Design Of Fuzzy State Feedback Controller Research Articles

A new Takagi-Sugeno fuzzy system approach for fuzzy state feedback controller design and its application to malware propagation on heterogeneous complex network

Abstract— Nowadays, digital transformation has brought many great changes and is becoming an essential part of real life, however, it also goes along with a considerable likelihood of being targeted in cyberattack. Indeed, the more businesses embrace digital transformation or use online services, the more opportunities hackers have to expand their cyberattacks. Hence, there is an essential need on analyzing and predicting of cyberattack on network systems. For this aim, we propose to study a controlled fractional network-based SCIRS (Susceptible - Carrier - Infectious - Recovered - Susceptible) malware propagation model and its stabilization problem based on fractional interconnected Takagi-Sugeno fuzzy system. A fuzzy state feedback controller is proposed to asymptotically stabilize the unstable malware-free equilibrium of the proposed malware propagation model and then, we establish sufficient conditions in terms of linear matrix inequalities. The effectiveness of proposed approach is illustrated by a case study of SCIRS malware propagation model on heterogeneous complex network.

<inline-formula><tex-math>$H_\infty$</tex-math></inline-formula> Fuzzy Control for a Class of Nonlinear Coupled ODE-PDE Systems With Input Constraint

This paper deals with the problem of $H_\infty$ fuzzy control design with an input constraint for a class of coupled systems, which consist of an $n$ -dimensional nonlinear subsystem of ordinary differential equations (ODEs) and a scalar linear parabolic subsystem of partial differential equation (PDE) connected in feedback. Initially, the nonlinear coupled system is represented by a Takagi–Sugeno (T–S) fuzzy-coupled ODE-PDE model. Then, based on the fuzzy model and parallel distributed compensation scheme, a fuzzy state feedback control design is developed via Lyapunov's direct method, such that the resulting closed-loop fuzzy-coupled system is exponentially stable, and a prescribed $H_\infty$ performance of disturbance attenuation is satisfied. The existing condition of the proposed $H_\infty$ fuzzy controllers is given in terms of linear matrix inequalities (LMIs). Moreover, in order to make the attenuation level as small as possible while the input constraint is respected to avoid the high magnitude, a suboptimal $H_\infty$ -constrained fuzzy control problem is also addressed, which is formulated as an LMI optimization problem. Finally, the proposed method is applied to the control of a hypersonic rocket car to illustrate its effectiveness.

Nonfragile Control With Guaranteed Cost of T–S Fuzzy Singular Systems Based on Parallel Distributed Compensation

This paper investigates the nonfragile-guaranteed cost control problem for a class of uncertain nonlinear singular state-delayed systems that is described by Takagi-Sugeno models. The upper bound of state delay is assumed to be available. A linear quadratic cost function is specified as the performance index of the closed-loop system. Attention is focused on the fuzzy state feedback controller design via parallel distributed compensation scheme, which not only guarantees the regular, impulse-free, and asymptotically stable of the closed-loop fuzzy singular delay system, but also provides an optimized upper bound of the guaranteed cost function for the possibility of feedback gain variation and all admissible uncertainties. All derived sufficient conditions are given in terms of linear matrix inequalities. Some numerical examples are provided to illustrate the effectiveness of the proposed design scheme.

An LMI Approach of Robust H∞ Fuzzy State-Feedback Controller Design for HIV/AIDS Infection System with Dual Drug Dosages

This paper examines the problem of designing robust H∞ controllers for for HIV/AIDS infection system with dual drug dosages described by a Takagi-Sugeno (TS) fuzzy model. Based on a linear matrix inequality (LMI) approach, we develop an H∞ controller which guarantees the L2-gain of the mapping from the exogenous input noise to the regulated output to be less than some prescribed value for the system. A sufficient condition of the controller for this system is given in term of Linear Matrix Inequalities (LMIs). The effectiveness of the proposed controller design methodology is finally demonstrated through simulation results. It has been shown that the anti-HIV vaccines are critically important in reducing the infected cells. Keywords— H∞ Fuzzy control; Takagi-Sugeno (TS) fuzzy model; Linear Matrix Inequalities (LMIs); HIV/AIDS infection system

Distributed Fuzzy Control Design of Nonlinear Hyperbolic PDE Systems With Application to Nonisothermal Plug-Flow Reactor

This paper considers the problem of fuzzy control design for a class of nonlinear distributed parameter systems that is described by first-order hyperbolic partial differential equations (PDEs), where the control actuators are continuously distributed in space. The goal of this paper is to develop a fuzzy state-feedback control design methodology for these systems by employing a combination of PDE theory and concepts from Takagi-Sugeno (T-S) fuzzy control. First, the T-S fuzzy hyperbolic PDE model is proposed to accurately represent the nonlinear first-order hyperbolic PDE system. Subsequently, based on the T-S fuzzy-PDE model, a Lyapunov technique is used to analyze the closed-loop exponential stability with a given decay rate. Then, a fuzzy state-feedback control design procedure is developed in terms of a set of spatial differential linear matrix inequalities (SDLMIs) from the resulting stability conditions. Furthermore, utilizing the finite-difference approximation method (with a backward difference for the spatial derivative), a recursive algorithm is presented to solve the SDLMIs via the existing LMI optimization techniques. Finally, the developed design methodology is successfully applied to the control of a nonisothermal plug-flow reactor.

A New Approach to Guaranteed Cost Control of T-S Fuzzy Dynamic Systems With Interval Parameter Uncertainties

This paper investigates the problem of guaranteed cost control for Takagi-Sugeno fuzzy dynamic systems with interval parameter uncertainties. The parameter uncertainty is characterized by the matrix bound, which is quite natural in real applications. Attention is focused on the fuzzy state feedback controller design via the so-called parallel distributed compensation scheme, which guarantees the closed-loop system to be robustly stable with a prescribed upper bound of the cost function. By utilizing the instrumental idea of delay dividing, a new Lyapunov-Krasovskii functional is introduced, which leads the resultant conditions to be much less conservative than most existing results in the literature. Some other new ideas such as basis dependence are also employed, which help to reduce the conservatism. All the results are formulated in the form of linear matrix inequalities (LMIs), which can readily be solved via standard numerical software. Finally, illustrative examples are given to show the less conservatism and applicability of the obtained results.

Synchronization of Chaotic Systems Using Time-Delayed Fuzzy State-Feedback Controller

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> This paper presents the fuzzy-model-based control approach to synchronize two chaotic systems subject to parameter uncertainties. A fuzzy state-feedback controller using the system state of response chaotic system and the time-delayed system state of drive chaotic system is employed to realize the synchronization. The time delay which complicates the system dynamics makes the analysis difficult. To investigate 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 chaotic systems. Furthermore, the membership grades of the T-S fuzzy models become uncertain due to the existence of parameter uncertainties which further complicates the system analysis. To ease the stability analysis and produce less conservative analysis result, the membership functions of both T-S fuzzy models and fuzzy controller are considered. Stability conditions are derived using Lyapunov-based approach to aid the design of fuzzy state-feedback controller to synchronize the chaotic systems. Simulation examples are presented to illustrate the merits of the proposed approach. </para>

Formula omitted] fuzzy state-feedback control design for nonlinear systems with [formula omitted]-stability constraints: An LMI approach

This paper considers the problem of designing an H ∞ fuzzy controller for a class of nonlinear systems with pole placement constraints. Based on an LMI approach, we develop a state-feedback controller that guarantees the L 2 -gain of the mapping from the exogenous input noise to the regulated output is less than some prescribed value and the closed-loop system is D -stable. Numerical examples are provided to illustrate the design developed in this paper.