Predictive functional control based on fuzzy T-S model for HVAC systems temperature control

In heating, ventilating and air-conditioning （HVAC） systems, there exist severe nonlinearity, time-varying nature, disturbances and uncertainties. A new predictive functional control based on Takagi-Sugeno （T-S） fuzzy model was proposed to control HVAC systems. The T-S fuzzy model of stabilized controlled process was obtained using the least squares method, then on the basis of global linear predictive model from T-S fuzzy model, the process was controlled by the predictive functional controller. Especially the feedback regulation part was developed to compensate uncertainties of fuzzy predictive model. Finally simulation test results in HVAC systems control applications showed that the proposed fuzzy model predictive functional control improves tracking effect and robustness. Compared with the conventional PID controller, this control strategy has the advantages of less overshoot and shorter setting time, etc.

New delay-dependent robust stability and stabilization for uncertain T-S fuzzy time-delay systems under imperfect premise matching

To alleviate the conservativeness of the stability criterion for Takagi-Sugeno （T-S） fuzzy time-delay systems, a new delay-dependent stability criterion was proposed by introducing a new augmented Lyapunov function with an additional triple-integral term, which was firstly u3ed to derive the stability criterion for T-S fuzzy time-delay systems. By the same approach, the robust stability issue for fuzzy time-delay systems with uncertain parameters was also considered. On the other hand, in order to enhance the design flexibility, a new design approach for uncertain fuzzy time-delay systems under imperfect premise matching was also proposed, which allows the fuzzy controller to employ different membership functions from the fuzzy time-delay model. By the numerical examples, the proposed stability conditions are less conservative in the sense of getting larger allowable time-delay and obtaining smaller feedback control gains. For instance, when the allowable time-delay increases from 7.3 s to 12 s for an uncertain T-S fuzzy control system with time-delay, the norm of the feedback gains decreases from （34.299 2, 38.560 3） to （10.073 3, 11.349 0）, respectively. Meanwhile, the effectiveness of the proposed design method was illustrated by the last example with the robustly stable curves of system state under the initial condition of x（0） = [3 -1].

Passivity Control for Uncertain T-S Fuzzy Descriptor Systems

By means of matrix decomposition method a criterion is presented for the admissibility of T-S fuzzy descriptor system. Then, the problem of passivity control is studied for a kind of T-S fuzzy descriptor system with uncertain parameters, and sufficient conditions which make the closed-loop system admissible and strictly passive are obtained based on linear matrix inequality (LMI). The nonstrict LMIs restricted conditions which characterize the descriptor system are transformed into strict ones, so testing admissibility and passivity of the system can be finished simultaneously. The design scheme of state feedback controller is also obtained. Finally, a numerical example is given to show the validity and feasibility of the proposed approach.

Statistic PID Tracking Control for Non-Gaussian Stochastic Systems Based on T-S Fuzzy Model

A new robust proportional-integral-derivative （PID） tracking control framework is considered for stochastic systems with non-Gaussian variable based on B-spline neural network approximation and T-S fuzzy model identification. The tracked object is the statistical information of a given target probability density function （PDF）, rather than a deterministic signal. Following B-spline approximation to the integrated performance function, the concerned problem is transferred into the tracking of given weights. Different from the previous related works, the time delay T-S fuzzy models with the exogenous disturbances are applied to identify the nonlinear weighting dynamics. Meanwhile, the generalized PID controller structure and the improved convex linear matrix inequalities （LMI） algorithms are proposed to fulfil the tracking problem. Furthermore, in order to enhance the robust performance, the peak-to-peak measure index is applied to optimize the tracking performance. Simulations are given to demonstrate the efficiency of the proposed approach.

