State-feedback stabilisation for fuzzy bilinear uncertain system with disturbance via fuzzy control approach

This article presents a fuzzy control scheme for a class of Takagi–Sugeno (T–S) fuzzy uncertain bilinear system with disturbance (FUBSD). First, the T–S FUBSD is established and based on the parallel distributed compensation method, the overall robust H _∞ fuzzy controller is proposed to globally stabilise the T–S FUBSD. Then, some sufficient conditions are derived to guarantee the robust stabilisability of the overall fuzzy control system via linear matrix inequalities. Finally, a numerical example is utilised to demonstrate the validity and effectiveness of the proposed control scheme.     

Delay-dependent H ∞ control of linear discrete-time systems with an interval-like time-varying delay

The free-weighting-matrix approach is developed to study the H _∞ control of linear discrete-time systems with an interval-like time-varying delay. First, a delay- and range-dependent criterion for a given H _∞ performance is derived. Second, a memoryless H _∞ state-feedback controller is designed based on a performance analysis. Finally, two numerical examples demonstrate the effectiveness of the proposed method and show that both the upper bound and range of an interval-like time-varying delay affect the stability and/or H _∞ performance of a system.     

Dynamic output feedback H ∞ control for affine fuzzy systems

This article investigates the problem of designing H _∞ dynamic output feedback controllers for nonlinear systems, which are described by affine fuzzy models. The system outputs have been chosen as premise variables, which can guarantee that the plant and the controller always switch to the same region. By using a piecewise Lyapunov function and adding slack matrix variables, a piecewise-affine dynamic output feedback controller design method is obtained in the formulation of linear matrix inequalities (LMIs), which can be efficiently solved numerically. In contrast to the existing work, the proposed approach needs less LMI constraints and leads to less conservatism. Finally, numerical examples illustrate the effectiveness of the new result.     

A distributed control algorithm for internal flow management in a multi-zone climate unit

We examine a distributed control problem for internal flow management in a multi-zone climate unit. The problem consists of guaranteeing prescribed indoor climate conditions in a cascade connection of an arbitrarily large number of communicating zones, in which air masses are exchanged to redirect warm air from hot zones (which need to be cooled down) to cold zones (which need to be heated up), and to draw as much fresh air as possible to hot zones, relying on the ventilation capacity of neighbouring “collaborative” zones. The controller of each zone must be designed so as to achieve the prescribed climate condition, while fulfilling the constraints imposed by the neighbouring zones—due to their willingness to cooperate or not in the air exchange—and the conservation of flow, and despite the action of unknown disturbances. We devise control laws which yield hybrid closed-loop systems, depend on local feedback information, take on values in a finite discrete set, and cooperate with neighbour controllers to achieve different compatible control objectives, while avoiding conflicts.     

Robust H ∞ networked control for discrete-time fuzzy systems with state quantisation

The problem of robust H _∞ control for uncertain discrete-time Takagi and Sugeno (T-S) fuzzy networked control systems (NCSs) with state quantisation is investigated. A new model of network-based control with simultaneous consideration of network-induced delays and packet dropouts is proposed. By using a fuzzy Lyapunov–Krasovskii functional (LKF), we derive a less conservative delay-dependent stability condition for the closed-loop NCSs. Robust H _∞ fuzzy controller is developed for the asymptotical stabilisation of the NCSs. Since it is not expressed as strict LMI conditions, the cone complementary linearisation procedure is exploited to solve the nonconvex feasibility problem. A numerical example shows the feasibility applications of the proposed technique.     

Application of facial reduction to H ∞ state feedback control problem

One often encounters numerical difficulties in solving linear matrix inequality (LMI) problems obtained from H _∞ control problems. For semidefinite programming (SDP) relaxations for combinatorial problems, it is known that when either an SDP relaxation problem or its dual is not strongly feasible, one may encounter such numerical difficulties. We discuss necessary and sufficient conditions to be not strongly feasible for an LMI problem obtained from H _∞ state feedback control problems and its dual. Moreover, we interpret the conditions in terms of control theory. In this analysis, facial reduction, which was proposed by Borwein and Wolkowicz, plays an important role. We show that the dual of the LMI problem is not strongly feasible if and only if there exist invariant zeros in the closed left-half plane in the system, and present a remedy to remove the numerical difficulty with the null vectors associated with invariant zeros in the closed left-half plane. Numerical results show that the numerical stability is improved by applying it.     

Delay-dependent H ∞ controller design for linear neutral systems with discrete and distributed delays

This article considers the delay-dependent H _∞ control problem for linear neutral systems with both discrete and distributed delays. The problem we address is to design a state feedback controller such that the resulting closed-loop system is asymptotically stable and satisfies a prescribed H _∞ performance level. First, a delay-dependent sufficient condition for the solvability of the problem is obtained in terms of matrix inequalities. Then, by using the cone complementarity linearization approach, an H _∞ controller is developed based on the solvability condition. Finally, numerical examples are provided to demonstrate the effectiveness of the proposed method.     

