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Resilient fuzzy stabilization is capable of providing much less conservative results than conventional fuzzy stabilization while the alert threshold condition should be always satisfied at each sampling instant. In order to make the alert threshold condition more easily to be guaranteed, the short paper employs the switching-type gain-scheduling control law so that the real-time information, which is specific to the current sampling instant, can be integrated into resilient fuzzy stabilization. More importantly, a new kind of time-variant balanced matrix is introduced for the first time for adjusting positive/negative terms of different monomials in a more flexible way. As a result, the conservatism of resilient fuzzy stabilization can be further reduced even if the alert threshold condition becomes more difficult to be violated. Finally, the advantage of the developed method is tested and validated via related comparisons on a benchmark example. [ABSTRACT FROM AUTHOR]

This article focuses on the design of fuzzy secure control for a class of coupled systems, which are modeled by a nonlinear $N$ -dimensional ($N$ -D) parabolic partial differential equation (PDE) subsystem and an ordinary differential equation (ODE) subsystem. Under stochastic deception attacks, a fuzzy secure control scheme is designed, which is effective to tolerate the attacks and ensure the desired performance for the considered systems. A new fuzzy-dependent Poincare–Wirtinger’s inequality (PWI) is proposed. Compared with the traditional Poincare’s inequality, the fuzzy-dependent PWI is more flexible and less conservative. Meanwhile, an augmented Lyapunov–Krasovskii functional (LKF) is newly constructed, which strengthens the correlations of the PDE subsystem and ODE subsystem. Then, on the ground of the fuzzy-dependent PWI and the augmented LKF, new exponential stabilization criteria are set up for the PDE-ODE coupled systems. Finally, a hypersonic rocket car is presented to verify the effectiveness and less conservatism of the obtained results. [ABSTRACT FROM AUTHOR]

A novel multi-instant gain-scheduling scheme is proposed in order to further improve the state estimation performance of discrete-time Takagi–Sugeno fuzzy systems in this article. Different from those existing methods, the enabled working pattern at each sampling instant can be determined in cycle according to utilization of the updated information of adjacent normalized fuzzy weighting functions in depth, and then the featured time-varying free matrices are introduced for each working pattern, which can remove those existing constraints on traditional free matrices. Consequently, the conservatism can be reduced significantly and it does broaden the range of application for observer-based fuzzy state estimation. Despite the fact that the quantity of the free matrices becomes much bigger than before, it needs to be pointed out that the actual computational complexity only increases by a small amount through depressing the number of cycles. Given that the developed designing process belongs to an offline computation, it is an acceptable tradeoff between the increasement of computational burdens and the reduction of conservatism. In the end, the effectiveness of the developed method is illustrated through the detailed analysis of numerical simulations. [ABSTRACT FROM AUTHOR]

This article is devoted to the development of multi-instant gain-scheduling stabilization of discrete-time Takagi–Sugeno fuzzy systems by developing a time-variant balanced matrix approach. Many of the reported advances have provided more and more relaxed results via choosing higher order dependent gain matrices, which will be a trouble in the case of real-time implementation. Therefore, a multi-instant gain-scheduling fuzzy state-feedback controller with different working modes is given to stabilize the closed-loop systems by updating the enabled pair of lower order gain matrices in cycle. For each possible working mode, the real-time situation information of the normalized fuzzy weighting functions can be fully considered by using a set of time-variant balanced matrices in accordance to certain rules and, thus, much freedom is introduced for proposing less conservative results. More importantly, our relaxed result is obtained without requiring higher order dependent gain matrices than the existing ones, i.e., its conservatism is reduced in a more meaningful way and thus it is more conducive to real-time implementation. Finally, both the effectiveness and the superiority of the proposed results are discussed and validated in the numerical section. [ABSTRACT FROM AUTHOR]

The problem of enhanced stabilization of discrete-time Takagi–Sugeno fuzzy system is investigated in depth via proposing a new way to employ much more information implied in various time-varying differences of multi-instant normalized fuzzy weighting functions. Benefit from the given comprehensive real-time scheduling model, these time-varying differences on time vertical dimension and two different transverse dimensions are for the first time integrated into fuzzy stabilization and two key alterable weights are also introduced. Consequently, much considerable freedom can be produced and, thus, it brings much less conservative results than the reported ones in recent literature. More importantly, a very simple workable way has been provided to online recognize the specific enabled mode at each sampling instant so that those existing time-consuming online operations in referred literature can be avoided to ease online implementation costs. Indeed, this feature is very beneficial to the practical application of our theoretical results. Finally, the superiority of our developed method over previous ones is validated adequately via two benchmark simulations. [ABSTRACT FROM AUTHOR]

