Switching Fuzzy Dynamic Output Feedback $H_{\infty}$ Control for Nonlinear Systems

This paper investigates the problem of event-triggered dynamic output feedback control for networked Takagi-Sugeno (T-S) fuzzy systems with asynchronous premise variables. Our attention is focused on the design of an event-triggered fuzzy dynamic output feedback controller that guarantees that the closed-loop system is asymptotically stable. First, with consideration of the limited bandwidth and restricted network resource, an event-triggered communication scheme is proposed to save the limited network resource. Second, different from the existing results in the literature, a fuzzy dynamic output feedback controller with asynchronous premise variables is constructed such that the premise membership functions are not necessarily the same as the networked T-S fuzzy systems. Then, by using the Wirtinger inequality and some slack matrices, a less conservative stability and stabilization conditions for the existence of fuzzy dynamic output feedback controller are derived in the form of linear matrix inequalities, which can be solved by the standard MATLAB toolbox. Finally, an example is given to demonstrate the effectiveness of the designed event-triggered fuzzy dynamic output feedback controller.

This paper studies the problem of adaptive eventtriggered dynamic output feedback fuzzy control for nonlinear networked control systems. Two crucial factors, packet dropouts and actuator failure, are taken into consideration simultaneously. Takagi-Sugeno fuzzy model is introduced to describe considered systems. The Bernoulli random distribution process is employed to depict the phenomenon of data missing. The actuator failure model is adopted to depict actuator failure. An innovative adaptive event-triggered strategy is built to save computational resource. In the light of Lyapunov stability theory, a fuzzy dynamic output feedback controller is designed to guarantee the stochastic stability and H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> performance for considered systems. Finally, simulation results are provided to demonstrate the usefulness of the proposed control strategy.

Dynamic event-triggered security control for networked T-S fuzzy system with non-uniform sampling

This paper considers the problem of dynamic output feedback H ∞ controller design for linear systems with input and output imprecision. In the controlled systems, the measurement and control signal transmissions from the plant to the controller and the controller to the plant, respectively, are assumed to be imprecise, and norm-bounded uncertainties are utilized to model the phenomenon of the imprecise transmissions. Attention is focused on the design of an H ∞ controller such that the closed-loop system is asymptotically stable and has a prescribed H ∞ performance with respect to the imprecision effects. A linear fractional transformation approach is proposed to obtain LMI-based design conditions for the H ∞ controller. Finally, the usefulness of the developed approach will be demonstrated by a numerical example.

This paper is concerned with the Disturbance Rejection by Dynamic Output Feedback problem and aims at proposing new geometric and structural characterizations for the Fixed Poles of this problem in the case of minimal (controllable and observable) systems. The key notions behind theses results are those of self-bounded and self-hidden invariant subspaces as introduced by Basile and Marro. The Fixed Poles are uniquely characterized, moreover the geometric subspaces (some particular (C, A, B)-pairs) which lead to the minimal solutions (for which all the other poles can be freely assigned) are not unique. As a corollary, we propose a structural necessary and sufficient condition for the existence of (internally) stable solutions, which generalizes the sufficient structural condition proposed by Basile and Marro.

In this paper, a fuzzy adaptive output feedback control approach is developed for a class of SISO strict-feedback nonlinear systems with unmeasured states, unmodeled dynamics, and dynamical disturbances. In the backstepping recursive design, fuzzy logic systems are used to approximate the unknown nonlinear functions, a fuzzy adaptive high-gain observer is designed to estimate the unmeasured states; a dynamic signal is incorporated into the control scheme to dominate the dynamic uncertainties. Using the states estimates and combining the backstepping design technique, a fuzzy adaptive output feedback control is constructed recursively. It is proved that the proposed fuzzy adaptive output feedback control scheme can guarantee the all signals in the closed-loop system are semiglobally uniformly ultimately bounded (SUUB), and the observer and tracking error converges to a small neighborhood of the origin. The effectiveness of the proposed approach is illustrated via an example.

In this paper, we present a new scheme to design adaptive fuzzy output-feedback controller for uncertain nonlinear systems in the presence of input saturation. Fuzzy logic systems are utilized to approximate the unknown nonlinear functions, and a state filter is designed to estimate unmeasured states. Combining the backstepping recursive design with modular design techniques, a new adaptive fuzzy output control scheme is synthesized. Unlike some existing control schemes for systems with input saturation, the developed controller dose not require assumptions on the states available and nonlinear systems satisfying the matching condition. It is proved that the proposed control approach can guarantee that all the signals of the resulting closed-loop system are semi-globally uniformly ultimately bounded, and the tracking error converges to a small neighborhood of the origin. A simulation is included to illustrate the effectiveness of the proposed approach.

The problem of fuzzy static output feedback H <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</inf> control is investigated for a class of nonlinear systems with time-varying delay. Specifically, the considered system is approximated by a Takagi-Sugeno (T-S) fuzzy model. By using linear matrix inequality (LMI) methods, we design a fuzzy static output feedback H <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</inf> controller, which guarantees asymptotic stability and a prescribed H <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</inf> index for the resulting closed-loop system. In contrast to the existing results, the gains of controller are obtained by solving a set of LMIs. The proposed method is easy to implement and can be applied to linear systems. A numerical example is provided to illustrate the effectiveness of the developed method.

