An L∞ bound for solutions of the Cahn-Hilliard equation

In this paper we consider the equation

The Euler Equation and¶Absolute Minimizers of L∞ Functionals

The Aronsson-Euler equation for the functional

Intrinsic Geometry and Analysis of Diffusion Processes and L ∞-Variational Problems

The aim of this paper is twofold. First, we obtain a better understanding of the intrinsic distance of diffusion processes. Precisely, (a) for all n ≧ 1, the diffusion matrix A is weak upper semicontinuous on Ω if and only if the intrinsic differential and the local intrinsic distance structures coincide; (b) if n = 1, or if n ≧ 2 and A is weak upper semicontinuous on Ω, the intrinsic distance and differential structures always coincide; (c) if n ≧ 2 and A fails to be weak upper semicontinuous on Ω, the (non-)coincidence of the intrinsic distance and differential structures depend on the geometry of the non-weak-upper-semicontinuity set of A. Second, for an arbitrary diffusion matrix A, we show that the intrinsic distance completely determines the absolute minimizer of the corresponding L ^∞-variational problem, and then obtain the existence and uniqueness for given boundary data. We also give an example of a diffusion matrix A for which there is an absolute minimizer that is not of class C ¹. When A is continuous, we also obtain the linear approximation property of the absolute minimizer.     

Delay-dependent robust stability and H_∞ analysis of stochastic systems with time-varying delay

This paper investigates the robust stochastic stability and H∞ analysis for stochastic systems with time-varying delay and Markovian jump. By using the freeweighting matrix technique, i.e., He's technique, and a stochastic Lyapunov-Krasovskii functional, new delay-dependent criteria in terms of linear matrix inequalities are derived for the the robust stochastic stability and the H∞ disturbance attenuation. Three numerical examples are given. The results show that the proposed method is efficient and much less conservative than the existing results in the literature.     

Adaptive fuzzy H ∞ tracking design of SISO uncertain nonlinear fractional order time-delay systems

In this paper, a fuzzy logic controller equipped with training algorithms is developed such that the H ^?? tracking performance should be satisfied for a model-free nonlinear fractional order time delay system which is infinite dimensional in nature and time delay is a source of instability. In order to deal with the linguistic uncertainties caused from delay terms, the adaptive time delay fuzzy logic system is constructed to approximate the unknown time delay system functions. By incorporating Lyapunov stability criterion with H ^?? tracking design technique, the free parameters of the adaptive fuzzy controller can be tuned on line by output feedback control law and adaptive law. Moreover, the tracking error and external disturbance can be attenuated to arbitrary desired level. The numerical results show the effectiveness of the proposed adaptive H ^?? tracking scheme.     

Decentralized direct adaptive output feedback fuzzy H ∞ tracking design of large-scale nonaffine nonlinear systems

A novel H _∞ tracking-based decentralized direct adaptive output feedback fuzzy controller is developed for a class of interconnected nonaffine uncertain nonlinear systems in this paper. By virtue of the proper filtering of the observation error dynamics to assure its strictly positive realness, the observer-based decentralized direct adaptive fuzzy control (DAFC) scheme is presented for a class of large-scale nonaffine nonlinear systems by the combination of H _∞ tracking technique, implicit function theorem, a state observer and a fuzzy inference system. The output feedback and adaptation mechanisms for each subsystem depend upon local measurements not only to achieve asymptotical tracking of a reference trajectory but to guarantee arbitrary small attenuation level of the mismatched errors and external disturbances on the tracking error. Simulation results confirm the effectiveness of the proposed decentralized output feedback scheme.     

转台伺服系统的H∞设计

—本文将Ｈ∞控制理论用于转台伺服系统的设计，对该系统进行Ｈ∞优化设计作了探讨，重点讨论了权函数的选择问题，并根据系统带有未建模特性的实际情况，给出选择权函数的方法     

TSAI–TOKAD (T–T) Graph: The Combination of Non-oriented and Oriented Graphs for the Kinematics of Articulated Gear Mechanisms

The non-oriented and oriented linear graph techniques are used for the kinematic analysis of bevel-gear trains. In this paper, these two techniques are compared and the weaknesses of each technique are shown. In order to overcome the weaknesses of these techniques a new graphical technique called Tsai–Tokad (T–T) graph is introduced incorporating the important feature of the non-oriented graph which helps to determine the transfer vertex and the oriented graph technique. The theory is demonstrated by the kinematic analysis of articulated robotic mechanism used by Cincinnati Milacron T³     

