Markovian Jump Fuzzy Systems Research Articles

Cooperative Design of Asynchronous Controller and Dynamic Packet Dropouts Compensator for Strictly Dissipative T–S Fuzzy Markov Jump Systems

Cooperative Design of Asynchronous Controller and Dynamic Packet Dropouts Compensator for Strictly Dissipative T–S Fuzzy Markov Jump Systems

Mismatched Quantized H ∞ Output-Feedback Control of Fuzzy Markov Jump Systems With a Dynamic Guaranteed Cost Triggering Scheme

Mismatched Quantized <i>H</i> _∞ Output-Feedback Control of Fuzzy Markov Jump Systems With a Dynamic Guaranteed Cost Triggering Scheme

Collaborative Optimization Design of Event-based Asynchronous Filter for Discrete-time T-S Fuzzy Markov Jump Systems

Collaborative Optimization Design of Event-based Asynchronous Filter for Discrete-time T-S Fuzzy Markov Jump Systems

Finite-Time Asynchronous Switching Control for Fuzzy Markov Jump Systems by Applying Polynomial Membership Functions

Finite-Time Asynchronous Switching Control for Fuzzy Markov Jump Systems by Applying Polynomial Membership Functions

Asynchronous Switching Control for Fuzzy Markov Jump Systems With Periodically Varying Delay and Its Application to Electronic Circuits

Asynchronous Switching Control for Fuzzy Markov Jump Systems With Periodically Varying Delay and Its Application to Electronic Circuits

Asynchronous Dissipative Control of Discrete-Time Fuzzy Markov Jump Systems With Dynamic State and Input Quantization

A numerically tractable two-step approach based on backtrack and optimization searches is proposed for asynchronous quantized dissipative control of discrete-time fuzzy Markov jump systems (DFMJSs) under the networked control framework. The asynchrony of modes between the plant and controller is described by a hidden Markov model. Both dynamic state and input quantization are considered. The dynamic zooming factors of the quantizers are designed as piecewise functions with respect to their arguments to avoid division by zero. A fuzzy asynchronous quantized controller is devised to make sure that the closed-loop system is stochastically stable 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">$(\mathcal {Q},\mathcal {S},\mathcal {R})$</tex-math></inline-formula> - dissipative via using a quadratic Lyapunov function and equivalent matrix transformations. Then, the iterative two-step approach is used to determine the optimal dissipativity level and the corresponding control gain and quantization parameters. Analysis and control synthesis for DFMJSs without quantization are also presented, covering some previous results as special cases. Finally, a single-link robot arm system and another numerical example are utilized to validate the present asynchronous dissipative control approaches for the quantization and non-quantization cases, respectively.

Finite-Region Dissipative Control for 2-D Fuzzy Jump Systems Under Hidden Mode Detection

In this work, we consider the problem of finite-region asynchronous dissipative control and pay more attention to the transient behavior of a class of two-dimensional fuzzy Markov jump systems (MJSs). First, the considered plant is modeled based on a well-known Fornasini–Marchesini equation. The asynchronization phenomenon between the system modes and controller modes is characterized by a hidden Markov model. Then, by a fuzzy-basis-dependent and mode-dependent Lyapunov function, sufficient conditions are established, which can make the overall closed-loop fuzzy dynamic MJSs be finite-region bounded with a strictly <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$(T, S, R)$</tex-math> </inline-formula> - <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\theta$</tex-math> </inline-formula> -dissipative performance. Finally, a numerical example concerning the Darboux equation is employed to validate the effectiveness and performance of the presented control scheme.

Compensation-Based Output Feedback Control for Fuzzy Markov Jump Systems With Random Packet Losses.

