Takagi-Sugeno Fuzzy Model Research Articles

Delayed nonquadratic [formula omitted]-stabilization of continuous-time nonlinear Takagi–Sugeno fuzzy models

This work deals with the design of fuzzy controllers for stabilization of continuous-time nonlinear systems subject to L2 disturbances, which are represented by nonlinear Takagi–Sugeno fuzzy models, i.e., Takagi–Sugeno fuzzy models with nonlinear consequents. A nonquadratic Lyapunov function is used to derive sufficient design conditions based on linear matrix inequality constraints as well as to reduce the conservativeness when compared to existing control approaches in the literature. Furthermore, the nonquadratic Lyapunov function is defined in terms of an integral membership function, which leads to a delayed nonquadratic L2-stabilization condition. This condition avoids the well-known difficulties in dealing with time derivatives of membership functions and/or path-independent conditions, found in most of the nonquadratic control approaches for continuous-time Takagi–Sugeno fuzzy models. Two numerical examples are performed to illustrate the reduction in conservativeness provided by the proposed approach.

Static Output Feedback Quantized Control for Fuzzy Markovian Switching Singularly Perturbed Systems With Deception Attacks

This article focuses on static output feedback control for fuzzy Markovian switching singularly perturbed systems (FMSSPSs) with deception attacks and asynchronous quantized measurement output. Different from the previous work, both the logarithmic quantizer and the static output feedback controller are dependent on the operation system; by means of hidden Markov models, their modes run asynchronously with that of FMSSPSs. Additionally, the deception attacks are guided by a Bernoulli variable, and nonlinear characteristics are modeled by the Takagi–Sugeno fuzzy model. By resorting to a mode-dependent Lyapunov functional, several criteria are acquired and strictly <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$(\mathscr {Q},\mathscr {S},\mathscr {R})\text{--}\gamma$</tex-math></inline-formula> -dissipative of FMSSPSs can be ensured. Finally, a dc motor model is expressed to illustrate the effectiveness of the asynchronous control scheme.

Sparse and Decoupling Control Strategies Based on Takagi-Sugeno Fuzzy Models.

In order to better handle the coupling effects when controlling multiple-input multiple-output (MIMO) systems, taking the decentralized control structure as the basis, this paper proposes a sparse control strategy and a decoupling control strategy. Type-1 and type-2 Takagi-Sugeno (T-S) fuzzy models are used to describe the MIMO system, and the relative normalized gain array-based criterion is employed to measure the coupling effects. The main contributions include: 1) compared to the previous studies, a manner with less computational cost to build fuzzy models for the MIMO systems is provided, and a more accurate method to construct the so-called effective T-S fuzzy model (ETSM) to express the coupling effects is developed; 2) for the sparse control strategy, four indexes are defined in order to extend a decentralized control structure to a sparse one. Afterward, an ETSM-based method is presented that a sparse control system can be realized by designing multiple independent single-input single-output (SISO) control loops; and 3) for the decoupling control strategy, a novel and simple ETSM-based decoupling compensator is developed that can effectively compensate for both steady and dynamic coupling effects. As a result, the MIMO controller design can be transformed to multiple noninteracting SISO controller designs. Both of the sparse and decoupling strategies allow to use linear SISO control algorithms to regulate a closely coupled nonlinear MIMO system without knowing its exact mathematical functions. Two examples are used to show the effectiveness of the proposed strategies.