Tracking control of uncertain switched nonlinear cascade systems: a nonlinear H ∞ sliding mode control method

This paper considers the tracking control problem for a class of uncertain switched nonlinear cascade systems via the multiple Lyapunov functions (MLFs) method. Each subsystem under consideration is composed of two cascade-connected parts: the null space dynamics part and the range space dynamics part. The two main robust control strategies, nonlinear H _∞ control (NHC) and the sliding mode control (SMC), are integrated to function in a complementary manner for tracking control tasks. Furthermore, sufficient conditions for the solvability of the tracking control problem of the switched system and design of both switching laws and controllers are presented. Finally, a simulation example is provided to demonstrate the feasibility of the developed method.     

平台稳定回路H∞鲁棒控制设计

平台是一个耦合系统,表现在转动惯量耦合和力矩耦合。在设计稳定回路时平台模型与实际物理模型有差别,因此要求所设计的控制器具有鲁棒稳定性。H∞控制理论是目前解决鲁棒控制问题比较成功且比较完善的理论体系,本利用H∞控制理论,研究了平台稳定回路多输入多输出（MIMO）控制器的设计。最后通过计算机仿真,验证了控制器的正确性。     

平台稳定回路H_∞鲁棒控制设计

平台是一个耦合系统 ,表现在转动惯量耦合和力矩耦合。在设计稳定回路时平台模型与实际物理模型有差别 ,因此要求所设计的控制器具有鲁棒稳定性。 H∞ 控制理论是目前解决鲁棒控制问题比较成功且比较完善的理论体系 ,本文利用 H∞ 控制理论 ,研究了平台稳定回路多输入多输出 ( MIMO)控制器的设计。最后通过计算机仿真 ,验证了控制器的正确性。     

Optimum design of dynamic vibration absorbers for a beam, based on H ∞ and H 2 Optimization

The solutions to H _∞ and H ₂ optimization problems of a variant dynamic vibration absorber (DVA) applied to suppress vibration in beam structures are derived analytically. The H _∞ optimum parameters such as tuning frequency and damping ratios are expressed based on fixed-point theory to minimize the resonant vibration amplitude, as well as, the H ₂ optimum parameters to minimize the total vibration energy or the mean square motion of a beam under random force excitation as analytical formulas. The reduction in maximum amplitude responses and mean square motion of a beam using the traditional vibration absorber is compared with the proposed dynamic absorber. Numerical results show the non-traditional DVA under optimum conditions has better vibration suppression performance on beam structures than the traditional design of DVA. Furthermore, comparing H _∞ and H ₂ optimization procedures shows that for a beam under random force excitation, use of H₂ optimum parameters resulting in smaller mean square motion than the other optimization.     

Active vibration isolation of machinery and sensitive equipment using H ∞ control criterion and particle swarm optimization method

Isolating the sensitive equipment from vibrating base or the foundation from machinery vibration is of practical importance in a number of engineering fields. With the development of the vibration control techniques and increasing requirements for the higher-performance vibration isolation in industry and everyday life, active vibration isolation exhibits the best performances. In this paper, active vibration isolation reducing vibration transmitted from vibrating base to sensitive equipment and from machinery to foundation was investigated. Controller as static output feedback was considered to design components of active isolation system. An active control is provided by using H _∞ control criteria to design this controller. This criterion is presented as a cost function and then optimized by Particle Swarm Optimization (PSO) algorithm. The approach is validated using numerical simulation. Results show that this static output feedback H _∞ controller using PSO algorithm can get good performance to reduce the effect of unwanted vibration and disturbances.     

