Stability analysis of sampled-data fuzzy controller for nonlinear systems based on switching T–S fuzzy model

This paper investigates the system stability of a sampled-data fuzzy-model-based control system, formed by a nonlinear plant and a sampled-data fuzzy controller connected in a closed loop. The sampled-data fuzzy controller has an advantage that it can be implemented using a microcontroller or a digital computer to lower the implementation cost and time. However, discontinuity introduced by the sampling activity complicates the system dynamics and makes the stability analysis difficult compared with the pure continuous-time fuzzy control systems. Moreover, the favourable property of the continuous-time fuzzy control systems which is able to relax the stability analysis result vanishes in the sampled-data fuzzy control systems. A Lyapunov-based approach is employed to derive the LMI-based stability conditions to guarantee the system stability. To facilitate the stability analysis, a switching fuzzy model consisting of some local fuzzy models is employed to represent the nonlinear plant to be controlled. The comparatively less strong nonlinearity of each local fuzzy model eases the satisfaction of the stability conditions. Furthermore, membership functions of both fuzzy model and sampled-data fuzzy controller are considered to alleviate the conservativeness of the stability analysis result. A simulation example is given to illustrate the merits of the proposed approach.     

Application of fuzzy control to a road tunnel ventilation system

This paper deals with the serious problems of ventilation system in a large road tunnel. Higher visibility and lower concentration of carbon monoxide are the key issues concerning the ventilation system. Prior to designing the fuzzy control model, a configuration layout of the ventilation system including sensing, control and traffic prediction as well is conceptually constructed. Based on the layout that offers assignments of sensors and control elements, a fuzzy logic control model is developed. Membership functions of sensor errors and control increments are physically submitted in order to set up the fuzzy logic rules. Timing and spacing filtering in terms of weighting approaches is employed in the fuzzy logic rules. A dynamic equation describing the concentration of air pollution is also given so as to cooperate with the fuzzy logic rules and to play roles in the computer simulation. The result of computer simulation involving five cases indicates that a multi-level scheme is able to solve the engineering problems.     

Indirect adaptive fuzzy observer and controller design based on interval type-2 T-S fuzzy model

This paper presents the design scheme of the indirect adaptive fuzzy observer and controller based on the interval type-2 (IT2) T-S fuzzy model. The nonlinear systems can be well approximated by IT2 T-S fuzzy model, in which the fuzzy rules’ antecedents are interval type-2 fuzzy sets and consequents are linear state equations. The proposed IT2 T-S fuzzy model is a combination of IT2 fuzzy system and T-S fuzzy model, and also inherits the benefits of type-2 fuzzy logic systems, which is able to directly handle uncertainties and can minimize the effects of uncertainties in rule-based fuzzy system. These characteristics can improve the accuracy of the system modeling and reduce the number of system rules. The proposed method using feedback control, adaptive laws, and on-line object parameters are adjusted to ensure observation error bounded. In addition, using Lyapunov synthesis approach and Lipschitz condition, the stability analysis is conducted. The simulation results show that the proposed method can handle unpredicted disturbance and data uncertainties very well in advantage of the effectiveness of observation and control.     

Type-2 T–S fuzzy impulsive control of nonlinear systems

A novel impulsive control approach based on interval Type-2 T–S fuzzy model has been presented for nonlinear systems in this paper. This approach makes up for the drawback of Type-1 fuzzy impulsive control, which cannot fully handle the uncertainties in describing the complex nonlinear systems by Type-1 fuzzy membership functions and cannot give rigorous fuzzy rules. Further more, this approach uses the “broad band” effect of the Type-2 membership functions to solve the noise of training data and exterior disturbance of the Type-1 fuzzy impulsive control. By using Lyapunov theory and Lipschitz condition, which is combined with integrated approaches such as comparison methods and linear matrix inequalities, the Type-2 fuzzy impulsive controller is designed and the general asymptotical stability analysis of the systems is given. Finally, the simulation of the inverted pendulum model demonstrates the validity and superiority of the proposed method by easily determining the membership functions and choosing minimum number of fuzzy rules and the method can handle random disturbance and data uncertainties very well.     

自组织结构的变论域模糊控制

针对变论域模糊控制,提出一种新的自组织结构的变论域模糊控制方法。自组织结构算法可以调整变论域模糊系统结构以及动态获得模糊规则,进一步减小变论域模糊控制项的稳态逼近误差。通过进一步理论分析可知,自组织结构算法仅仅保证了系统瞬时的切换是平稳的,但不能保证系统的闭环稳定性。给出了所提出控制方法的适用条件。通过与固定模糊系统结构的变论域模糊控制比较,仿真结果表明,所提出控制方法不仅使得系统的稳态跟踪误差更平稳,而且使得输入控制信号更加平滑。     

Stability analysis and stabilization of LPV systems with jumps and (piecewise) differentiable parameters using continuous and sampled-data controllers