This article considers an adaptive fuzzy control problem for nonstrict-feedback nonlinear stochastic systems, which contain input delay, output constraints, and unknown control coefficients, simultaneously. First, an original stochastic nonlinear mapping and the Pade approximation transformation techniques are developed to solve the symmetric output constraints and input delay. Then, an adaptive fuzzy controller is designed for the unknown nonlinear systems, in which the Nussbaum function is employed to deal with the unknown time-varying control coefficients. Tracking errors are ensured to converge to a small neighborhood around the origin, and the system output does not violate the predefined constrained conditions. All the signals of the closed-loop systems have proven to remain bounded in probability. Moreover, the asymmetric output-constrained control is also studied. Two simulation examples are provided to show the effectiveness of the developed method. [ABSTRACT FROM AUTHOR]

This article proposes an enhanced switching stabilization of Takagi–Sugeno fuzzy systems by developing a new fuzzy switching controller. A distinctive feature of the proposed approach is the enhanced ability to utilize the updated information of the normalized fuzzy weighting functions at each sampling point. Compared with those recent results in the literature, two key performance indexes, i.e., reducing the conservatism and alleviating the online computational burden, can be improved together while the off-line computational burden increases as a tradeoff but is still affordable from the point of algorithmic complexity. As a result, the efficiency of fuzzy stabilization is enhanced and thus its scope of application can be enlarged much more than before. Finally, the superiority of the proposed approach is illustrated by some simulation comparisons. [ABSTRACT FROM AUTHOR]

This article focuses on the exponential synchronization problem of T–S fuzzy reaction–diffusion neural networks (RDNNs) with additive time-varying delays (ATVDs). Two control strategies, namely, fuzzy time sampled-data control and fuzzy time–space sampled-data control are newly proposed. Compared with some existing control schemes, the two fuzzy sampled-data control schemes cannot only tolerate some uncertainties but also save the limited communication resources for the considered systems. A new fuzzy-dependent adjustable matrix inequality technique is proposed. According to different fuzzy plant and controller rules, different adjustable matrices are introduced. In comparison with some traditional estimation techniques with a determined constant matrix, the fuzzy-dependent adjustable matrix approach is more flexible. Then, by constructing a suitable Lyapunov–Krasovskii functional (LKF) and using the fuzzy-dependent adjustable matrix approach, new exponential synchronization criteria are derived for T–S fuzzy RDNNs with ATVDs. Meanwhile, the desired fuzzy time and time–space sampled-data control gains are obtained by solving a set of linear matrix inequalities (LMIs). In the end, some simulations are presented to verify the effectiveness and superiority of the obtained theoretical results. [ABSTRACT FROM AUTHOR]

This paper addresses the problem of reducing the conservatism for stabilization of discrete-time Takagi–Sugeno fuzzy systems via a new extended representation approach. Different from previous slack variable methods, an advanced slack variable method without limitations is proposed for further making good use of available fuzzy weighting functions. Owing to the introduction of extended representations for homogenous polynomials, those strong limitations in recent literature are relaxed and thus the primary and secondary sequences of all normalized fuzzy weighting functions can be mapped to one augmented multi-indexed matrix for each homogeneous polynomial. Therefore, less conservative stabilization conditions can be provided as a result of these effective measures and thus a part of the online computational cost is transferred to the offline implementation. Finally, the benefits of the proposed method are illustrated by means of numerical experiments. [ABSTRACT FROM AUTHOR]

The problem of observer-based state estimation of discrete-time fuzzy systems is investigated by constructing a joint switching mechanism for adjacent instants. Thanks to the usage of both the proposed spatial partitioning method and a set of new free matrix-valued variables, abundant information about size differences of all the normalized fuzzy weighting functions for adjacent instants can be interactively integrated into the fuzzy observer design for the first time. Compared with the recent result from three important aspects (conservatism level, online computational burden, and offline computational burden), three positive results can be obtained: 1) it provides a chance for reducing the conservatism by a large margin; 2) the required online computational burden remains unchanged as referred ones; and 3) as a tradeoff, the required offline computational burden increases to some extent but is still affordable from the view of complexity analysis. Finally, two numerical simulations have been given to validate the effectiveness of our developed theoretical results. [ABSTRACT FROM AUTHOR]