Stabilization of Discrete-time 2-D T-S Fuzzy Systems Based on New Relaxed Conditions

This paper is concerned with the problem of stabilization of the Roesser type discrete-time nonlinear 2-D system that plays an important role in many practical applications. First, a discrete-time 2-D T-S fuzzy model is proposed to represent the underlying nonlinear 2-D system. Second, new quadratic stabilization conditions are proposed by applying relaxed quadratic stabilization technique for 2-D case. Third, for sake of further reducing conservatism, new non-quadratic stabilization conditions are also proposed by applying a new parameter-dependent Lyapunov function, matrix transformation technique, and relaxed technique for the underlying discrete-time 2-D T-S fuzzy system. Finally, a numerical example is provided to illustrate the effectiveness of the proposed results.

Guaranteed cost control for T-S fuzzy systems with time-varying delays

This paper deals with the problem of guaranteed cost control for nonlinear systems with time-varying delays which is represented by Takagi-Sugeno （T-S） fuzzy models with time-varying delays.The derivatives of time-varying delay are not necessary to be bounded.Based on the free weighting matrix method,sufficient conditions for the existence of fuzzy guaranteed cost controller via state feedback are given in terms of linear matrix inequalities （LMIs）.A minimizing method is also proposed to search the suboptimal upper bound of the guaranteed cost function.The results are delay-dependent but contain delay-independent criteria as a special case.A numerical example is presented to demonstrate the effectiveness and less conservativeness of our work.

Controller design of uncertain nonlinear systems based on T-S fuzzy model

A robust control for uncertain nonlinear systems based on T-S fuzzy model is discussed in this paper. First, a T-S fuzzy system is adopted to model the uncertain nonlinear systems. Then, for the system with input variables adopting standard fuzzy partitions, the efficient maximal overlapped-rules group （EMORG） is presented, and a new sufficient condition to check the stability of T-S fuzzy system with uncertainty is derived, which is expressed in terms of Linear Matrix Inequalities. The derived stability condition, which only requires a local common positive definite matrix in each EMORG, can reduce the conservatism and difficulty in existing stability conditions. Finally, a simulation example shows the proposed approach is effective.

Robust passive control for discrete-time T-S fuzzy systems with delays

This article deals with the robust stability analysis and passivity of uncertain discrete-time Takagi- Sugeno （T-S） fuzzy systems with time delays. The T-S fuzzy model with parametric uncertainties can approximate nonlinear uncertain systems at any precision. A sufficient condition on the existence of robust passive controller is established based on the Lyapunov stability theory. With the help of linear matrix inequality （LMI） method, robust passive controllers are designed so that the closed-loop system is robust stable and strictly passive. Furthermore, a convex optimization problem with LMI constraints is formulated to design robust passive controllers with the maximum dissipation rate. A numerical example illustrates the validity of the proposed method.

Decentralized state observer scheme for uncertain time-delay T-S fuzzy interconnected systems

This paper focuses on a class of T-S fuzzy interconnected systems with time delays and time-varying parameter uncertainties. Observer-based output feedback decentralized controller is designed such that the closed-loop interconnected system is asymptotically stable in the Lyapunov sense in probability for all admissible uncertainties and time delays. Sufficient conditions for robustly asymptotically stability of the systems are given in terms of a set of linear matrix inequalities （LMIs）.

Stability analysis of T-S fuzzy control systems with interval plants

The stability of a type of Takagi-Sugeno ( T-S) fuzzy control systems is considered. The plant of T-S fuzzy system has parameter uncertainties. By using the off-axis circle criterion and Kharitonov Theorem,a sufficient condition is derived to analyze the global asymptotic stability of T-S fuzzy control system. The proposed method has a graphical explanation which facilitates stability analysis. A numerical example is also given to demonstrate how to use our approach in analyzing certain T-S fuzzy control systems.

New Approach to Stability Analysis and Stabilization of Discrete-Time T-S Fuzzy Descriptor Systems

The problems of stability and state feedback control for a class of discrete-time T-S fuzzy descriptor systems are investigated in this paper. Based on fuzzy Lyapunov function,a set of slack variables is introduced to remove the basic semi-definite matrix inequality condition to check the regularity,causality and stability of discrete-time T-S fuzzy descriptor systems; a new sufficient condition for the discrete-time T-S fuzzy descriptor systems to be admissible is proposed in terms of strict linear matrix inequalities( LMIs). And a sufficient condition is proposed for the existence of state feedback controller in terms of a set of coupled strict LMIs.Finally,an illustrative example is presented to demonstrate the effectiveness of the proposed approach.

