Interval Type-2 Takagi-Sugeno Fuzzy Model Research Articles

Extended Dissipative Control for Interval Type-2 T-S Fuzzy Markov Jump Systems Subject to Actuator Faults

In this paper, the issue of extended dissipative control for interval type-2 fuzzy Markov jump systems subject to actuator faults is investigated. It is different from the traditional T-S fuzzy method, the interval type-2 fuzzy set is introduced to model the system, and the nonlinearity with parameter uncertainty is captured using the interval type-2 Takagi-Sugeno fuzzy model. During the implementation of the control process, the possible actuator failures are fully considered when designing a controller, and a fault-tolerant control strategy is employed to enhance the elasticity of the designed controller. It is worth noting that, in order to better adapt to the characteristics of interval type-2 fuzzy system, the designed controller follows non-parallel distribution compensation rules, that is, the designed controller does not have the same premise structure and fuzzy rules as the system model, which further improves the flexibility of controller design. Some sufficient conditions ensuring the stability with the extended dissipative performance of the systems are established. In the meanwhile, the obtained results with less conservatism are ensured owing to the boundary information of membership functions considered in the stability analysis. Finally, two numerical examples are provided to indicate the effectiveness of the proposed method.

On Designing the Event-Triggered Multistep Model Predictive Control for Nonlinear System Over Networks With Packet Dropouts and Cyber Attacks

In this article, the event-triggered multistep model predictive control for the discrete-time nonlinear system over communication networks under the influence of packet dropouts and cyber attacks is studied. First, the interval type-2 Takagi-Sugeno fuzzy model is applied to express the discrete-time nonlinear system and an event-triggered mode, which is capable of determining whether the sampled signal ought to be delivered into the unreliable network, is designed to economize communication resources. Second, two Bernoulli processes are introduced to represent the randomly happening packet dropouts in the unreliable network and the randomly occurring deception attacks on the actuator side from the adversaries. Third, under the assumption that the system states are unmeasurable, a multistep parameter-dependent model predictive controller is synthesized via optimizing one series of feedback laws for a given period of time, which leads to improved control performance than that of the one-step approach. Moreover, the results on the recursive feasibility and closed-loop stability related to the networked system are achieved, which explicitly consider the external disturbance and input constraint. Finally, simulation experiments on the mass-spring-damping system are carried out to illustrate the rationality and effectiveness of the provided control strategy.

Quantized Interval Type-2 Fuzzy Control for Persistent Dwell-Time Switched Nonlinear Systems With Singular Perturbations.

This article investigates the problem of quantized fuzzy control for discrete-time switched nonlinear singularly perturbed systems, where the singularly perturbed parameter (SPP) is employed to represent the degree of separation between the fast and slow states. Taking a full account of features in such switched nonlinear systems, the persistent dwell-time switching rule, the technique of singular perturbation and the interval type-2 Takagi-Sugeno fuzzy model are introduced. Then, by means of constructing SPP-dependent multiple Lyapunov-like functions, some sufficient conditions with the ability to ensure the stability and an expected H∞ performance of the closed-loop system are deduced. Afterward, through solving a convex optimization problem, the gains of the controller are obtained. Finally, the correctness of the proposed method and the effectiveness of the designed controller are demonstrated by an explained example.

A modified interval type-2 Takagi-Sugeno fuzzy neural network and its convergence analysis

In this paper, to compute the firing strength values of type-2 fuzzy models, a soft version of minimum is presented, which endows the fuzzy model with the ability to solve large dimensional problems. In addition, a conjugate gradient method is borrowed to train the designed interval type-2 Takagi-Sugeno fuzzy model. Compared with the existing gradient-based learning strategy, this scheme can efficiently enhance the fuzzy model performance. Last but not least, convergence analysis for this modified interval type-2 Takagi-Sugeno fuzzy neural network (MIT2TSFNN) is conducted in detail, which proves that the gradient of the error function tends to zero with the iteration increasing (weak convergence) and the sequence of model parameters (weights) convergences to a fixed point (strong convergence). To validate the effectiveness of the proposed MIT2TSFNN and its theoretical results, simulation results of six regression and six classification problems are presented.

Aperiodic Sampled-Data-Based Control for Interval Type-2 Fuzzy Systems via Refined Adaptive Event-Triggered Communication Scheme

This article is devoted to event-triggered stabilization for a class of interval type-2 (IT2) fuzzy systems with aperiodic sampling. First, the IT2 Takagi-Sugeno fuzzy model and sampled-data controllers are established subject to mismatched membership functions. Second, considering a nonuniform sampling case, a refined adaptive event-triggered communication scheme is proposed in a hierarchy form to dynamically adjust the direction and rate of the event-triggered threshold parameter by state changing trend and relative state error, respectively. Thus, a complete dual-directional regulating mechanism with sensitivity to state variation is reasonably created to give extra flexibility, which is beneficial for a preferable tradeoff between control performance and network resource. Third, considering the practical behaviors on the sampling interval, a novel integral type of time-dependent Lyapunov function is constructed. Then, the stability criterion and the controller design approach are derived. Finally, the numerical examples are provided to demonstrate the effectiveness and advantages of the proposed methods.