This paper studies the adaptive event-triggered fuzzy control issue for active vehicle suspension systems with uncertainties. Takagi–Sugeno fuzzy model is applied for considered systems. In the process of designing controller, a crucial problem, actuator failure, is taken into account. An adaptive event-triggered mechanism is adopted to economize limited communication resource. Compared with the traditional event-triggered scheme with a constant threshold, the adaptive event-triggered mechanism can save more resource effectively. Based on Lyapunov stability theory, an adaptive event-triggered fuzzy control approach is proposed to guarantee the desired performance. Meanwhile, suspension constrained requirements are also ensured. Finally, simulation examples are presented to testify the feasibility of the approach proposed in this paper. [ABSTRACT FROM AUTHOR]

This paper is focused on the issue of scheduling stabilization of Takagi–Sugeno fuzzy control systems by the aid of digging down much deeper of implicit information in the underlying systems. An event-triggered real-time scheduler that decides which control mode should be executed at any given instant is constructed by periodically evaluating the joint-distribution-type of multi-instant normalized fuzzy weighting functions at every sampled instant. Profiting from the proposed event-triggered scheduling policy, the proper control mode for the current instant is updated in order to adapt time-varying situations once if the underlying joint-distribution-type changes, and thus previous implementations of control tasks with an unchanged control mode can be further relaxed in this paper. The effectiveness of our approach is verified by several simulation examples in the end. [ABSTRACT FROM AUTHOR]

This paper investigates the problem of fuzzy H ∞ control design for a class of discrete-time nonlinear control systems via a multi-samples approach. A new fuzzy H ∞ controller, which is parameter-dependent on not only the current-time but also the one-step-past membership functions, is developed to derive less conservative design conditions for ensuring both the asymptotic stability and the prescribed H ∞ performance index of the obtained closed-loop system. Thanks to the usage of both a new fuzzy Lyapunov function and an extension of the homogenous matrix polynomial methodology, linear matrix inequality (LMI)-based H ∞ control design conditions are obtained for minimizing the normal level in a systematic and relaxed way. In addition, further efforts are made by developing an efficient slack variable approach. Finally, two numerical examples are provided to illustrate the effectiveness of the results given in this paper. [ABSTRACT FROM AUTHOR]

This paper proposes relaxed stabilization conditions of discrete-time nonlinear systems in the Takagi–Sugeno (T–S) fuzzy form. By using the algebraic property of fuzzy membership functions, a novel nonparallel distributed compensation (non-PDC) control scheme is proposed based on a new class of fuzzy Lyapunov functions. Thus, relaxed stabilization conditions for the underlying closed-loop fuzzy system are developed by applying a new slack variable technique. In particular, some existing fuzzy Lyapunov functions and non-PDC control schemes are special cases of the new Lyapunov function and fuzzy control scheme, respectively. Finally, two numerical examples are provided to illustrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

The problem of enhancing the adaptability against unreliable communication channels for fuzzy system is investigated by proposing a new multi-instant fuzzy switching controller with a more flexible switching manner. Compared with recent methods in the reported literature, more switching modes have been designed according to the updated information at each sampling instant and thus much more freedom can be created by introducing and assigning additional variables for all the possible switching modes. As a result, the adaptability against unreliable communication channels can be enhanced from two aspects: for the same health quality of communication channels, much larger controllable domain can be provided; or for the same system parameters, a worse health quality of communication channels can be affordable. Finally, several advantages over previous fuzzy approaches are verified by means of numerical simulations. • The adaptability against unreliable communication channels is inhanced by proposing a new multi-instant fuzzy switching controller. • More switching modes have been designed according to the updated information at each sampling instant and thus much more freedom can be created. • For the same health quality of communication channels, much larger controllable domain is obtained. [ABSTRACT FROM AUTHOR]

In this paper, the periodic tracking control problem is considered for nonlinear systems with some parameters uncertainties and disturbances. First, a T-S fuzzy approach is employed to model nonlinear systems. Second, considering the partly state unmeasured and periodic tracking reference signal, fuzzy state observer and fuzzy modified repetitive controller (FMRCr) are designed based on the modified repetitive control (MRC) approach. To achieve signal tracking and H ∞ disturbance attenuation performance, a two-dimensional model approach and singular-value decomposition technique of system output matrix are developed. Then, by the Lyapunov stability theory, some sufficient conditions are obtained for FMRC closed-loop system with stabilization and H ∞ disturbance attenuation performance in linear matrix inequality (LMI) form. Correspondingly, the controller gains and observer gains are solved by LMI toolbox. Two numerical examples are provided to illustrate the validity of the method. [ABSTRACT FROM AUTHOR]