Takagi–Sugeno Fuzzy Unknown Input Observers to Estimate Nonlinear Dynamics of Autonomous Ground Vehicles: Theory and Real-Time Verification

In this article, we address the simultaneous estimation problem of the lateral speed, the steering input, and the effective engine torque, which play a fundamental role in vehicle handling, stability control, and fault diagnosis of autonomous ground vehicles. Due to the involved longitudinal-lateral coupling dynamics and the presence of unknown inputs (UIs), a new nonlinear observer design technique is proposed to guarantee the asymptotic estimation performance. To this end, we make use of a specific Takagi-Sugeno (TS) fuzzy representation with nonlinear consequents to exactly model the nonlinear vehicle dynamics within a compact set of the vehicle state. This TS fuzzy modeling not only allows reducing significantly the real-time computational effort in estimating the vehicle variables but also enables an effective way to deal with unmeasured nonlinearities. Moreover, via a generalized Luenberger observer structure, the UI decoupling can be achieved without requiring a priori UI information. Using Lyapunov stability arguments, the UI observer design is reformulated as an optimization problem under linear matrix inequalities, which can be effectively solved with standard numerical solvers. The effectiveness of the proposed TS fuzzy UI observer design is demonstrated with real-time hardware-in-the-loop experiments.

Formula omitted] control for continuous-time Takagi–Sugeno fuzzy model by applying generalized Lyapunov function and introducing outer variables

For fuzzy systems, it is known that membership function dependent Lyapunov function can reduce the conservatism that has arisen from quadratic Lyapunov function but the time derivative of membership function is hard to be dealt with. In this technical paper, a kind of generalized Lyapunov function (called homogeneous polynomially membership functions dependent (HPMFD) Lyapunov function ) is designed and the corresponding HPMFD switching is proposed to deal with the time derivative of membership function. In addition, the generalized outer variable is constructed to further improve the results. The final example shows the effectiveness of the proposed method.

Design of a Decoupling Fuzzy Control Scheme for Omnidirectional Inverted Pendulum Real-World Control

In this study, an omnidirectional inverted pendulum (ODIP) is controlled based on a dual Takagi–Sugeno (TS) fuzzy control scheme. The ODIP is a handmade system. It contains two subsystems. The lower mechanism system includes a brushless rim motor, a system platform, batteries, and an encoder. The upper mechanism system is mainly composed of a circuit system, a motor fixed platform, a motor, and a flywheel. The proposed controller combines two fuzzy control approaches for ODIP system control with disturbances and uncertainties. The core of the ODIP operating system is an embedded controller, which executes real-world control processes. Moreover, to address the coupling problem, the shafts of the two motors are oriented in orthogonal directions. Then, the two fuzzy controllers can be designed independently without coupling. In the proposed controller, the Takagi–Sugeno fuzzy model is adopted for fuzzy modeling of the ODIP. The conception of parallel distributed compensation (PDC) is utilized to develop fuzzy control from TS fuzzy models. The format of linear matrix inequalities (LMIs) can formulate sufficient conditions. The main contributions of this study are (1) the implementation of an ODIP and (2) the application of the proposed dual Takagi–Sugeno (TS) fuzzy control scheme for real-time control of the ODIP. Finally, the efficiency of the proposed control scheme is illustrated by the experimental results presented in this study.

H∞ Output-Feedback Anti-Swing Control for a Nonlinear Overhead Crane System With Disturbances Based on T-S Fuzzy Model

In this paper, the $H_{\infty }$ output-feedback controller for a nonlinear overhead crane system with external disturbances was developed. Firstly, the Takagi-Sugeno fuzzy model was used to represent the overhead crane system nonlinearity. A fuzzy-based state observer was then built to estimate the values of immeasurable variables. Secondly, a novel control design called virtual-desired variable synthesis was used to converting the tracking control into a stabilization problem. It was primarily used to define the internal desired states, making the design procedure clear and easy. The $H_{\infty }$ performance criterion was used to attenuate external disturbances, and the closed-loop model stability was investigated using the quadratic Lyapunov function. Finally, three simulations were conducted to verify the feasibility and effectiveness of the proposed method. The results have shown that there is practically no positioning error and residual payload swing. Thus, in theory, any type of bounded external disturbances can be eliminated using the proposed method. Additionally, the convergence time is half of its model predictive control method counterpart and one-third of the standard $H_{\infty }$ controller. Hence, it provides a reference for actual control of the overhead crane systems, mostly due to its good performance.

