Hankel-Norm-Based Model Reduction for Stochastic Discrete-Time Nonlinear Systems in Interval Type-2 T-S Fuzzy Framework

This article is concerned with the problem of the Hankel-norm model reduction for stochastic discrete-time nonlinear systems in interval type-2 (IT2) Takagi-Sugeno (T-S) fuzzy framework. The IT2 T-S fuzzy model is an efficient model for describing uncertain nonlinear systems, and the model reduction is to simplify the high-order complex systems by reducing the order of the original system. The aim of this article is to reduce the order of the original stochastic discrete-time IT2 fuzzy system into lower order system without ignoring the influence of IT2 membership functions. First, the Hankel-norm performance of the stochastic discrete-time IT2 fuzzy model is analyzed. Then, based on the projection theorem and cone complementary linearization approach, a convex Hankel-norm-based model reduction approach subject to conditions in the form of linear matrix inequalities (LMIs) is obtained. A membership-functions-dependent (MFD) technique is applied to capture the information of IT2 membership functions and further reduce the conservativeness. A numerical example is presented to illustrate the effectiveness of the proposed results.

Robust Sliding Mode-Based Learning Control for MIMO Nonlinear Nonminimum Phase System in General Form

The tracking control of a multi-input multioutput nonlinear nonminimum phase system in general form is discussed. This system is assumed to be suffering from parameter uncertainties and unmodeled dynamics, and the priori information of them is unknown. By considering both the exact model and uncertain model, the sliding mode-based learning controller is proposed. By designing an appropriate sliding surface and a learning controller, the stability of the closed-loop system is guaranteed for both the exact model and uncertain model. To overcome the disadvantage caused by parameter uncertainties and unmodeled dynamics, a fuzzy logical system is adopted here. A numerical simulation result carried on vertical takeoff and landing aircraft is taken as an example to validate the effectiveness of the presented controller.

A Novel Hybrid Fuzzy Grey TOPSIS Method: Supplier Evaluation of a Collaborative Manufacturing Enterprise

Recently, there is of significant interest in developing multi-criteria decision making (MCDM) techniques with large applications for real-life problems. Making a reasonable and accurate decision on MCDM problems can help develop enterprises better. The existing MCDM methods, such as the grey comprehensive evaluation (GCE) method and the technique for order preference by similarity to an ideal solution (TOPSIS), have their one-sidedness and shortcomings. They neither consider the difference of shape and the distance of the evaluation sequence of alternatives simultaneously nor deal with the interaction that universally exists among criteria. Furthermore, some enterprises cannot consult the best professional expert, which leads to inappropriate decisions. These reasons motivate us to contribute a novel hybrid MCDM technique called the grey fuzzy TOPSIS (FGT). It applies fuzzy measures and fuzzy integral to express and integrate the interaction among criteria, respectively. Fuzzy numbers are employed to help the experts to make more reasonable and accurate evaluations. The GCE method and the TOPSIS are combined to improve their one-sidedness. A case study of supplier evaluation of a collaborative manufacturing enterprise verifies the effectiveness of the hybrid method. The evaluation result of different methods shows that the proposed approach overcomes the shortcomings of GCE and TOPSIS. The proposed hybrid decision-making model provides a more accurate and reliable method for evaluating the fuzzy system MCDM problems with interaction criteria.

Model Approximation for Switched Genetic Regulatory Networks

The model approximation problem is studied in this paper for switched genetic regulatory networks (GRNs) with time-varying delays. We focus on constructing a reduced-order model to approximate the high-order GRNs considered under the switching signal subject to certain constraints, such that the approximation error system between the original and reduced-order systems is exponentially stable with a disturbance attenuation performance. The stability conditions and the disturbance attenuation performance are established by utilizing two integral inequality bounding techniques and the average dwell-time method for the approximation error system. Then, the solvability conditions for the reduced-order models for the GRNs are also established using the projection method. Furthermore, the model approximation problem can be transferred into a sequential minimization problem that is subject to linear matrix inequality constraints by using the cone complementarity algorithm. Finally, several examples are provided to illustrate the effectiveness and the advantages of the proposed methods.

