Static Output-Feedback Tracking Control for Positive Polynomial Fuzzy Systems

Fu, Lining; Lam, Hak‐Keung; Liu, Fucai; Xiao, Bo; Zhong, Zhixiong

doi:10.1109/tfuzz.2021.3065521

Cited by 18 publications

(17 citation statements)

References 52 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…∂x k with the kth component x k of x) induced from the gradient function ∂xP (x)x ∂x in the derivation process will increase the analysis difficulty. In this case, it leads to the fact that the quadratic Lyapunov function is commonly adopted in most of studies especially for complicated control problems, e.g., the output-feedback control design in [15]. Recently, to relax the using of quadratic Lyapunov function during the design, the homogeneous polynomial Lyapunov function (HPLF) has been put forward as an alternative solution [16].…”

Section: ∂P (X)mentioning

confidence: 99%

“…To the best of authors' knowledge, even the reference tracking problem and robust control problem have been investigated [15], [20], [34], there is no research to address the observer-based reference tracking control design for stochastic polynomial fuzzy system (SPFS) with the influence of external disturbance, measurement noise and system/sensor fault signal. Hence, an observer-based fault-tolerant tracking control strategy should be further investigated for SPFS.…”

Section: ∂P (X)mentioning

confidence: 99%

“…the estimation error x − x and the tracking error x − x r , respectively, R > 0 is the control weighing matrix, V 1 (x 0 , x r,0 , x0 ) is the effect of initial condition to be deducted and t f > 0 is the terminal time. For the robust H ∞ fuzzy observer-based fault-tolerant tracking control strategy in (15), if one could specify a set of fuzzy polynomial control gains and polynomial observer gains…”

Section: B Robust H∞ Observer-based Fault-tolerant Tracking Control A...mentioning

confidence: 99%

“…Therein, the design conditions are derived in terms of sum-of-square (SOS) conditions which could be solved via SOSTOOLS [12]. Several control design problems of fuzzy polynomial system have been investigated including the sliding mode control design [13], the observer-based control design [14] and the output-feedback control design [15]. However, by applying the polynomial matrix P (x) in the Lyapunov function during the design, the partial derivative of P (x) (i.e.,…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Robust H_∞ Fuzzy Observer-Based Fault-Tolerant Tracking Control for Nonlinear Stochastic System: A Sum of Square Approach

Lee

Chen

2022

IEEE Access

View full text Add to dashboard Cite

In this study, the robust H ∞ fuzzy observer-based fault-tolerant tracking control strategy is proposed for the stochastic polynomial fuzzy system (SPFS) under the effect of external disturbance, measurement noise, system/sensor fault signals and continuous/discontinuous internal random fluctuations. At first, the smoothed models of fault signals are constructed to describe their dynamic behavior. Then, by integrating the SPFS with the smoothed models of fault signals as one augmented system, the state/fault signal estimation problem can be transformed to a state estimation problem of augmented system by the proposed polynomial fuzzy observer. With the utilization of estimated state/fault signals and reference trajectory, a fuzzy polynomial fault-tolerant tracking controller can be implemented. To attenuate the effect of undesired external disturbance and measurement noise on the state/fault signal estimation and tracking control performance, the robust H ∞ fuzzy observer-based fault-tolerant tracking control strategy is proposed in this study. By utilizing the homogeneous Lyapunov function and Lipschiz condition, the Itô-Lévy formula is reformulated to relax the compensation terms of stochastic processes during the design. Then, the design conditions are derived in terms of interpolation function-dependent matrix inequality and consequently transformed to a two-step sum of square (SOS) condition design problem for the robust H ∞ fuzzy observer-based fault-tolerant tracking control strategy. A simulation example of double lane maneuvering task for autonomous ground vehicle (AGV) is provided to illustrate the effectiveness of proposed method. Index terms: Observer-based tracking control, polynomial fuzzy system, stochastic control, fault-tolerant control, sum of square (SOS).

show abstract

Section: ∂P (X)mentioning

confidence: 99%

Section: ∂P (X)mentioning

confidence: 99%

Section: B Robust H∞ Observer-based Fault-tolerant Tracking Control A...mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Robust H_∞ Fuzzy Observer-Based Fault-Tolerant Tracking Control for Nonlinear Stochastic System: A Sum of Square Approach