Linear Parameter-Varying (LPV) systems with jumps and piecewise differentiable parameters is a class of hybrid LPV systems for which no tailored stability analysis and stabilization conditions have been obtained so far.¹ We fill this gap here by proposing an approach based on a clock- and parameter-dependent Lyapunov function yielding stability conditions under both constant and minimum dwell-times. Interesting adaptations of the latter result consist of a minimum dwell-time stability condition for uncertain LPV systems and LPV switched impulsive systems. The minimum dwell-time stability condition is notably shown to naturally generalize and unify the well-known quadratic and robust stability criteria all together. Those conditions are then adapted to address the stabilization problem via timer-dependent and a timer- and/or parameter-independent (i.e. robust) state-feedback controllers, the latter being obtained from a relaxed minimum dwell-time stability condition involving slack-variables. Finally, the last part addresses the stability of LPV systems with jumps under a range dwell-time condition which is then used to provide stabilization conditions for LPV systems using a sampled-data state-feedback gain-scheduled controller. The obtained stability and stabilization conditions are all formulated as infinite-dimensional semidefinite programming problems which are then solved using sum of squares programming. Examples are given for illustration.     

Hybrid Impulsive Control of Stochastic Systems with Multiplicative Noise Under Markovian Switching

A problem of state output feedback stabilization of discrete-time stochastic systems with multiplicative noise under Markovian switching is considered. Under some appropriate assumptions, the stability of this system under pure impulsive control is given. Further under hybrid impulsive control, the output feedback stabilization problem is investigated. The hybrid control action is formulated as a combination of the regular control along with an impulsive control action. The jump Markovian switching is modeled by a discrete-time Markov chain. The control input is simultaneously applied to both the stochastic and the deterministic terms. Sufficient conditions based on stochastic semi-definite programming and linear matrix inequalities (LMIs) for both stochastic stability and stabilization are obtained. Such a nonconvex problem is solved using the existing optimization algorithms and the nonconvex CVX package. The robustness of the stability and stabilization concepts against all admissible uncertainties are also investigated. The parameter uncertainties we consider here are norm bounded. Two examples are given to demonstrate the obtained results.     

模糊不确定时滞系统的保成本控制

讨论了基于T-S模型的不确定时滞系统的保成本控制问题.文章采用并行补偿状态反馈控制方法和时滞相关稳定性分析方法,通过引入一个带调节因子的Lyapunov-Krasovskii泛函,利用线性矩阵不等式的形式给出了状态反馈控制器存在的充分条件.当调节因子取不同值时,最小保成本值和反馈增益也是不同的,不同的反馈增益导致不同的动态性能,因此,可以通过选取合适的调节因子来优化闭环系统的动态性能. 最小保成本值可以看作调节因子的函数,因此,可以通过求解一个凸优化问题来求得最小的保成本值和最优的调节因子,文章给出了一个求解最小保成本值的算法.并利用仿真示例验证了所给方法的有效性.     

基于LMI的时滞关联模糊大系统的分散镇定

讨论了具有时滞关联的连续时间模糊大系统的分散镇定问题 ,基于李亚普诺夫稳定性理论及大系统分散控制理论 ,给出了保证该时滞模糊大系统闭环渐近稳定的 LMI形式的充分条件 .满足这些充分条件的分散化并行分布补偿 ( DPDC)控制器参数可通过 MATLAB的 LMI工具箱有效的对其进行求取 .     

具有数据丢失的网络化控制系统的基于观测器的镇定

研究具有数据丢失的网络化控制系统的基于观测器的镇定问题。受控对象是由T-S模糊模型描述的非线性时滞系统。把数据丢失过程建模成独立同分布过程。利用模糊Lyapunov函数方法得到了闭环系统随机稳定的充分条件,其基于观测器的反馈控制器可通过求解一组线性矩阵不等式来设计。一个仿真例子说明方法的有效性。     

T–S fuzzy-model-based robust stabilization for a class of nonlinear discrete-time networked control systems

In this paper, the robust stabilization problem is investigated for a class of nonlinear discrete-time networked control systems (NCSs). To study the system stability and facilitate the design of fuzzy controller, Takagi–Sugeno (T–S) fuzzy models are employed to represent the system dynamics of the nonlinear discrete-time NCSs with effects of the approximation errors taken into account, and a unified model of NCSs in the T–S fuzzy model is proposed by modeling the approximation errors as norm-bounded uncertainties in system metrics, where non-ideal network Quality of Services (QoS), such as data dropout and network-induced delay, are coupled in a unified framework. Then, based on the Lyapunov–Krasovskii functional, sufficient conditions are derived for the existence of a fuzzy controller. By these criteria, two approaches to design a fuzzy controller are developed in terms of linear matrix inequalities (LMIs). Finally, illustrative examples are provided to show the effectiveness of the proposed methods.     