Fuzzy Finite Memory State Estimation for Electro-Hydraulic Active Suspension Systems

This paper presents a novel nonlinear estimator called the fuzzy finite memory (FFM) state estimator for electro-hydraulic active suspension systems, based on fuzzy techniques and finite impulse response. The Takagi-Sugeno fuzzy model is introduced to effectively describe highly nonlinear suspension systems with electro-hydraulic actuator dynamics. Compared with the conventional state estimator, which has an infinite memory structure and requires whole data from the initial to current time, the proposed fuzzy state estimator with a finite memory structure guarantees robustness against external disturbances and modeling uncertainty. The simulation results verify that the developed fuzzy finite memory state estimator is more robust under external disturbances and modeling uncertainties than the existing infinite impulse response nonlinear estimator.

Research on Path Tracking and Anti-roll Control of Commercial Vehicle Based on Takagi-Sugeno Fuzzy Model

Abstract With the increasing demand for intelligent commercial vehicles, the path tracking technology of commercial vehicle autonomous driving systems has become a research hotspot. However, commercial vehicles are prone to roll over when they are making an emergency obstacle avoidance or making a sharp turn on the road surface with high adhesion coefficient, resulting in serious traffic accidents. In this paper, a steering control method based on the T-S fuzzy model for automatic driving of commercial vehicles is proposed, which takes path tracking and anti-roll as control objectives. Firstly, the three-degree-of-freedom model of commercial vehicle and the vehicle-road dynamic model was established to obtain the vehicle-road general model. Then, considering the influence of the nonlinear change of vehicle speed on the system performance, the speed is taken as the variable parameter of the system. Taking the speed as the prerequisite variable, the fuzzy rule is designed, and the vehicle-road model is transformed into a T-S fuzzy model. Then, the fuzzy controller is designed according to the Lyapunov method and the parallel distributed compensation (PDC) algorithm. Finally, sufficient conditions for the system to satisfy the H∞ performance index under the action of the fuzzy controller are given in the form of linear matrix inequality (LMI). LMI toolbox is used to solve the problem, and the robustness of the system is guaranteed. Simulation results show that the system can ensure the accuracy of path tracking and greatly reduce the risk of vehicle rollover.

Fractional order PID controller for the stabilisation of chaotic systems using Takagi-Sugeno fuzzy model

Fractional order PID controller for the stabilisation of chaotic systems using Takagi-Sugeno fuzzy model

Fault isolation and fault-tolerant control for Takagi-Sugeno fuzzy time-varying delay stochastic distribution systems

A fault isolation, estimation, and fault-tolerant control (FTC) scheme for nonlinear time-varying delay stochastic distribution control systems was presented in this paper. The Takagi-Sugeno fuzzy model was adopted to approach the nonlinear dynamics of time-varying delay systems. According to the output equivalence principle and Laplace transformation, an augmented state vector was given to solve the time-varying delay problem. When multiple actuator faults and interference occur simultaneously, fault detection, isolation and fault estimation was designed to obtained the fault information. To decouple faults and obtain the value and location information of the fault, the system was separated into two parts through the designed multiple conversion matrices, in which one subsystem was only affected by one actuator fault. This has simplified the design of fault isolation and estimation. A adaptive observer for fault estimation was given. Then, fault information such as the time, location, and size was determined. The observer gain matrices were calculated using linear matrix inequality (LMI). When a fault was detected and diagnosed, a FTC algorithm was devised using the proportional-integral control scheme to compensate the fault as much as possible. It has been shown that even if multiple faults actuator occurred simultaneously, the FTC controller still ensured the output probability density function of the system traced the desired probability density function when a fault occurred. Finally, the expected results were obtained through the simulation example, which confirmed the effectiveness of the method.