An Optimal Divisioning Technique to Stabilization Synthesis of T-S Fuzzy Delayed Systems

This paper investigates the problem of stability analysis and stabilization for Takagi-Sugeno (T-S) fuzzy systems with time-varying delay. By using appropriately chosen Lyapunov-Krasovskii functional, together with the reciprocally convex a new sufficient stability condition with the idea of delay partitioning approach is proposed for the delayed T-S fuzzy systems, which significantly reduces conservatism as compared with the existing results. On the basis of the obtained stability condition, the state-feedback fuzzy controller via parallel distributed compensation law is developed for the resulting fuzzy delayed systems. Furthermore, the parameters of the proposed fuzzy controller are derived in terms of linear matrix inequalities, which can be easily obtained by the optimization techniques. Finally, three examples (one of them is the benchmark inverted pendulum) are used to verify and illustrate the effectiveness of the proposed technique.

Novel Fuzzy Modeling and Synchronization of Chaotic Systems With Multinonlinear Terms by Advanced Ge-Li Fuzzy Model

Ge and Li proposed an alternative strategy to model and synchronize two totally different nonlinear systems in the end of 2011, which provided a new version for fuzzy modeling and has been applied to several fields to simplify their modeling works and solve the mismatch problems [1]-[17]. However, the proposed model limits the number of nonlinear terms in each equation so that this model could not be used in all kinds of nonlinear dynamic systems. As a result, in this paper, a more efficient and comprehensive advanced-Ge-Li fuzzy model is given to further release the limitation and improve the effectiveness of the original one. The novel fuzzy model can be applied to all kinds of complex nonlinear systems--this is the universal strategy and only m x 2 fuzzy rules as well as two linear subsystems are needed to simulate nonlinear behaviors (m is the number of states in a nonlinear dynamic system), whatever the nonlinear terms are copious or complicated. Further, the fuzzy synchronization of two nonlinear dynamic systems with totally distinct structures can be achieved via only two sets of control gains designed through the novel fuzzy model as well as its corresponding fuzzy synchronization scheme. Two complicated dynamic systems are designed to be the illustrations, Mathieu-Van der pol system with uncertainties and Quantum-cellular neural networks nano system with uncertainties, to show the effectiveness and feasibility of the novel fuzzy model.

Adaptive Fuzzy Control of Strict-Feedback Nonlinear Time-Delay Systems With Unmodeled Dynamics

In this paper, an approximated-based adaptive fuzzy control approach with only one adaptive parameter is presented for a class of single input single output strict-feedback nonlinear systems in order to deal with phenomena like nonlinear uncertainties, unmodeled dynamics, dynamic disturbances, and unknown time delays. Lyapunov-Krasovskii function approach is employed to compensate the unknown time delays in the design procedure. By combining the advances of the hyperbolic tangent function with adaptive fuzzy backstepping technique, the proposed controller guarantees the semi-globally uniformly ultimately boundedness of all the signals in the closed-loop system from the mean square point of view. Two simulation examples are finally provided to show the superior effectiveness of the proposed scheme.

Filtering of Interval Type-2 Fuzzy Systems With Intermittent Measurements

In this paper, the problem of fuzzy filter design is investigated for a class of nonlinear networked systems on the basis of the interval type-2 (IT2) fuzzy set theory. In the design process, two vital factors, intermittent data packet dropouts and quantization, are taken into consideration. The parameter uncertainties are handled effectively by the IT2 membership functions determined by lower and upper membership functions and relative weighting functions. A novel fuzzy filter is designed to guarantee the error system to be stochastically stable with H∞ performance. Moreover, the filter does not need to share the same membership functions and number of fuzzy rules as those of the plant. Finally, illustrative examples are provided to illustrate the effectiveness of the method proposed in this paper.