Hilbert空间中具无界控制的无限时区线性二次最优控制问题

本文研究了Hilbert空间中一类由解析半群支配的具无界控制的无限时区线性二次最优控制问题,其中指标中的控制项加权算子要求强制而状态项加权算子可允许为不定号.在指数能稳条件下,证明了任意的最优控制及其最优轨线必定连续,建立了正实引理作为此问题唯一可解的充要条件,并用代数Riccati方程的解给出了最优控制的闭环综合。     

Fuzzy controller of the air system of a diesel engine: Real-time simulation

In this paper a fuzzy controller is proposed to regulate the intake manifold pressure and the fresh mass airflow of diesel engines simultaneously. The instrumentation set usually embedded in a mass-produced passenger car has been considered. Unlike many multi-variable controllers, the proposed structure requires neither an internal model nor identification algorithms. In comparison to controllers embedded at present in standard engine control units (ECUs), it improves the trajectory tracking of desired outputs during simulation of EURO cycles. Because of its performance, the fuzzy controller has been implemented in an electronics control unit. Some real-time results are presented.     

三维水平井轨道设计模糊最优控制模型

建立了三维水平井井眼轨道设计模糊非线性多目标最优控制模型 ,利用模糊集理论把该模型转化为非线性规划问题 ,并把该模型应用到水平井的实际生产中 ,得到满意的结果 .     

小参数时变非线性系统的技术稳定性

分析一类含小参数的时变非线性系统关于给定状态约束集合的技术稳定性.根据向量微分比较原理和基本的单调性准则,利用向量V函数方法给出由系统系数表达的技术稳定性判据.并讨论了基于派生系统和线性化方法研究非线性系统技术稳定性的条件.另外,对于派生时变线性系统的指数稳定性给出了简单的代数判据.最后给出示例说明文中方法.     

一类不确定非线性系统的执行器故障模糊容错控制

针对一类状态不完全可测的不确定非线性系统,研究了带有执行器故障的容错控制问题.采用 T-S模型对非线性系统进行模糊建模,利用并行分布补偿(PDC)算法设计了状态现潮器和基于状态现 潮器的客错控制,给出了保证该模糊容错控制系统稳定的充分条件.根据李雅普诺夫稳定性理论和线性 矩阵不等式(LMI),证明了所提出的模糊容错控制方法不但使得模糊控制系统渐近稳定,而且能够取得 H∞性能指标.计算机仿真结果进一步验证了所提出方法的正确性.     

基于粗糙集的模糊决策算法

给出一种从连续决策表中提取模糊决策规则的规则提取算法。首先,转化连续属性值为模糊值;然后,给出两个不同对象的模糊属性值关于相应连续属性的相似度;其次,给出了λ相似关系与λ相似类的定义。根据λ相似关系,给出粗糙-模糊空间中的下近似与上近似概念;最后,结合模糊集与粗糙集理论的思想,给出一种从连续值域决策表获取决策规则的算法,并通过实例说明该算法的有效性。     

A modified coupled map car following model and its traffic congestion analysis

Based on the coupled map car following model which was presented by Konishi et al. [Konishi KJ, Kokame H, Hirate K. Phys Rev E 1999;60:4000-7.] (for short, KKH), a modified coupled map car following model is proposed. In this model two successive vehicles’ headway distances in front of the considered one are incorporated in the optimal velocity (for short, OV) function. The stability condition is given for the change of the speed of the preceding vehicle on the base of the control theory. The control scheme in KKH model is applied to the modified model and the feedback gains are determined. Comparison between the modified model and KKH model is carried out. And the corresponding numerical simulation results show that the temporal behavior obtained by our model is better than that by KKH model. The simulation results are in good agreement with the theoretical analysis.     

Integral sliding mode control for T–S fuzzy descriptor systems

The present study focuses on designing the integral sliding-mode control (ISMC) for generalized Takagi–Sugeno (T–S) fuzzy singular stochastic systems by involving the Markovian jump type of system parameters. Distinct to the existing works, the present paper concerns about the derivation of sufficient conditions that ensure the global stability of considered T–S fuzzy stochastic singular Markovian jump systems with matched/mismatched uncertainties under fuzzy-based ISMC. In this regard, an improved fuzzy integral sliding manifold function with mode-dependent derivative-term coefficient is proposed where the matched uncertainties become unnecessary and the mismatched uncertainties have been disintegrated during the sliding mode phase. Based on Lyapunov stability theory, a suitable Lyapunov functional candidate by involving the information about the membership functions is constructed with singular and P-type matrices, the stochastic admissibility of corresponding sliding mode dynamics are derived. To proven the effectiveness of the proposed method, a physical experimental problem on cart and pendulum is adapted and simulated via the derived theoretical results and the corresponding results are provided.     

Robust design of rule-based fuzzy controllers

This paper deals with the design of stable and robust rule-based fuzzy control systems. New expressions to compute indices which provide a measure of the stability and robustness of fuzzy control systems are presented. The relation between the modification of the rules and the stability is studied through the so-called sensitivity indices. The paper presents procedures that make use of these indices to improve the design of fuzzy control systems, including the modification of the rules to obtain the global stability of an unstable system with multiple attractors, and to improve the dynamic behavior or the robustness of a non-linear plant. An example with a fuzzy controller for a system with non-linear damping and saturation in the actuation is presented to illustrate the design procedure.