A less conservative LMI condition for the robust stability of discrete-time uncertain systems

In this paper, a less conservative condition for the robust stability of uncertain discrete-time linear systems is proposed. The uncertain parameters, assumed to be time-invariant, are supposed to belong to convex bounded domains (polytope type uncertainty). The stability condition is formulated in terms of a set of linear matrix inequalities involving only the vertices of the polytope domain. A simple and numerically efficient feasibility test provides a set of Lyapunov matrices whose convex combination can be used to assess the stability of any dynamic matrix inside the uncertainty domain. Examples illustrate the results.     

基于非脆弱控制器设计的不确定模糊系统稳定性研究

研究不确定动态模糊系统的稳定性问题.提出一类不确定T-S动态模糊系统的非脆弱控制问题,并进行了控制器设计.首先给出不确定T-S动态模糊系统的模型;然后利用Lyapunov函数方法,研究连续不确定动态模糊系统的非脆弱控制器设计,得到基于LMI的不确定动态模糊系统的全局渐近稳定性条件.通过对一级倒立摆的不确定模糊非脆弱控制器设计的实例,表明了设计方法的可行性和有效性.     

Robust fuzzy stabilization of dithered chaotic systems using island-based random optimization algorithm

Applying dither to highly nonlinear systems may suppress chaotic phenomena, but dynamic performance, such as convergence rate and disturbance attenuation, is usually not guaranteed. This paper presents a dithered H_∞ robust fuzzy control scheme to stabilize chaotic systems that ensures disturbance attenuation bounds. In the proposed scheme, Takagi-Sugeno (T-S) fuzzy linear models are used to describe the relaxed models of the dithered chaotic system, and fuzzy controllers are designed based on an extension to the concept of parallel distributed compensation (PDC). Sufficient condition for the existence of the H_∞ robust fuzzy controllers is presented in terms of a novel linear matrix inequalities (LMI) form which takes full consideration of modeling error and disturbances, but cannot be solved by the standard procedures. In order to solve the LMI problem and to identify the chaotic systems as T-S fuzzy modes, we propose a compound optimization strategy called the island-based random-walk algorithm (IRA). The algorithm is composed of a set of communicating random-walk optimization procedures concatenated with the down-hill simplex method. The design procedure and validity of the proposed scheme is demonstrated via numerical simulation of the dithered fuzzy control of a chaotic system.     

An LMI approach to design robust fault detection filter for uncertain LTI systems

In this paper, the robust fault detection filter design problem for uncertain linear time-invariant (LTI) systems with both unknown inputs and modelling errors is studied. The basic idea of our study is to use an optimal residual generator (assuming no modelling errors) as the reference residual model of the robust fault detection filter design for uncertain LTI systems with modelling errors and, based on it, to formulate the robust fault detection filter design as an H_∞ model-matching problem. By using some recent results of H_∞ optimization, a solution of the optimization problem is then presented via a linear matrix inequality (LMI) formulation. The main results include the development of an optimal reference residual model, the formulation of robust fault detection filter design problem, the derivation of a sufficient condition for the existence of a robust fault detection filter and a construction of it based on the LMI solution parameters, the determination of adaptive threshold for fault detection. An illustrative design example is employed to demonstrate the effectiveness of the proposed approach.     

Non-fragile H∞ dynamic output feedback control for uncertain Takagi–Sugeno fuzzy systems with time-varying delay

This paper mainly focuses on the problem of non-fragile H_∞ dynamic output feedback control for a class of uncertain Takagi–Sugeno fuzzy systems with time-varying state delay. Based on a new type of Lyapunov–Krasovskii functional without ignoring any subtle integral terms in the derivatives, a less conservative dynamic output feedback controller with additive gain variations is designed, which guarantees that the closed-loop fuzzy system is asymptotically stable and satisfies a prescribed H_∞-performance level. Furthermore, the obtained parameter-dependent conditions are given in terms of solution to a set of linear matrix inequalities, which improve some existing relevant results. Finally, numerical examples are given to illustrate the effectiveness and merits of the proposed method.     

Observer-based H∞ controller for 2-D T–S fuzzy model

This paper develops a method of fuzzy observer-based H_∞ controller design for two-dimensional (2-D) discrete Takagi–Sugeno (T–S) fuzzy systems. By reformulating the system, a linear matrix inequality (LMI)-based sufficient condition is derived. Then the fuzzy controller and the fuzzy observer can be independently designed, which guarantee an H_∞ noise attenuation γ of the whole system. Owing to the introduction of free matrices, the presented design method has a wider range of application and can guarantee a better H_∞ performance of the closed-loop fuzzy control system. Simulation results have demonstrated the effectiveness of the proposed method.     

