Non-fragile guaranteed cost control for Takagi–Sugeno fuzzy hyperbolic systems

Chen, Minglai; Li, Junmin

doi:10.1080/00207721.2013.827259

Cited by 8 publications

(5 citation statements)

References 44 publications

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“…2. taking parameter uncertainty and actuator saturation into considerations, such as non-fragile guaranteed cost control [37] and robust control [38].…”

Section: Resultsmentioning

confidence: 99%

Exponentially stable guaranteed cost control for continuous and discrete-time Takagi–Sugeno fuzzy systems

et al. 2016

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This paper investigates exponentially stable guaranteed cost control (GCC) for a class of nonlinear systems which is represented by Takagi-Sugeno (T-S) fuzzy systems. State feedback controllers of parallel distributed compensation (PDC) structure are designed by the means of GCC for continuous and discrete-time T-S fuzzy systems respectively. GCC methods in this paper adopt quadratic performance functions, which take effects of control efforts, regulation errors and convergence rates into consideration simultaneously, to provide desirable performance and fast response for closed-loop systems. Sufficient design conditions that guarantee exponential stabilities of resulting closed-loop systems with predefined convergence rates are presented. By setting different convergence rates, response speed of the closed-loop nonlinear system can be adjusted. The proposed design procedures are eventually

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“…2. taking parameter uncertainty and actuator saturation into considerations, such as non-fragile guaranteed cost control [37] and robust control [38].…”

Section: Resultsmentioning

confidence: 99%

Exponentially stable guaranteed cost control for continuous and discrete-time Takagi–Sugeno fuzzy systems

et al. 2016

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“…Furthermore, non-fragile guaranteed cost control for T-S fuzzy hyperbolic systems has been presented in [29], and it gave the non-fragile guaranteed cost controller design which guarantee the magnitude of control input. Its controller was designed to guarantee that the fuzzy hyperbolic model was asymptotically stable and the cost function kept an upper bound.…”

Section: Introductionmentioning

confidence: 99%

Robust feedback control for T-S stochastic fuzzy hyperbolic system

Zhang

2014

Proceedings of the 33rd Chinese Control Conference

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This paper concerns the problems of Takagi-Sugeno (T-S) stochastic fuzzy hyperbolic control for nonlinear systems with or without parameter uncertainties. The state feedback controller is designed by parallel distributed compensation (PDC) method, and some sufficient conditions are formulated via linear matrix inequalities (LMIs) such that the system is asymptotically stable. The above approach is also extended to the output feedback controller of T-S fuzzy hyperbolic system with parameter uncertainties, and the desired controller can be easily obtained by using the Matlab LMI toolbox. The main advantage of the proposed model is that it can achieve small control amplitude via "soft" constraint approach. Finally, two simulation examples are utilized to demonstrate the validity and effectiveness of the proposed approaches.

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“…Therefore, a significant issue is determining how to design a controller and an observer that are able to tolerate some uncertainties in various processes, and is called non-fragile control. The problem of non-fragile controller design has been addressed, and a non-fragile guaranteed cost controller (Chen and Li, 2013), a non-fragile fuzzy dissipative static output feedback control (Guan and Liu, 2016), and a non-fragile robust H∞ control (Zhang et al, 2007) have been investigated. The researchers in (Li X. et al, 2017;Duan et al, 2019) focused on the issue of non-fragile observer design.…”

Section: Introductionmentioning

confidence: 99%

“…The problem of observerbased adaptive ISMC for T-S fuzzy descriptor systems with unmeasurable premise variables and uncertainties has not been previously studied. Finally, fruitful results have been obtained for non-fragile controllers and/or observers for T-S fuzzy systems such as those in (Zhang et al, 2007;Chen and Li, 2013;Guan and Liu, 2016;Li X. et al, 2017;Duan et al, 2019) Notation: in this study, R m and R n×m denote the ndimensional real Euclidean space and the set of n × m matrices with real elements, respectively. I is the identity matrix with appropriate dimensions.…”

Section: Introductionmentioning

confidence: 99%

Non-Fragile Observer-Based Adaptive Integral Sliding Mode Control for a Class of T-S Fuzzy Descriptor Systems With Unmeasurable Premise Variables

et al. 2022

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The issue of non-fragile observer-based adaptive integral sliding mode control for a class of Takagi–Sugeno (T-S) fuzzy descriptor systems with uncertainties and unmeasurable premise variables is investigated. General nonlinear systems are represented by nonlinear T-S fuzzy descriptor models, because premise variables depend on unmeasurable system states and fuzzy models have different derivative matrices. By introducing the system state derivative as an auxiliary state vector, original fuzzy descriptor systems are transformed into augmented systems for which system properties remain the same. First, a novel integral sliding surface, which includes estimated states of the sliding mode observer and controller gain matrices, is designed to obtain estimation error dynamics and sliding mode dynamics. Then, some sufficient linear matrix inequality (LMI) conditions for designing the observer and the controller gains are derived using the appropriate fuzzy Lyapunov functions and Lyapunov theory. This approach yields asymptotically stable sliding mode dynamics. Corresponding auxiliary variables are introduced, and the Finsler's lemma is employed to eliminate coupling of controller gain matrices, observer gain matrices, Lyapunov function matrices, and/or observer gain perturbations. An observer-based integral sliding mode control strategy is obtained to assure that reachability conditions are satisfied. Moreover, a non-fragile observer and a non-fragile adaptive controller are developed to compensate for system uncertainties and perturbations in both the observer and the controller. Finally, example results are presented to illustrate the effectiveness and merits of the proposed method.

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Non-fragile guaranteed cost control for Takagi–Sugeno fuzzy hyperbolic systems

Cited by 8 publications

References 44 publications

Exponentially stable guaranteed cost control for continuous and discrete-time Takagi–Sugeno fuzzy systems

Exponentially stable guaranteed cost control for continuous and discrete-time Takagi–Sugeno fuzzy systems

Robust feedback control for T-S stochastic fuzzy hyperbolic system

Non-Fragile Observer-Based Adaptive Integral Sliding Mode Control for a Class of T-S Fuzzy Descriptor Systems With Unmeasurable Premise Variables

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