis results can be achieved. Connections among the proposed conditions and existing results are also discussed concretely. Several existing results can be viewed as particular cases of the proposed conditions.     

Matrix inequality‐based observer design for a class of distributed transport‐reaction systems

The problem of designing a globally exponentially convergent observer for a class of (linear in transport and nonlinear in generation) semi‐linear parabolic distributed systems is addressed within a matrix inequality framework, yielding (i) sufficient convergence conditions with physical meaning and (ii) the weight of a Lyapunov functional as design degree of freedom. The proposed approach is illustrated and tested with a representative case example in chemical reaction engineering. Copyright © 2013 John Wiley & Sons, Ltd.