Robust adaptive fuzzy filters output feedback control of strict-feedback nonlinear systemsIn this paper, an adaptive fuzzy robust output feedback control approach is proposed for a class of single input single output (SISO) strict-feedback nonlinear systems without measurements of states. The nonlinear systems addressed in this paper are assumed to possess unstructured uncertainties, unmodeled dynamics and dynamic disturbances, where the unstructured uncertainties are not linearly parameterized, and no prior knowledge of their bounds is available. In recursive design, fuzzy logic systems are used to approximate unstructured uncertainties, and K-filters are designed to estimate unmeasured states. By combining backstepping design and a small-gain theorem, a stable adaptive fuzzy output feedback control scheme is developed. It is proven that the proposed adaptive fuzzy control approach can guarantee the all the signals in the closed-loop system are uniformly ultimately bounded, and the output of the controlled system converges to a small neighborhood of the origin. The effectiveness of the proposed approach is illustrated by a simulation example and some comparisons.

For nonlinear space-varying parabolic partial differential equation systems (PPDESs) with random time-varying delay, this article introduces a dynamic fuzzy boundary output feedback (DFBOF) control under noncollocated boundary measurement (NCBM). Initially, the nonlinear delayed PPDESs are represented by Takagi–Sugeno (T–S) fuzzy models and random time-varying delay is considered by taking the influence of uncertain factors, which belongs to two intervals in a probabilistic way. Since the system state is not fully available and NCBM makes the boundary control design very difficult, a fuzzy observer under NCBM is presented to surmount the design difficulty. Subsequently, an observer-based fuzzy boundary controller is proposed and spatial linear matrix inequality (SLMI)-based sufficient conditions to ensure mean-square exponential stability are obtained for closed-loop delayed PPDESs by utilizing the Lyapunov direct method and Wirtinger inequality. Then, to solve the SLMIs, the feasibility conditions of DFBOF controller design for nonlinear delayed PPDES are expressed in LMIs. Finally, two examples are offered to demonstrate the validity of the presented dynamic fuzzy boundary control approach.

Iterative redesign techniques are proposed to integrate the design of the structural parameters and the active control parameters for vector second-order lumped-parameter structural systems. The objective is to minimize the required active control effort to satisfy given output variance constraints and robust performance constraints. The problem is formulated as an iterative sequential control design followed by control/structure redesign. Each step of the iterative algorithm is formulated as a linear matrix inequality (LMI) optimization problem that can be solved effectively using available LMI solvers. Convergence of the proposed algorithm to a solution that provides improved control effort and robust stability compared to the single-step structural and control design is guaranteed. Both static state-feedback and dynamic output feedback problems are considered.

Based on the singular value decomposition approach, an observer-based controller design for a class of Takagi-Sugeno fuzzy descriptor models (TSFDMs) with measurable premise variables is developed in this paper. The convergence of the closed-loop state system is studied by using the Lyapunov theory and asymptotic stability conditions are given in terms of linear matrix inequalities (LMIs). Finally, an application based on rolling disc process is presented to evaluate the performance of the proposed dynamic controller design.

The design problem of fuzzy unknown inputs observer (FUIO) and its application to fault detection and fault tolerant control strategy for dynamic Takagi-Sugeno (T-S) fuzzy systems described by ordinary differential or difference equations is widely investigated in the literature see e.g. [1]–[9]. The aim of the paper is to extend this observer design to a class of discrete-time T-S implicit systems (DTSISs) with measurable premise variables allowing the simultaneous estimation of the unknown states and unknown inputs (UIs). Indeed, an augmented fuzzy implicit model which regroups the state variables and UIs is firstly given. Based on the singular value decomposition approach, a new FUIO design in explicit structure is secondly proposed. The exponential convergence of the augmented state estimation error is established by using the Lyapunov theory and the stability conditions are given in terms of linear matrix inequalities (LMIs). Finally, an illustrative application is given to show the good performances of the proposed method.

In this paper, we investigate the design of observers tailored for discrete T-S fuzzy time-delay singular systems, considering the presence of process disturbances and measurable premise variables. An observer with more design degrees of freedom than the commonly used Luenberger observer is designed. By constructing an asymmetric Lyapunov-Krasovskii functional, a criterion ensuring the existence of the fuzzy state observer is provided, which eliminates the limitations of the positive definiteness and symmetry of the previous functional matrix. In the process of solving the inequality, the relaxation matrix is incorporated to acquire additional flexibility and alleviate the conservatism of parameter design. Ultimately, two numerical instances are provided to thoroughly validate the rationale and efficacy of the approach.

In this paper, fault detection technique is concerned for nonlinear systems which are described by Takagi-sugeno (T-S) fuzzy parts with measurable premise variables and uncertainty parts. In addition, the real system is likely to contain a fault signal owing to various factors. As a result, it is difficult to stabilize the control system when a fault occurs. With the aid of the Kalman-Yakubovic-Popov (KYP) lemma in finite-frequency domains, a new linear-matrix-inequality-based fault detection method for control systems is obtained, which not only guarantees the stability and reliability for unlinear dynamic systems in fault-free case and faulty cases, but also optimize the fault sensitivity performance index and gain the sensitivity to fault. It should be noted that this method can reduce the complexity that comes from the design of filter and fault detection respectively. Finally, the numeral examples and its simulation results are given to illustrate the effectiveness of the proposed design method.