This article is concerned with the problem of compensation-based output feedback control for Takagi-Sugeno fuzzy Markov jump systems subject to packet losses. The phenomenon of packet losses is assumed to randomly occur in the feedback channel, which is modeled by a Bernoulli process. Employing the single exponential smoothing method as a compensation scheme, the missing measurements are predicted to help offset the impact of packet losses on system performance. Then, an asynchronous output feedback controller is designed by the hidden Markov model. Based on the mode-dependent Lyapunov function, some novel sufficient conditions on the controller existence are derived such that the closed-loop system is stochastically stable with strict dissipativity. Besides, an algorithm for determining the optimal smoothing parameter is proposed. Finally, the validity and advantages of the design approach are manifested by some simulation results.

Reachable Set Estimation for T–S Fuzzy Markov Jump Systems With Time-Varying Delays via Membership Function Dependent H∞ Performance

This article considers the reachable set estimation problem and membership function dependent <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$H_\infty$</tex-math></inline-formula> performance analysis for a class of fuzzy Markov jump systems (FMJSs) with mode-dependent time-varying delays and bounded external disturbances via sampled-data control. First, mode-dependent sampled-data control for the FMJS is designed using the Takagi–Sugeno (T–S) fuzzy method. Then, a novel stochastic Lyapunov–Krasovskii functional (LKF) is constructed in mode-dependent augmented form by taking full advantage of the variable characteristics related to the actual sampling pattern. At the same time, a membership function dependent <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$H_\infty$</tex-math></inline-formula> performance index is introduced for the first time to attenuate the impact of disturbances on the closed-loop FMJS. Based on the novel <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$H_\infty$</tex-math></inline-formula> performance index and LKF, new delay-dependent conditions are derived in the framework of linear matrix inequalities to ensure stochastic stability of the closed-loop system and its reachable set is bounded by an ellipsoid in the presence of bounded disturbances. Finally, two illustrated application problems validate theoretical results with less conservatism in the sense of enlarging the sampling period and minimizing the disturbance attenuation level.

Fuzzy-Model-Based Asynchronous Fault Detection for Markov Jump Systems With Partially Unknown Transition Probabilities: An Adaptive Event-Triggered Approach

This article addresses the event-triggered asynchronous fault detection (FD) problem of fuzzy-model-based nonlinear Markov jump systems (MJSs) with partially unknown transition probabilities. For this objective, the nonlinear plant is modeled as an interval type-2 (IT2) fuzzy MJS with the aid of the IT2 fuzzy sets capturing the uncertainties of the membership functions. An adaptive event-triggered scheme is introduced to bring down the costs of the communication network from the system to the fuzzy fault detection filter (FDF), in which the triggering parameter can be adaptively tuned with the system dynamics. A hidden Markov model (HMM) is employed to characterize the asynchronous phenomenon between the system and the FDF. Unlike the existing results, the transition probabilities of the plant and the FDF are allowed to be partially known. By using the Lyapunov and the membership-function-dependent methods, the existence conditions of the FDF are derived. Finally, the proposed FD methods are verified by a numerical simulation.

Improved asynchronous stabilization method for nonhomogeneous Markovian jump fuzzy systems with incomplete transition rates

This paper proposes an improved asynchronous stabilization method for nonhomogeneous Markovian jump fuzzy systems (MJFSs) with incomplete transition rates via a nonparallel distributed compensation (non-PDC) control scheme. To cover a more realistic situation in the continuous-time MJFS domain, this paper focuses on addressing the following issues differently from previous studies: 1) emergence of a nonhomogeneous Markov process and asynchronous control mode, 2) separation of the Lyapunov matrix from the control gain within stabilization conditions, and 3) relaxation of stabilization conditions subject to multiple time-varying parameters. Specifically, the effects of nonhomogeneity and asynchronism are simultaneously reflected in the stabilization conditions, and separation and relaxation techniques are additionally developed as needed. Finally, the advantages of our method are illustrated through two examples: the first is provided to show the effectiveness of the proposed separation technique, and the second is provided to show that the relaxed stabilization conditions are less conservative than previous results.

Adaptive Event-Triggered Finite-Time Dissipative Filtering for Interval Type-2 Fuzzy Markov Jump Systems With Asynchronous Modes.