Relaxed observer design of discrete-time T-S fuzzy systems via a novel slack variable approach

The problem of further studies on observer design for discrete-time Takagi-Sugeno fuzzy systems is investigated in this paper. Different from the existing result, a new slack variable approach is presented by developing some useful matrix equalities which rely on both the current-time and the past-time normalized fuzzy weighting functions. As a result, the relaxation quality of recent fuzzy observer design is significantly enhanced. Moreover, the conditions for the existence of a fuzzy H(∞) observer that minimizes an upper bound to H(∞) norms are also proposed. Finally, two numerical examples are provided to show that the given results are less conservative than other results available in the literature.

State Estimation of Discrete-Time Takagi-Sugeno Fuzzy Systems in a Network Environment

In this paper, we investigate the H∞ filtering problem of discrete-time Takagi'Sugeno (T-S) fuzzy systems in a network environment. Different from the well used assumption that the normalized fuzzy weighting function for each subsystem is available at the filter node, we consider a practical case in which not only the measurement but also the premise variables are transmitted via the network medium to the filter node. For the network characteristics, we consider the multiple packet dropouts which are described by using a Markov chain. It is assumed that the filter uses the most recent packet. If there are packet dropouts occurring, the filter adopts the information for the last received packet. Suppose that the mode of the Markov chain is ordered according to the number of consecutive packet dropouts from zero to a preknown maximal value. For each mode of the Markov chain, it only has at most two jumping actions: 1) jump to the first mode and the current packet is transmitted successfully and 2) jump to the next mode and the number of consecutive packet dropouts increases by one. We aim to design mode-dependent and fuzzy-basis-dependent T-S fuzzy filter by using the transmitted packet subject to the described network issue. With the augmentation technique, we obtain a stochastic filtering error system in which the filter parameters and the Markovian jumping variable are all involved. A sufficient condition which guarantees the stochastic stability and the H∞ performance is derived with the Lyapunov method. Based on the sufficient condition, we propose the filter design method and the filter parameters can be determined by solving a set of linear matrix inequalities (LMIs). A tunnel-diode circuit in a network environment is presented to show the effectiveness and the advantage of the proposed design approach.

Multitask TSK fuzzy system modeling by mining intertask common hidden structure

The classical fuzzy system modeling methods implicitly assume data generated from a single task, which is essentially not in accordance with many practical scenarios where data can be acquired from the perspective of multiple tasks. Although one can build an individual fuzzy system model for each task, the result indeed tells us that the individual modeling approach will get poor generalization ability due to ignoring the intertask hidden correlation. In order to circumvent this shortcoming, we consider a general framework for preserving the independent information among different tasks and mining hidden correlation information among all tasks in multitask fuzzy modeling. In this framework, a low-dimensional subspace (structure) is assumed to be shared among all tasks and hence be the hidden correlation information among all tasks. Under this framework, a multitask Takagi-Sugeno-Kang (TSK) fuzzy system model called MTCS-TSK-FS (TSK-FS for multiple tasks with common hidden structure), based on the classical L2-norm TSK fuzzy system, is proposed in this paper. The proposed model can not only take advantage of independent sample information from the original space for each task, but also effectively use the intertask common hidden structure among multiple tasks to enhance the generalization performance of the built fuzzy systems. Experiments on synthetic and real-world datasets demonstrate the applicability and distinctive performance of the proposed multitask fuzzy system model in multitask regression learning scenarios.

Induced l₂ filtering of fuzzy stochastic systems with time-varying delays

This paper is concerned with the problem of induced l2 filter design for a class of discrete-time Takagi-Sugeno fuzzy Itô stochastic systems with time-varying delays. Attention is focused on the design of the desired filter to guarantee an induced l2 performance for the filtering error system. A new comparison model is proposed by employing a new approximation for the time-varying delay state, and then, sufficient conditions for the obtained filtering error system are derived by this comparison model. A desired filter is constructed by solving a convex optimization problem, which can be efficiently solved by standard numerical algorithms. Finally, simulation examples are provided to illustrate the effectiveness of the proposed approaches.