Fuzzy-Model-Based Output Feedback Reliable Control for Network-Based Semi-Markov Jump Nonlinear Systems Subject to Redundant Channels

Multi-Instant Gain-Scheduling Fuzzy Observer of Discrete-Time Takagi-Sugeno Systems and Its Application: An Efficient Balanced Matrix Approach

The problem of relaxed state estimation of discrete-time Takagi-Sugeno fuzzy systems is studied by constructing a novel multi-instant gain-scheduling fuzzy observer. First, a multi-instant gain-scheduling mechanism with a single adjustable parameter is given for the first time in order to produce more reasonable switch modes over previous results reported in recent literature. Second, for every switch mode, a batch of specified observer gain matrices is determined by developing an efficient balanced matrix approach so that the updated values of adjacent normalized fuzzy weighting functions can be flexibly exploited. Since the implied information of each specific switch mode is capable of being absorbed and utilized more thoroughly by the aid of the refined higher-order balanced matrices, the conservatism can be prominently reduced at the price of consuming extra computational burden within the allowable range. Finally, two benchmark examples are provided to test and verify the progressiveness of our proposed approach.

Finite-frequency control for nonlinear semi-Markov jump systems with piecewise transition probabilities

Considering the frequency effect of external disturbances, this paper concerns the finite-frequency control problem for nonlinear semi-Markov jump systems (SMJSs) with piecewise transition probabilities (TPs) via the Takagi-Sugeno (T-S) fuzzy modeling approach. More precisely, the piecewise TPs are assumed to switch stochastically within limits, which implies that the corresponding distributions of sojourn time (ST) also vary randomly. Furthermore, another upper semi-Markov chain is utilized to characterize TPs variation in a finite set. With the aid of Finsler's lemma and Parseval's theorem, sufficient criteria for the controlled SMJS are constructed to meet the desired disturbance attenuation performance in the frequency domain. Then, the mode-dependent controllers are developed to use the TP information more efficiently. In particular, a novel matrix method is proposed to decouple the mode-dependent variables and controller gains by selecting slack matrices. Eventually, a numerical example is transmitted to demonstrate the validity and merits of established results.

Asynchronous Guaranteed Cost Control of 2-D Markov Jump Roesser Systems

This article is concerned with the problem of guaranteed cost control for 2-D Markov jump Roesser systems with mismatched modes. The hidden Markov model is introduced to describe the asynchronous phenomenon caused by mismatched modes, and an asynchronous linear state-feedback control law is designed based on this model. With the help of the 2-D Lyapunov function and linear matrix inequality (LMI) techniques, sufficient conditions are established to ensure the asymptotic stability of the concerned system with a bound of the predefined guaranteed cost under three different boundary conditions, respectively. Finally, an algorithm that concludes the design processes of the optimal asynchronous guaranteed cost control law is proposed, and a numerical example is provided to verify its effectiveness.

Distributed Robust Kalman Filtering for Markov Jump Systems With Measurement Loss of Unknown Probabilities

This article is concerned with a distributed filtering problem for Markov jump systems subject to the measurement loss with unknown probabilities. A centralized robust Kalman filter is designed by using variational Bayesian methods and a modified interacting multiple model method based on information theory (IT-IMM). Then, a distributed robust Kalman filter based on the centralized filter and a hybrid consensus method called hybrid consensus on measurement and information (HCMCI) is designed. Moreover, boundedness of the estimation errors and the estimation error covariances are studied for the distributed robust Kalman filter.

Dissipativity-based synthesis for semi-Markovian systems with simultaneous probabilistic sensors and actuators faults: A modified event-triggered strategy

Aided by a modified event-triggered communication policy (ETCP), this article addresses the dissipativity-based control synthesis problem for semi-Markovian switching systems (SMSSs) with simultaneous multiplicative probabilistic faults on sensors and actuators modules. The resulting model under consideration is more extensive, which covers semi-Markovian switching coefficients, transmission delays, and randomly occurring sensors and actuators faults in a unified systematic analytical framework instead of investigating separately in some existing works. More specifically, the probabilistic faults are assumed to happen on both the sensors and actuators modules simultaneously, and the distortion probability for each sensor and actuator is irrelevant, which can be characterized by multiplicate mutually independent stochastic variables that obeys certain statistical features and probabilistic distribution delineate on the interval [0,✠](✠≥1). To reduce the bandwidth usage, a novel event-triggered strategy is designed. Additionally, in the light of this newly developed ETCP, and considering the effects of the signal transmission delays and multitudinous probabilistic failures, a generalized and more realistic faulty pattern for SMSSs is presented, which is more fit for real applications. Hereby, the principal superiority of the established new type faulty pattern lies in its practicality and generality, which contains some previous faulty models as special scenarios. By constructing an appropriate semi-Markovian Lyapunov functional (SMLF) together with mathematical analysis technique and matrix inequality decoupling operation, sojourn-time-dependent sufficient conditions for determining both the control gain matrices and triggered configuration coefficients are developed and formulated in terms of a group of feasible linear matrix inequalities (LMIs). Eventually, several practical examples are exploited to substantiate the validity and practicability of the developed control design methodology.