This article investigates the adaptive event-triggered finite-time dissipative filtering problems for the interval type-2 (IT2) Takagi-Sugeno (T-S) fuzzy Markov jump systems (MJSs) with asynchronous modes. By designing a generalized performance index, the H∞ , L2-L∞ , and dissipative fuzzy filtering problems with network transmission delay are addressed. The adaptive event-triggered scheme (ETS) is proposed to guarantee that the IT2 T-S fuzzy MJSs are finite-time boundedness (FTB) and, thus, lower the energy consumption of communication while ensuring the performance of the system with extended dissipativity. Different from the conventional triggering mechanism, in this article, the parameters of the triggering function are based on an adaptive law, which is obtained online rather than as a predefined constant. Besides, the asynchronous phenomenon between the plant and the filter is considered, which is described by a hidden Markov model (HMM). Finally, two examples are presented to show the availability of the proposed algorithms.

Event-Triggered and Asynchronous Reduced-Order Filtering Codesign for Fuzzy Markov Jump Systems

This article is devoted to the investigation of reduced-order dissipative filtering for Takagi&#x2013;Sugeno (T&#x2013;S) fuzzy Markov jump systems with the event-triggered mechanism. For the proposed event-triggered mechanism, its threshold parameter is constructed as a special diagonal matrix which can improve system performance by flexibly adjusting the matrix elements. Due to the impact of the sampling behaviors and the environmental disturbance, the asynchronization between the filter and the estimated system is considered in this article, which can be characterized by the hidden Markov model. Through handling the linear matrix inequalities (LMIs) with some slack matrices, event-triggered fuzzy filters are designed to guarantee the resulting system is stochastically stable and strictly dissipative. The proposed filter parameters are obtained by solving LMIs. Ultimately, both the effectiveness and advantages of the proposed reduced-order filter with the event-triggered mechanism are verified by a practical example.

LSTM-Based Intelligent Fault Detection for Fuzzy Markov Jump Systems and Its Application to Tunnel Diode Circuits

This brief investigates the intelligent fault detection problem for a class of Takagi-Sugeno fuzzy Markov jump systems. The considered systems are modeled by a set of fuzzy rules and membership functions. With the help of deep learning technique, an intelligent fault detection method based on long short-term memory (LSTM) neural network with an attention mechanism is proposed. The improved LSTM model can accurately capture the fault features by making full use of previous information. Finally, the proposed approach is applied to the tunnel diode circuits and corresponding experiments are conducted to demonstrate its effectiveness, which achieves better performance in comparison with other conventional method for detection.

Robust Nonfragile Guaranteed Cost Control for Uncertain Fuzzy Markov Jump Systems with Time-Varying Delays

This paper aims to investigate the problem of robust nonfragile guaranteed cost control for uncertain discrete-time Takagi–Sugeno fuzzy systems with Markov jumping parameters and time-varying delay. A nonfragile fuzzy-basis-dependent and mode-dependent controller is designed and a sufficient condition is developed to ensure that the resulting closed-loop system is robust asymptotically stable in mean square with guaranteed cost index not exceeding the specified upper bound. Subsequently, the controller gain and minimum upper bound of the guaranteed cost index can be obtained by solving a set of linear matrix inequalities. Compared with the existing literature, this paper enormously reduces the conservatism of the result obtained. Finally, numerical and practical examples are provided to demonstrate the performance of the proposed approach.

Event-Based Dissipative Control of Interval Type-2 Fuzzy Markov Jump Systems Under Sensor Saturation and Actuator Nonlinearity

This article proposes a new design of an event-based dissipative asynchronous controller for the interval type-2 (IT2) fuzzy Markov jump systems (MJSs) subject to sensor saturation and actuator nonlinearity. By resorting to a generalized performance index, the <inline-formula><tex-math notation="LaTeX">${H_\infty }$</tex-math></inline-formula>, passive, and dissipative fuzzy control problems are solved in a unified framework. The event-based scheme is developed for the IT2 fuzzy MJSs subject to sensor saturation and actuator nonlinearity, and the energy consumption of communication can be reduced. Moreover, the system and controller modes are asynchronous, and a hidden Markov model is employed to observe the modes of the original system. The membership-function-dependent approach is applied to analyze the stability of the closed-loop system. Finally, two examples are given to demonstrate the effectiveness of the proposed algorithms.

