Fuzzy tracking control design for nonlinear dynamic systems via T-S fuzzy model

Tseng, Chung‐Shi; Chen, Bor‐Sen; Uang, Huey-Jian

doi:10.1109/91.928735

Cited by 574 publications

(35 citation statements)

References 27 publications

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“…The physical meaning of fuzzy rule k is that if the premise variables z 1, i ( t ), z 2, i ( t ), ⋯, z g , i ( t ) are with the fuzzy sets F k 1 , F k 2 , ⋯, F kg , then the synchronization error dynamics in (12) can be represented by interpolating the linearized synchronization error dynamics in (20) via the fuzzy basis. The fuzzy synchronization error dynamics in (20) is referred as follows [32,40,46]:…”

Section: Resultsmentioning

confidence: 99%

Robust synchronization control scheme of a population of nonlinear stochastic synthetic genetic oscillators under intrinsic and extrinsic molecular noise via quorum sensing

Chen

Hsu

2012

BMC Systems Biology

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BackgroundCollective rhythms of gene regulatory networks have been a subject of considerable interest for biologists and theoreticians, in particular the synchronization of dynamic cells mediated by intercellular communication. Synchronization of a population of synthetic genetic oscillators is an important design in practical applications, because such a population distributed over different host cells needs to exploit molecular phenomena simultaneously in order to emerge a biological phenomenon. However, this synchronization may be corrupted by intrinsic kinetic parameter fluctuations and extrinsic environmental molecular noise. Therefore, robust synchronization is an important design topic in nonlinear stochastic coupled synthetic genetic oscillators with intrinsic kinetic parameter fluctuations and extrinsic molecular noise.ResultsInitially, the condition for robust synchronization of synthetic genetic oscillators was derived based on Hamilton Jacobi inequality (HJI). We found that if the synchronization robustness can confer enough intrinsic robustness to tolerate intrinsic parameter fluctuation and extrinsic robustness to filter the environmental noise, then robust synchronization of coupled synthetic genetic oscillators is guaranteed. If the synchronization robustness of a population of nonlinear stochastic coupled synthetic genetic oscillators distributed over different host cells could not be maintained, then robust synchronization could be enhanced by external control input through quorum sensing molecules. In order to simplify the analysis and design of robust synchronization of nonlinear stochastic synthetic genetic oscillators, the fuzzy interpolation method was employed to interpolate several local linear stochastic coupled systems to approximate the nonlinear stochastic coupled system so that the HJI-based synchronization design problem could be replaced by a simple linear matrix inequality (LMI)-based design problem, which could be solved with the help of LMI toolbox in MATLAB easily.ConclusionIf the synchronization robustness criterion, i.e. the synchronization robustness ≥ intrinsic robustness + extrinsic robustness, then the stochastic coupled synthetic oscillators can be robustly synchronized in spite of intrinsic parameter fluctuation and extrinsic noise. If the synchronization robustness criterion is violated, external control scheme by adding inducer can be designed to improve synchronization robustness of coupled synthetic genetic oscillators. The investigated robust synchronization criteria and proposed external control method are useful for a population of coupled synthetic networks with emergent synchronization behavior, especially for multi-cellular, engineered networks.

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Section: Resultsmentioning

confidence: 99%

Robust synchronization control scheme of a population of nonlinear stochastic synthetic genetic oscillators under intrinsic and extrinsic molecular noise via quorum sensing

Chen

Hsu

2012

BMC Systems Biology

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“…The T-S fuzzy models are extensively employed to represent nonlinear systems [27][28][29]. A discrete affine T-S fuzzy model is used to capture the dynamics of the USC boiler-turbine system:…”

Section: Fuzzy Extended State Observermentioning

confidence: 99%

A Sustainable Power Plant Control Strategy Based on Fuzzy Extended State Observer and Predictive Control

et al. 2018

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The control of an ultra-supercritical (USC) boiler–turbine power plant is critical in maintaining the safety of the sustainable power grid. However, it is challenging due to the internal nonlinearity, hard manipulation constraints, and widespread uncertainties. To this end, a fuzzy extended state observer (FESO)-based stable fuzzy predictive control (SFPC) approach is developed in this paper. First, the control difficulties of the USC boiler–turbine unit are analyzed. Then, based on a Takagi–Sugeno (T–S) fuzzy model, a new FESO is developed for nonlinear systems to achieve a more precise observation performance. The gain of FESO is determined by solving a series of linear matrix inequalities, while guaranteeing the stability of FESO. Then, by combining the proposed FESO with the SFPC, an integrated FESO–SFPC algorithm is devised. The disturbance rejection ability of the FESO–SFPC algorithm is analyzed theoretically. Simulation results on a 1000 MW USC boiler–turbine power plant model further validate the effectiveness of the proposed method.