Finite-Time Extended Dissipative Filtering for Singular T-S Fuzzy Systems With Nonhomogeneous Markov Jumps

This article investigates the finite-time extended dissipative filtering for singular T-S fuzzy Markov jump systems with time-varying transition probabilities (TPs). The time-varying TPs are considered to reside in a polytope. By resorting to a generalized performance index, the H_∞ , L₂-L_∞ , passive, and dissipative performance can be solved in a unified framework. Combining the free-weighting method and the proposed recursive method, a sufficient condition on singular stochastic extended dissipative finite-time boundedness (SSEDFTB) for a fuzzy filtering error system is obtained. By proposing a decoupling principle called double variables-based decoupling principle (DVDP) and a variable substitution principle (VSP), a novel condition on the existence of the fuzzy filter is presented in terms of linear matrix inequalities (LMIs). Compared with the existing works, the assumption on state variables and the constraints of slack matrices are overcome, which leads to more practical and less conservative results. A practical example is provided to demonstrate the effectiveness of the design methods.

Two-Dimensional Asynchronous Sliding-Mode Control of Markov Jump Roesser Systems

In this article, asynchronous sliding-mode control (SMC) is investigated for 2-D discrete-time Markov jump systems. As the system modes are not always accessible to the controller, the hidden Markov model is employed to describe the asynchronization between the system modes and controller. A new 2-D sliding surface is constructed and the corresponding asynchronous SMC law is designed under the framework of the hidden Markov model. By Lyapunov function and linear matrix inequality (LMI) approaches, the reachability of system dynamics to the predefined sliding surface is investigated, and sufficient conditions are established to guarantee that the underlying 2-D system is asymptotically mean-square stable (AMSS) with an H_∞ disturbance attenuation performance. Then, an algorithm is provided to derive the asynchronous 2D-SMC law. Finally, an example is given to verify the validity and effectiveness of the new SMC law design algorithm.

A Novel Self-Organizing Fuzzy Neural Network to Learn and Mimic Habitual Sequential Tasks

In this article, a new self-organizing fuzzy neural network (FNN) model is presented which is able to simultaneously and accurately learn and reproduce different sequences. Multiple sequence learning is important in performing habitual and skillful tasks, such as writing, signing signatures, and playing piano. Generally, it is indispensable for pattern generation applications. Since multiple sequences have similar parts, local information such as some previous samples is not sufficient to efficiently reproduce them. Instead, it is necessary to consider global and discriminative information, maybe in the very initial samples of each sequence, to first recognize them, and then predict their next sample based on the current local information. Therefore, the structure of the proposed network consists of two parts: 1) sequence identifier, which computes a novel sequence identity value based on initial samples of a sequence, and detects the sequence identity based on proper fuzzy rules and 2) sequence locator, which locates the input sample in the sequence. Therefore, by integrating outputs of these two parts in fuzzy rules, the network is able to produce the proper output based on the current state of each sequence. To learn the proposed structure, a gradual learning procedure is proposed. First, learning is performed by adding new fuzzy rules, based on coverage measure, using available correct data. Next, the initialized parameters are fine-tuned, by the gradient descent algorithm, based on fed back approximated network output as the next input. The proposed method has a dynamic structure able to learn new sequences online. Finally, to investigate the effectiveness of the presented approach, it is used to simultaneously learn and reproduce multiple sequences in different applications, including sequences with similar parts, different patterns, and writing different letters. The performance of the proposed method is evaluated and compared with other existing methods, including the adaptive network-based fuzzy inference system, GDFNN, CFNN, and long short-term memory (LSTM). According to these experiments, the proposed method outperforms traditional FNNs and LSTM in learning multiple sequences.