Fractional order PID controller for the stabilisation of chaotic systems using Takagi-Sugeno fuzzy model

In this paper, we propose a new fractional PIαDβ controller design to control chaotic systems. The controller design is based on the predictive control proposed by Yamamoto et al. (2001) and the fractional calculus. The parameters of the controller are determined by minimising the energy of the chaotic states using particle swarm optimisation. In order to obtain a simple model structure, we have used Takagi-Sugeno technique. A fractional PDβ and conventional predictive controllers have been also used as a comparative technique, in order to show the effectiveness of the proposed design one. The simulation results on Lorenz and Chen chaotic systems show the efficiency of the proposed fractional controller to reject disturbances and noises. These results show also that the fractional controller gives better results and overcome those of the fractional PDβ and conventional predictive controllers.

Relaxed Stabilization Conditions for TS Fuzzy Systems With Optimal Upper Bounds for the Time Derivative of Fuzzy Lyapunov Functions

This paper initially proposes an optimization problem and after presents its optimal solution. Then, this result is applied to obtain relaxed conditions to design controllers for nonlinear plants described by Takagi-Sugeno (TS) models, based on fuzzy Lyapunov function (FLF) and Linear Matrix Inequalities (LMI). The FLF is given by $V(x(t)) = x(t)^{T}P(\alpha (x(t)))x(t)$ , where $x(t)$ is the plant state vector, $P(\alpha (x(t))) = \alpha _{1}(x(t))P_{1} + \alpha _{2}(x(t))P_{2} + \cdots + \alpha _{r}(x(t))P_{r}$ , $P_{i}=P_{i}^{T} > 0$ and $\alpha _{i}(x(t))$ is the weight related to the local model $i$ in the representation of the plant by TS fuzzy models, for $i=1,2,\cdots,r$ . When one calculates the time derivative of this $V(x(t))$ , it appears the term $x(t)^{T}\dot {P}(\alpha (x(t)))x(t)$ , that is usually handled using conservative upper bounds, supposing that the bounds of the time derivative of $\alpha _{i}(x(t))$ , $i=1,2,\cdots,r$ , are available. The main result of this paper is a procedure to obtain optimal upper bounds for the term $x(t)^{T}\dot {P}(\alpha (x(t)))x(t)$ , such that they contemplate the maximum value and are always smaller than or equal to the maximum value. It is a relevant result on this subject, because these optimal upper bounds do not add any constraint. With these optimal upper bounds, a relaxed design method for stabilization of TS fuzzy models is proposed. Two numerical examples illustrate the effectiveness of this procedure.

Nonlinear Takagi-Sugeno Fuzzy Observer Design for a Ball and Beam System

Abstract This paper deal with the problem of unmeasured premise variable (UPV) in T-S fuzzy observer for ball and beam (BAB) system with friction. The observer design with UPV is rather challenging and with computational burden. Different from previous results to obtain the observer design condition based on a traditional TS fuzzy model, the work here presents a method by reformulating the BAB system as T-S fuzzy model with nonlinear consequent parts that has shown to reduce the number of fuzzy rules. The proposed method guarantees asymptotic convergence of state estimation. The conditions for the observer design is given in the form of linear matrix inequality (LMI) formulations. Simulation result illustrates effectiveness of the proposed method.

Fuzzy remodeling and synchronization of nonlinear systems

Synchronization is one of the crucial control problems in coordinated behavior systems. A wide range of applications necessitates the development and improvement of approaches to solving the linearization problem for non-linear systems with complex behavior. Hence the paper offers an approach to solving the problem of chaotic system coordinate synchronization based on the use of fuzzy remodeling and superstability conditions. It is shown that transition from general (non-linear) synchronization problem statement to fuzzy description with fuzzy Takagi-Sugeno models allows transforming the initial task to a well understood problem of fuzzy T-S system stabilization that describes the dynamics synchronization error. As a candidate solution for the problem we offer a way of implementing superstability conditions that reduce the task of finding fuzzy regulator to solving a linear programming task. It is shown that implementation of superstability conditions not only presents a simple way of solving the problem, but also has practical value. Superstability provides the monotonesness of the transient process of synchronization without sharp spikes of solution norm. The efficiency of the offered approach is demonstrated by the example of synchronization of two hyperchaotic systems. To prove the efficiency of superstability conditions the solution of the robust synchronization problem with parametric uncertainty in system matrices is given. The presented results can be applied for synchronization of various nonlinear systems demonstrating chaotic dynamics.