Event-triggered interval Type-2 T-S fuzzy control for nonlinear networked systems

In this paper, an event-triggered disturbance attenuation and rejection scheme is proposed for nonlinear networked systems with limited bandwidth and multiple disturbances based on the interval type-2 Takagi-Sugeno fuzzy model. A fuzzy disturbance observer is constructed to estimate the disturbance generated by the exogenous system, and then such kind of disturbance can be rejected. Sufficient conditions are presented such that a fuzzy H∞ controller can be designed to guarantee the stability of the resulting closed-loop system with a prescribed performance index, regardless of disturbances. An event-triggered control scheme is designed to reduce the frequency of the controller updating and thus save the network resources. A numerical example is given to demonstrate the validity of the new design methods presented.

Output Feedback Predictive Control of Interval Type-2 T–S Fuzzy Systems With Markovian Packet Loss

This paper investigates the synthesis approach of output feedback model predictive control (OFMPC) for nonlinear systems over networks where the data quantization and packet loss may occur simultaneously. The nonlinear system, which is subjected to parameter uncertainties, is represented by the interval type-2 Takagi–Sugeno fuzzy model. The quantization error is treated as sector bound uncertainties by using the sector bound approach, and a binary Markov chain is introduced to characterize the phenomenon of packet loss of the networked control systems (NCSs). The synthesis approach of OFMPC provided in this paper involves an offline designed state observer using the linear matrix inequality technique and an online model predictive control optimization problem, which minimizes an upper bound of the expect value of the infinite horizon performance cost based on the obtained estimated state. A new technique of refreshing the estimation error bound, which plays the key role of guaranteeing the recursive feasibility of optimization problem, is provided. An example is given to demonstrate the effectiveness of the proposed new design techniques.

State Feedback Control for Interval Type-2 Fuzzy Systems With Time-Varying Delay and Unreliable Communication Links

This study explores the stabilization problem of nonlinear systems subject to parameter uncertainties, time-varying delay, and data-packet dropouts. An interval type-2 Takagi-Sugenofuzzy model is employed to represent nonlinear systems subject to parameter uncertainties. The lower and upper membership functions of the system enable parameter uncertainties to be captured effectively. To enhance the flexibility of design, the proposed state feedback controller does not share the premise membership functions of the model. Unlike the majority of existing results, the present study simultaneously considers parameter uncertainties, time-varying delay, and data-packet dropouts in nonlinear control systems. A novel finite-sum inequality that includes well-known inequalities as special cases, is developed to derive new stability conditions in the form of linear matrix inequalities. Several examples of simulation are used to demonstrate the effectiveness of the proposed approach.

Observer-Based $H_\infty$ Repetitive Control for Fractional-Order Interval Type-2 TS Fuzzy Systems

This study explores the observer-based $H_\infty$ repetitive control problem for a class of fractional-order systems subject to external disturbances described by an interval type-2 Takagi-Sugeno fuzzy model approach. By combining the Lyapunov method and linear matrix inequalities technique, a tracking control input is designed with a prescribed disturbance attenuation performance level such that all states of the resulting closed-loop control system will be bounded and the tracking error can fluctuate near the origin in a small neighborhood. The main attention of this work is focused on the design of the repetitive tracking controller to asymptotically stabilize the fractional-order nonlinear systems and to achieve $H_\infty$ tracking performance. Precisely, a new set of sufficient conditions is derived in the form of linear matrix inequalities that ensure the desired stability and $H_\infty$ performance, and the controller gain is then computed. Finally, a numerical example is exploited to demonstrate the effectiveness and potential of the proposed control design technique.

State and Output Feedback Control of Interval Type-2 Fuzzy Systems With Mismatched Membership Functions

This paper is concerned with the problems of state and output feedback control for interval type-2 (IT2) fuzzy systems with mismatched membership functions. The IT2 fuzzy model and the IT2 state and output feedback controllers do not share the same membership functions. A novel performance index, which is expressed as an extended dissipativity performance, is introduced to be a generalization of $H_{\infty }$ , $L_{2}$ – $L_{\infty }$ , passive, and dissipativity performances indexes. First, the IT2 Takagi–Sugeno fuzzy model and the controllers are constructed by considering the mismatched membership functions. Second, on the basis of Lyapunov stability theory, the IT2 fuzzy state and output feedback controllers are designed, respectively, to guarantee that the closed-loop system is asymptotically stable with extended dissipativity performance. The existence conditions of the two kinds of controllers are obtained in terms of convex optimization problems, which can be solved by standard software. Finally, simulation results are provided to illustrate the effectiveness of the proposed methods.

Interval type-2 fuzzy inverse controller design in nonlinear IMC structure

In the recent years it has been demonstrated that type-2 fuzzy logic systems are more effective in modeling and control of complex nonlinear systems compared to type-1 fuzzy logic systems. An inverse controller based on type-2 fuzzy model can be proposed since inverse model controllers provide an efficient way to control nonlinear processes. Even though various fuzzy inversion methods have been devised for type-1 fuzzy logic systems up to now, there does not exist any method for type-2 fuzzy logic systems. In this study, a systematic method has been proposed to form the inverse of the interval type-2 Takagi–Sugeno fuzzy model based on a pure analytical method. The calculation of inverse model is done based on simple manipulations of the antecedent and consequence parts of the fuzzy model. Moreover, the type-2 fuzzy model and its inverse as the primary controller are embedded into a nonlinear internal model control structure to provide an effective and robust control performance. Finally, the proposed control scheme has been implemented on an experimental pH neutralization process where the beneficial sides are shown clearly.