Adaptive control of discrete-time state-space T–S fuzzy systems with general relative degree

Qi, Ruiyun; Tao, Gang; Tan, Chang; Yao, Xiaoyu

doi:10.1016/j.fss.2012.10.011

Cited by 30 publications

(18 citation statements)

References 29 publications

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“…affinein-the-input, triangular or other). Additional results about adaptive fuzzy controllers which are based on transformations into canonical forms can be found in [25][26][27].…”

Section: E = (A − B K T )E + Bu C + B(w +D)mentioning

confidence: 99%

“…On the other hand, differential flatness theory enables to transform the system's generic description x = f(x, u) into the canonical form and from that point on to develop adaptive control schemes. Consequently, differential flatness theory extends the class of nonlinear control systems to which adaptive neural / fuzzy control can be applied and this is a significant benefit for adaptive control theory [25][26][27][28].…”

Section: Introductionmentioning

confidence: 99%

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Flatness-Based Adaptive Fuzzy Control of Autonomous Submarines

Rigatos

Siano

2015

Intell Ind Syst

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The paper proposes adaptive fuzzy control based on differential flatness theory for autonomous submarines. It is proven that the dynamic model of the submarine, having as state variables the vessel's depth and its pitch angle, is a differentially flat one. This means that all its state variables and its control inputs can be written as differential functions of the flat output and its derivatives. By exploiting differential flatness properties the system's dynamic model is written in the multivariable linear canonical (Brunovsky) form, for which the design of a state feedback controller becomes possible. After this transformation, the new control inputs of the system contain unknown nonlinear parts, which are identified with the use of neurofuzzy approximators. The learning procedure for these estimators is determined by the requirement the first derivative of the closed-loop's Lyapunov function to be a negative one. Moreover, the Lyapunov stability analysis shows that H-infinity tracking performance is succeeded for the feedback control loop and this assures improved robustness to the aforementioned model uncertainty as well as to external perturbations. The efficiency of the proposed adaptive fuzzy control scheme is confirmed through simulation experiments.Electronic supplementary material The online version of this article

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“…affinein-the-input, triangular or other). Additional results about adaptive fuzzy controllers which are based on transformations into canonical forms can be found in [25][26][27].…”

Section: E = (A − B K T )E + Bu C + B(w +D)mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Flatness-Based Adaptive Fuzzy Control of Autonomous Submarines

Rigatos

Siano

2015

Intell Ind Syst

View full text Add to dashboard Cite

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“…On the one side, adaptive fuzzy control has been proven to be an efficient nonlinear control method [13][14][15][16][17][18][19][20]. On the other side, differential flatness theory stands for a major direction in the design of nonlinear control systems [21][22][23][24][25][26][27].…”

Section: Introductionmentioning

confidence: 99%

Flatness-Based Adaptive Neurofuzzy Control of Chaotic Dynamical Systems

Rigatos

Siano

2016

Intell Ind Syst

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The paper proposes a solution to the problem of control of nonlinear chaotic dynamical systems, which is based on differential flatness theory and on adaptive fuzzy control. An adaptive fuzzy controller is designed for chaotic dynamical systems, under the constraint that the system's model is unknown. The control algorithm aims at satisfying the H ∞ tracking performance criterion, which means that the influence of the modeling errors and the external disturbances on the tracking error is attenuated to an arbitrary desirable level. After transforming the chaotic system's model into a linear form, the resulting control inputs are shown to contain nonlinear elements which depend on the system's parameters. The nonlinear terms which appear in the control inputs are approximated with the use of neurofuzzy networks. It is shown that a suitable learning law can be defined for the aforementioned neuro-fuzzy approximators so as to preserve the closed-loop system stability. With the use of Lyapunov stability analysis it is proven that the proposed adaptive fuzzy control scheme results in H ∞ tracking performance. The efficiency of the adaptive fuzzy control method is checked through simulation experiments, using as case study the Lorenz chaotic oscillator.

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“…In [17], a T-S fuzzy model is proposed to represent the nonlinear model of microelectromechanical systems gyroscope; a robust adaptive sliding mode control with online identification for the upper bounds of external disturbances and an adaptive estimator for the model uncertainty parameters are proposed in the Lyapunov framework. In [18], a new normal form of a global noncanonical form T-S fuzzy model was derived, and a new solution framework was developed for adaptive control of general discrete-time state-space T-S fuzzy systems with a relative degree. In [19], a novel design scheme of stable adaptive fuzzy control for a class of nonlinear systems was proposed.…”

Section: Introductionmentioning

confidence: 99%

Adaptive Stabilization Control for a Class of Complex Nonlinear Systems Based on T-S Fuzzy Bilinear Model

Xing

Shi

2015

Mathematical Problems in Engineering

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This paper proposes a stable adaptive fuzzy control scheme for a class of nonlinear systems with multiple inputs. The multiple inputs T-S fuzzy bilinear model is established to represent the unknown complex systems. A parallel distributed compensation (PDC) method is utilized to design the fuzzy controller without considering the error due to fuzzy modelling and the sufficient conditions of the closed-loop system stability with respect to decay rate are derived by linear matrix inequalities (LMIs). Then the errors caused by fuzzy modelling are considered and the method of adaptive control is used to reduce the effect of the modelling errors, and dynamic performance of the closed-loop system is improved. By Lyapunov stability criterion, the resulting closed-loop system is proved to be asymptotically stable. The main contribution is to deal with the differences between the T-S fuzzy bilinear model and the real system; a global asymptotically stable adaptive control scheme is presented for real complex systems. Finally, illustrative examples are provided to demonstrate the effectiveness of the results proposed in this paper.

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Adaptive control of discrete-time state-space T–S fuzzy systems with general relative degree

Cited by 30 publications

References 29 publications

Flatness-Based Adaptive Fuzzy Control of Autonomous Submarines

Flatness-Based Adaptive Fuzzy Control of Autonomous Submarines

Flatness-Based Adaptive Neurofuzzy Control of Chaotic Dynamical Systems

Adaptive Stabilization Control for a Class of Complex Nonlinear Systems Based on T-S Fuzzy Bilinear Model

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