VARIATIONAL METHOD AND COMPUTATION FOR H_∞ CONTROL

ＩｎｔｒｏｄｕｃｔｉｏｎＨ∞ｃｏｎｔｒｏｌｔｈｅｏｒｙｈａｓｂｅｅｎｗｅｌｌｄｅｖｅｌｏｐｅｄｓｉｎｃｅｔｈｅＤＧＫＦｐａｐｅｒ[1],ｗｈｅｒｅｔｈｅｆｕｎｄａｍｅｎｔａｌｅｑｕａｔｉｏｎｓｆｏｒＨ∞ ｍｅａｓｕｒｅｍｅｎｔｆｅｅｄｂａｃｋｃｏｎｔｒｏｌａｒｅｄｅｒｉｖｅｄｆｒｏｍｔｈｅｓｅｐａｒａｔｉｏｎｐｒｉｎｃｉｐｌｅ ,ａｓｉｎＬＱＧｃｏｎｔｒｏｌｔｈｅｏｒｙ[2～ 5 ].Ｈｏｗｅｖｅｒ,ｔｈｅｃｏｍｐｕｔａｔｉｏｎｆｏｒｆｉｎｉｔｅｈｏｒｉｚｏｎ [0 ,ｔｆ]ｐｒｏｂｌｅｍａｎｄｔｈｅｄｅｔｅｒｍｉ…     

Reconsideration of inviscid shock interactions and transition phenomena on double-wedge geometries in a M ∞ = 9 hypersonic flow

Shock polar analysis as well as 2-D numerical computation technique are used to illustrate a diverse flow topology induced by shock/shock interaction in a M _∞ = 9 hypersonic flow. New flow features associated with inviscid shock wave interaction on double-wedge-like geometries are reported in this study. Transition of shock interaction, unsteady oscillation, and hysteresis phenomena in the RR ↔ MR transition, and the physical mechanisms behind these phenomena are numerically studied and analyzed.     

压电智能板结构的H∞振动控制

研究了压电智能板结构的H∞振动控制问题。先采用4节点矩形弯曲薄板单元(含12个位移自由度,2个电自由度)的有限元模型,利用Ham ilton原理得到了智能板结构的运动微分方程,然后综合运用模态截断法、最小实现法和平衡降阶法,对压电智能板结构的系统状态方程进行了降阶处理,得到了可观可控且低阶的近似状态方程,针对该降阶后的系统,利用H∞控制理论求解出能抑制干扰的动态输出反馈控制器,并将该控制器作用到降阶处理前的原系统中,从而能实现原系统抗干扰的振动控制。最后,以智能悬臂薄板结构为例,讨论了降阶过程中出现的一些问题和结论,并求出了相应的动态输出反馈控制器。仿真结果表明,文中的方法可实现压电智能板结构对干扰的抑制。     

基于H∞滤波技术的传递对准方法

从实际应用的角度出发,提出利用跟踪微分滤波器抑制机翼挠曲变形产生的影响,通过杆臂效应补偿消除干扰加速度,用延时补偿算法减少由数据传输延迟造成的量测信息误差。在此基础之上,采用"速度 姿态"匹配方案,研究了基于H_∞滤波估计的快速传递对准方法。大量数值仿真、静态试验、动态跑车试验表明,这些方法有收敛速度较快、精度较高的特点,并具有较强的抗干扰能力。试验也验证了传递对准方法的有效、可行,能满足控制系统对导航信息的精度要求。     

T–S fuzzy control design for a class of nonlinear networked control systems

This paper is devoted to controlling a class of nonlinear systems over a communication network in the presence of packet transmission delays, packet losses, quantization errors, and sampling-related phenomena. Specifically, based on the Takagi–Sugeno (T–S) fuzzy approach, this paper presents a way of designing a quantized controller that allows all the states of nonlinear NCSs to converge exponentially to a bounded ellipsoid. In particular, this paper provides a method capable of exploiting fully the time-varying delay term d(t), induced by Jensen inequality, for nonlinear NCSs.     

Robust adaptive sliding mode control of MEMS gyroscope using T–S fuzzy model

In this paper, a multi-input multi-output Takagi–Sugeno (T–S) fuzzy model is proposed to represent the nonlinear model of micro-electro mechanical systems (MEMS) gyroscope and improve the tracking and compensation performance. A robust adaptive sliding mode control with on-line identification for the upper bounds of external disturbances and an adaptive estimator for the model uncertainty parameters are proposed in the Lyapunov framework. The adaptive algorithm of model uncertainty parameters could compensate the error between the optimal T–S model and the designed T–S model, and decrease the chattering of the sliding surface. Based on Lyapunov methods, these adaptive laws can guarantee that the system is asymptotically stable. For the purpose of comparison, the designed controller is also implemented on the nonlinear model of MEMS gyroscope. Numerical simulations are investigated to verify the effectiveness of the proposed control scheme on the T–S model and the nonlinear model.