Hybrid Dynamic Variables-Dependent Event-Triggered Fuzzy Model Predictive Control

This article focuses on dynamic event-triggered mechanism(DETM)-based model predictive control(MPC) for T-S fuzzy systems.A hybrid dynamic variables-dependent DETM is carefully devised,which includes a multiplicative dynamic variable and an additive dynamic variable.The addressed DETM-based fuzzy MPC issue is described as a “min-max” optimization problem(OP).To facilitate the co-design of the MPC controller and the weighting matrix of the DETM,an auxiliary OP is proposed based on a new Lyapunov function and a new robust positive invariant(RPI) set that contain the membership functions and the hybrid dynamic variables.A dynamic event-triggered fuzzy MPC algorithm is developed accordingly,whose recursive feasibility is analysed by employing the RPI set.With the designed controller,the involved fuzzy system is ensured to be asymptotically stable.Two examples show that the new DETM and DETM-based MPC algorithm have the advantages of reducing resource consumption while yielding the anticipated performance.

Robust Optimal Output Tracking Control of A Midwater Trawl System Based on T-S Fuzzy Nonlinear Model

A robust optimal output tracking control method for a midwater trawl system is investigated based on T-S fuzzy nonlinear model. A simplified nonlinear mathematical model is first employed to represent a midwater trawl system, and then a T-S fuzzy model is adopted to approximate the nonlinear system. Since the strong nonlinearities and the external disturbance of the trawling system, a mixed H2/H∞ fuzzy output tracking control strategy via T-S fuzzy system is proposed to regulate the trawl depth to follow a desired trajectory. The trawl depth can be regulated by adjusting the winch velocity automatically and the tracking error can be minimized according to the robust optimal criterion. In order to validate the proposed control method, a computer simulation is conducted. The simulation results indicate that the proposed fuzzy robust optimal controller make the trawl net rapidly follow the desired trajectory under the model uncertainties and the extemal disturbance caused by wave and current.

Fuzzy Robust H1 Control for UncertainNonlinear Systems via Output Feedback

This paper is concerned with a fuzzy robust H∞ control problem via output feedbackfor a class of uncertain nonlinear systems. The uncertain nonlinear systemsare represented by fuzzy Takagi-Sugeno （T-S） model, and a fuzzy controller is designedbased on the state observer. A sufficient condition for the existence of fuzzycontroller is given in terms of the linear matrix inequalities （LMIs） and the adaptivelaw. Based on Lyapunov stability theorem, the proposed fuzzy control scheme suchthat the desired H∞performance is achieved in the sense that all the closed-loopsignals are uniformly ultimately bounded （UUB）. Simulation results indicate theeffectiveness of the developed control scheme. In this paper, a less conservativefuzzy tracking controller is proposed, where the matching condition and the upperbound are avoided. Comparing with the existing works, the dimension of the LMIsof this paper is reduced.

Robust fuzzy sliding-mode control for T-S model based permanent magnet synchronous motor

A fuzzy sliding-mode control (FSMC) scheme based on T-S fuzzy models was proposed for the permanent magnet synchronous motor (PMSM) drive system to solve the speed tracking problem. A T-S fuzzy model was firstly formed to represent the nonlinear system of PMSM. For converting the tracking control into a stabilization problem, a new control design was proposed to define the internal desired states. Then, the FSMC controller for PMSM system with parameter variation and load disturbance was designed based on the fuzzy model. The performance of the proposed controller was verified by experimental results on PMSM system. The results show that the FSMC scheme can drive the dynamics of PMSM into a designated sliding surface in finite time and guarantee the property of asymptotical stability. The information of upper bound of modeling errors as well as perturbations is not required when using the FSMC controller.