State feedback tracking control for indirect field-oriented induction motor using fuzzy approach

This paper deals with the synthesis of fuzzy controller applied to the induction motor with a guaranteed model reference tracking performance. First, the Takagi-Sugeno (T-S) fuzzy model is used to approximate the nonlinear system in the synchronous d-q frame rotating with field-oriented control strategy. Then, a fuzzy state feedback controller is designed to reduce the tracking error by minimizing the disturbance level. The proposed controller is based on a T-S reference model in which the desired trajectory has been specified. The inaccessible rotor flux is estimated by a T-S fuzzy observer. The developed approach for the controller design is based on the synthesis of an augmented fuzzy model which regroups the model of induction machine, fuzzy observer, and reference model. The gains of the observer and controller are obtained by solving a set of linear matrix inequalities (LMIs). Finally, simulation and experimental results are given to show the performance of the observer-based tracking controller.     

离散系统输出反馈强正实控制器综合

基于正实引理使用线性矩阵不等式(LMI)方法讨论了离散系统一般强正实控制问题的解,给出了任意阶输出反馈强正实控制器的存在条件.证明了给定离散系统可输出反馈强正实当且仅当三个LMI存在一个合适解,可低价输出反馈强正实当且仅当带秩约束条件的三个LMI存在一个合适解.     

基于模糊Lyapunov函数方法的模糊广义系统H∞控制

研究一类T-S模糊广义系统的容许性条件和H∞控制问题. 首先将原系统表示成增广系统, 进而基于新的模糊Lyapunov函数和模糊控制器得到容许性条件. 所得开环容许条件不要求子系统是容许的; 闭环容许条件中不含有控制输入矩阵与控制增益矩阵的乘积项. 对于H∞控制问题, 利用隶属度函数的性质对H∞控制条件进行了放宽, 并得到了改进的严格线性矩阵不等式(LMI)形式的H∞控制条件. 数值算例表明所得结论较已有文献具有较小的保守性.     

Sequential LMI approach for the design of a BMI‐based robust observer state feedback controller with nonlinear uncertainties

This paper aims at developing a robust observer–based estimated state feedback control design method for an uncertain dynamical system that can be represented as a linear time‐invariant system connected with an integral quadratic constraint–type nonlinear uncertainty. Traditionally, in existing design methodologies, a convex semidefinite constraint is obtained at the cost of conservatism and unrealistic assumptions. This paper avoids such assumptions and formulates, the design of the robust observer state feedback controller as the feasibility problem of a bilinear matrix inequality (BMI) constraint. Unfortunately, the search for a feasible solution of a BMI constraint is an NP‐hard problem in general. The applicability of a linearization method, such as the variable change method and the congruence transformation, depends on the specific structure of the problem at hand and cannot be generalized. This paper transforms the feasibility analysis of the BMI constraint into an eigenvalue problem and applies the convex‐concave–based sequential linear matrix inequality optimization method to search for a feasible solution. Furthermore, an augmentation of the sequential linear matrix inequality algorithm to improve its numerical stability is presented. In the application part, a vehicle lateral control problem is presented to demonstrate the applicability of the proposed algorithm to a real‐world estimated state feedback control design problem and the necessity of the augmentation for numerical stability.     

Decentralised direct adaptive fuzzy control for a class of large-scale nonaffine nonlinear systems and application to AHS

A novel decentralised direct adaptive fuzzy controller design is presented for a class of large-scale nonaffine uncertain nonlinear systems in this article. By integrating a fuzzy logic system and H _∞ tracking technique, the designed controller is able to adaptively compensate for interconnections and disturbances with unknown bounds, but none of the control and adaptation laws contains a sign function so that control chattering can be shunned. The closed-loop large-scale system is guaranteed to be asymptotically stable and obtain good H _∞ tracking performance. The control approach developed is applied to the following control problem of a string of vehicles within an automated highway system (AHS) and simulation results verify its validity.     

A new approach to robust and non-fragile H∞ control for uncertain fuzzy systems

This paper investigates the robust H_∞ control and non-fragile control problems for Takagi-Sugeno (T-S) fuzzy systems with linear fractional parametric uncertainties. The robust H_∞ control problem is to design a state feedback controller such that the robust stability and a prescribed H_∞ performance of the resulting closed-loop system is ensured. And the non-fragile H_∞ control problem is to design a state feedback controller with parameter uncertainties. Based on the linear matrix inequality (LMI) approach, new sufficient conditions for the solvability of the two problems are obtained. It is shown that the desired state feedback fuzzy controller can be constructed by solving a set of LMIs. Numerical examples are also provided to demonstrate the effectiveness of the proposed design method.     

Fractional‐Order Dynamic Output Feedback Sliding Mode Control Design for Robust Stabilization of Uncertain Fractional‐Order Nonlinear Systems

A robust fractional‐order dynamic output feedback sliding mode control (DOF‐SMC) technique is introduced in this paper for uncertain fractional‐order nonlinear systems. The control law consists of two parts: a linear part and a nonlinear part. The former is generated by the fractional‐order dynamics of the controller and the latter is related to the switching control component. The proposed DOF‐SMC ensures the asymptotical stability of the fractional‐order closed‐loop system whilst it is guaranteed that the system states hit the switching manifold in finite time. Finally, numerical simulation results are presented to illustrate the effectiveness of the proposed method.