Lee

Chen

2022

IEEE Access

View full text Add to dashboard Cite

show abstract

“…These systems have the inherent property that their state variables are always positive under non-negative initial conditions [2]. Due to the limitation of the positivity, when positive conditions and stability conditions exist at the same time, the generation of non-convex conditions is inevitable [3], which will make the analysis of positive nonlinear systems more complicated and scarce. Therefore, the study of positive nonlinear systems has both practical value and challenges in theory.…”

Section: Introductionmentioning

confidence: 99%

Tracking Control Design for Positive T-S Fuzzy Systems Under H∞ Performance

Liu

Meng

et al. 2021

Frontiers in Artificial Intelligence and Applications

Self Cite

View full text Add to dashboard Cite

This paper is dedicated to study the tracking control problem of the positive T-S Fuzzy systems under H∞ performance. Compared with general systems, the limitation of the positive systems will bring non-convex conditions into the stability analysis. In order to overcome the challenge brought by the transformation of non-convex conditions into convex conditions, a feasible solution is presented. In addition, by using the piecewise-linear membership functions (PLMFs) technology, more effective information of membership functions (MFs) is introduced, which effectively weakens the conservativeness of the stability conditions and achieves satisfactory tracking results. Ultimately, a simulation example is shown to confirm the reliability of the design method.

show abstract

Disturbance rejection based tracking control design for fuzzy switched systems with time‐varying delays and disturbances

Sakthivel

Harshavarthini

Mohanapriya

et al. 2022

Intl J Robust & Nonlinear

View full text Add to dashboard Cite

The disturbance rejection and tracking problem of T‐S fuzzy switched systems with uncertainties, input time‐varying delays and disturbances is addressed in this article. For that cause, a modified repetitive control protocol based on the improved‐equivalent‐input‐disturbance (IEID) estimator and extended Smith predictor approach has been proposed, which guarantees the perfect disturbance estimation and tracking performances with high precision. Specifically, by incorporating the transfer function of main feedback path in conventional Smith predictor block, the input time‐varying delays are effectively compensated. In the direction of estimating the disturbances, an active disturbance rejection technique called IEID estimator approach is precisely considered. By exploiting the output of the IEID estimator and parallel distributed compensation strategy, the fuzzy rule based modified repetitive control system is formulated. Further, by making use of Lyapunov method together with average dwell‐time approach, a set of sufficient conditions in the form of matrix inequalities are established. More respectively, by solving the developed matrix inequalities, the controller and observer gain matrices are determined. At last, the method proposed in this work is validated in terms of presenting the simulation results of two numerical examples, including boiler‐turbine system.

show abstract

Static Output-Feedback Tracking Control for Positive Polynomial Fuzzy Systems

Cited by 18 publications

References 52 publications

Robust H_∞ Fuzzy Observer-Based Fault-Tolerant Tracking Control for Nonlinear Stochastic System: A Sum of Square Approach

Robust H_∞ Fuzzy Observer-Based Fault-Tolerant Tracking Control for Nonlinear Stochastic System: A Sum of Square Approach

Tracking Control Design for Positive T-S Fuzzy Systems Under H∞ Performance

Disturbance rejection based tracking control design for fuzzy switched systems with time‐varying delays and disturbances

Contact Info

Product

Resources

About

Static Output-Feedback Tracking Control for Positive Polynomial Fuzzy Systems

Cited by 18 publications

References 52 publications

Robust H∞ Fuzzy Observer-Based Fault-Tolerant Tracking Control for Nonlinear Stochastic System: A Sum of Square Approach

Robust H∞ Fuzzy Observer-Based Fault-Tolerant Tracking Control for Nonlinear Stochastic System: A Sum of Square Approach

Tracking Control Design for Positive T-S Fuzzy Systems Under H∞ Performance

Disturbance rejection based tracking control design for fuzzy switched systems with time‐varying delays and disturbances

Contact Info

Product

Resources

About

Robust H_∞ Fuzzy Observer-Based Fault-Tolerant Tracking Control for Nonlinear Stochastic System: A Sum of Square Approach

Robust H_∞ Fuzzy Observer-Based Fault-Tolerant Tracking Control for Nonlinear Stochastic System: A Sum of Square Approach