Takagi-Sugeno Fuzzy Regulator Design for Nonlinear and Unstable Systems Using Negative Absolute Eigenvalue Approach

This paper introduces a Takagi-Sugeno(T-S)fuzzy regulator design using the negative absolute eigenvalue(NAE)approach for a class of nonlinear and unstable systems.The open-loop system is initially embodied by the traditional T-S fuzzy model and then,all closed-loop subsystems are combined using the proposed Max-Min operator in place of traditional weighted average operator from the controller side to lessen the coupling virtually and simplify the proposed regulator design.For each virtually decoupled closed-loop subsystem,the composite regulators(i.e.,primary and secondary regulators)are designed by the NAE approach based on the enhanced eigenvalue analysis.The Lyapunov function is utilized to guarantee the asymptotic stability of the overall T-S fuzzy control system.The most popular and widely used nonlinear and unstable systems like the electromagnetic levitation system(EMLS)and the inverted cart pendulum(ICP)are simulated for the wide range of the initial conditions and the enormous variation in the disturbance.The transient and steady-state performance of the considered systems using the proposed design are analyzed in terms of the decay rate,settling time and integral errors as IAE,ISE,ITAE,and ITSE to validate the effectiveness of the proposed approach compared to the most popular and traditional parallel distributed compensation(PDC)approach.

Robust Control for Interval Type-2 T-S Fuzzy Discrete Systems with Input Delays and Cyber Attacks

This paper focuses on the robust control issue for interval type-2 Takagi-Sugeno(IT2 T-S)fuzzy discrete systems with input delays and cyber attacks.The lower and upper membership functions are first utilized to IT2 fuzzy discrete systems to capture parameter uncertainties.By considering the influences of input delays and stochastic cyber attacks,a newly fuzzy robust controller is established.Afterward,the asymptotic stability sufficient conditions in form of LMIs for the IT2 closed-loop systems are given via establishing a Lyapunov-Krasovskii functional.Afterward,a solving algorithm for obtaining the controller gains is given.Finally,the effectiveness of the developed IT2 fuzzy method is verified by a numerical example.

Event-triggered fault detection for T-S fuzzy systems with local nonlinear models in finite-frequency domain

This article investigates the issue of event-triggered fault detection(FD)filter design for T-S fuzzy systems with local nonlinear models.A novel H−/H∞FD filter subject to the event triggering transmission mechanism is designed in finite-frequency domain.Then,a novel lemma,in which the nonlinear part and the event triggering mechanism are dealt appropriately,is presented to capture the sensitivity and robustness performances.In addition,the slack matrices are utilised to derive optimal filter parameters by solving a convex optimisation problem.The less conservative FD method can get better detection performances than those entire-frequency methods.Finally,an example is introduced to verify the new results.

Robust non-fragile control for discrete-delay nonlinear large-scale systems

Time-delays,due to the information transmission between subsystems,naturally exist in large-scale systems and the existence of the delay is frequently a source of instability. This paper considers the problems of robust non-fragile fuzzy control for a class of uncertain discrete nonlinear large-scale systems with time-delay and controller gain perturbations described by T-S fuzzy model. An equivalent T-S fuzzy model is represented for discrete-delay nonlinear large-scale systems. A sufficient condition for the existence of such non-fragile controllers is further derived via the Lyapunov function and the linear matrix inequality( LMI) approach. Simulation results demonstrate the feasibility and the effectiveness of the proposed design and the proper stabilization of the system in spite of controller gain variations and uncertainties.

Exponential Stability of Uncertain T-S Fuzzy Switched Systems with Time Delay

This paper discusses the delay-dependent exponential stability of a class of uncertain T-S fuzzy switched systems with time delay. The method is based on Lyapunov stability theorem and free weighting matrices approach. Two illustrative examples are given to demonstrate the effectiveness of the proposed method.