Fuzzy reduced-order filtering for nonlinear parabolic PDE systems with limited communication

This paper investigates a fuzzy reduced-order filter design for a class of nonlinear partial differential equation (PDE) systems. First, a Takagi-Sugeno (T-S) fuzzy model is considered to reconstruct the nonlinear PDE system. Then, the employment of an event-triggered mechanism (ETM) can effectively avoid signal redundancy and improve network resource utilization. Furthermore, based on the advantages of the fuzzy model and ETM, several Lyapunov functions are designed and the proposed filter parameters are obtained by adopting linear matrix inequality methods to satisfy the asymptotic stability condition with H∞ performance. Finally, a simulation example is presented to demonstrate the practicality and effectiveness of the proposed filter design method.

Robust H∞ fuzzy saturated control of photovoltaic system

This paper is focused on robust H ∞ fuzzy Maximum Power Point Tracking (MPPT) of photovoltaic (PV) system under actuator asymmetric saturation and different climate conditions. To adjust the output PV voltage, a DC-DC boost converter is used. This last is controlled by duty ratio that is remains practically saturated between 0 and 1. In order to consider of input limited, firstly, a polytopic model is investigated in fuzzy integral state feedback controller. Secondly, H ∞ stabilization conditions are derived in linear matrix inequalities (LMI) terms based on Takagi-Sugeno (T-S) fuzzy model and Lyapunov approach. Finally, the proposed control is applied to a PV system and our simulation results show the effectiveness of the proposed approaches.

Dynamic anti-windup controller design for Takagi-Sugeno fuzzy systems under saturations

Abstract This paper presents a new H∞ anti-windup dynamic output control developed for a class of nonlinear systems subject to both sensors and actuators saturations. First, the nonlinear system under consideration is represented by a Takagi-Sugeno (T-S) fuzzy model. Then, a dynamic output feedback (DOF) control strategy is proposed and the saturation constraints are transformed into dead-zone nonlinearities. Based on this transformation and by using the sector condition, the H∞ dynamic output stabilization conditions of the closed-loop system are given in terms of linear matrix inequalities (LMI). Finally, a numerical example is simulated to demonstrate the efficiency of the proposed design method.

Event-triggered control of TS fuzzy systems with guaranteed membership function mismatch

Abstract This paper proposes augmenting the traditional quadratic event-triggered conditions for Takagi-Sugeno (TS) fuzzy models, by also considering triggering conditions defined by a variation of the membership function values. Suitable Linear Matrix Inequality (LMI) conditions are presented that make full use of the proposed modified triggering conditions to co-design the control law and triggering conditions. Under some mild assumptions, the closed loop system is guaranteed to avoid the Zeno behavior for its triggering instants. A numerical example is presented to illustrate the proposed conditions.

Robust Model Predictive Control for Takagi-Sugeno Model With Bounded Disturbances—Pólya Approach

This paper proposes a general robust model predictive control (MPC) approach for the constrained Takagi-Sugeno (T-S) fuzzy model with additive bounded disturbances. We adopt the homogeneous polynomially parameter-dependent (HPP) Lyapunov matrix with the arbitrary complexity degree and the corresponding HPP control law for the controller design. By applying the Polya’s theorem and the extended nonquadratic boundedness property, a systematic approach to construct a set of sufficient conditions for assessing robust stability described by parameter-dependent linear matrix inequalities (LMIs) is established. The proposed approach is an improvement over existing approaches in terms of control performance and stabilizable model range. Numerical examples are provided to show the effectiveness of the proposed robust MPC approach.