Nonquadratic stabilization conditions for nonhomogeneous Markovian jump fuzzy systems with higher-level operation modes

This paper is concerned with the problem of designing a dissipative control for generalized nonhomogeneous Markovian jump fuzzy systems (MJFSs) that can cover both piecewise-homogeneous MJFSs and nonhomogeneous MJFSs through the use of dual modes, i.e., plant and higher-level modes. Based on a dual-mode-dependent fuzzy control law within a nonparallel distributed compensation (non-PDC) scheme, the nonquadratic stabilization conditions are first formulated in terms of multi-parameterized linear matrix inequalities (M-PLMIs), and then be transformed into a finite set of solvable LMIs without reducing M-PLMIs to PLMIs. Further, since the proposed relaxation technique can address the transition probabilities of plant and higher-level modes at once, the characteristics on mutual dependence between dual modes are fully incorporated into the nonquadratic stabilization conditions. Two illustrative examples are given to show the validity of the proposed approach.

An Improved Fuzzy Event-Triggered Asynchronous Dissipative Control to T–S FMJSs With Nonperiodic Sampled Data

In this article, an investigation about the issue of fuzzy event-triggered asynchronous dissipative control for T–S fuzzy Markov jump systems (FMJSs) with unknown transition probabilities and nonuniform sampling is conducted. First of all, a mode-dependent looped Lyapunov–Krasovskii functional (LKF) is proposed, which takes full use of the available information not only from sawtooth structure characteristics but also from the inner sampling dynamics. Meanwhile, a hidden Markov chain is employed to depict the mismatch between the original system and the state-dependent fuzzy event-triggered controller. Then, based on the LKF methodology, matrix inequality techniques, and the reciprocally convex combination protocol, some relaxed criteria with respect to the stochastic stable of the considered system and the desired dissipative performance are derived, simultaneously. A numerical experiment is given to illustrate the significance of the theoretical results.

Dissipativity-Based Disturbance Attenuation Control for T-S Fuzzy Markov Jumping Systems With Nonlinear Multisource Uncertainties and Partly Unknown Transition Probabilities.

This article is concerned with the dissipativity-based disturbance attenuation control for a class of Takagi-Sugeno (T-S) fuzzy Markov jump systems (FMJSs) suffering from nonlinear multisource disturbances. The considered system possesses nonlinear and stochastic jumping disturbances generated by multiple sources, constituting the main challenge to control design and dissipativity analysis. By proposing an adaptive fuzzy disturbance observer and a hybrid feedback controller, a novel fuzzy disturbance attenuation control structure has been constructed. In terms of strict linear matrix inequalities (LMIs), a new sufficient condition is established to guarantee the (Z, Y, X)-ε- dissipative and stochastic exponentially stability of the closed-loop FMJSs. Furthermore, for the concerned FMJSs with partly unknown transition probabilities, the sufficient conditions are also derived and the gains of controller or observer can be computed immediately. Finally, a numerical example is provided to verify the effectiveness of the proposed theory.

Dissipative control of interval type-2 nonhomogeneous Markovian jump fuzzy systems with incomplete transition descriptions

This paper investigates the problem of designing a dissipative controller for interval type-2 nonhomogeneous Markovian jump fuzzy systems (MJFSs) with incomplete transition descriptions. To explore a generalized model for MJFSs under realistic situations, the coexistence of incompletely known transition rates and mismatched membership functions is considered in MJFS models, and the corresponding stabilization conditions are derived in terms of multi-parameterized linear matrix inequalities (M-PLMIs). In addition, to handle the problem of M-PLMIs, two novel relaxation techniques are additionally proposed such that the use of redundant constraints on multiple time-varying parameters can be significantly reduced. Finally, the validity of the proposed method is demonstrated via two illustrative examples.