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“…If all state variables in (x, t) are used as premise variables then m = n. Following the "If-then" rules in (16), the overall fuzzy stochastic PDEs system for the ecosystem in (3) can be represented as follows (Chen et al, 1999;Tseng et al, 2001;Chen and Chang, 2009)…”

Section: Robust Fuzzy Tracking Control Design Approachmentioning

confidence: 99%

“…For a more precise approximation, the influence of the fuzzy approximation errors in (18) can be incorporated in the design of the robust reference tracking control, or it can be merged with the external disturbance d(x, t), whose effect could be attenuated by the proposed robust reference tracking strategy. The details of how to deal with the effect of fuzzy approximation errors can be found in our previous studies (Tseng et al, 2001;Chang and Chen, 2010). In this study, we estimated the fuzzy approximation errors based on the following assumption:…”

Section: Robust Fuzzy Tracking Control Design Approachmentioning

confidence: 99%

“…At present, there are no direct analytic or numerical solutions for HJII or HJI except for some simple cases. The T-S fuzzy method, which interpolates several local linear models to approximate a nonlinear system, has seen recent and widespread use in solving HJI problems for nonlinear systems described by ODEs (Tanaka and Sugeno, 1992;Chen et al, 1996;Tanaka et al, 1996Tanaka et al, , 1998Chen et al, 1999Chen et al, , 2000Tseng et al, 2001;Nguang and Shi, 2003;Tanaka and Wang, 2004). Based on the method of Galerkin, which is used to derive a set of nonlinear ODEs approximating a PDEs system (Wu and Li 2008;Yuan et al, 2008), several control design schemes have been proposed to stabilise nonlinear PDEs systems.…”

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confidence: 99%

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Natural Resource Management for Nonlinear Stochastic Biotic-Abiotic Ecosystems: Robust Reference Tracking Control Strategy Using Limited Set of Controllers

Lin¹,

Chen²

2015

J ENV INFORM

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ABSTRACT. The management of natural resources has become an important subject because of the increasing population. To meet human requirements for resources such as food and water, many control strategies have been proposed to improve biomass production and nutrient supply. However, implementing these strategies may be limited by the expense of large numbers of control devices and by the effects of stochastic perturbations. In this study, a robust reference tracking control strategy for the natural resource management of nonlinear stochastic biotic-abiotic ecosystems is proposed, using a limited set of controllers, to regulate the systematic dynamics achieving a desired reference trajectory under the influence of intrinsic fluctuations and environmental disturbances. To simplify the design procedure and make the robust reference tracking control strategy more feasible, we propose a fuzzy stochastic partial differrential equations system to represent the ecosystem, itself approximated by a fuzzy stochastic spatial state space model, based on a finite difference scheme. This allows replacement of a complex Hamilton-Jacobi integral inequality by an equivalent set of local linear matrix inequalities which can be easily solved. We verify the efficiency of the proposed approach using a nonlinear stochastic biomass-nutrient control example and compare the robust tracking control performance for different arrangements of control devices. Managers may select appropriate tracking control schemes based on this comparison. The robust reference tracking control strategy can be applied not only to agricultural systems but also to biophysical systems in ecological conservation, ecosystem restoration or engineering.

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Fuzzy tracking control design for nonlinear dynamic systems via T-S fuzzy model

Cited by 574 publications

References 27 publications

Robust synchronization control scheme of a population of nonlinear stochastic synthetic genetic oscillators under intrinsic and extrinsic molecular noise via quorum sensing

Robust synchronization control scheme of a population of nonlinear stochastic synthetic genetic oscillators under intrinsic and extrinsic molecular noise via quorum sensing

A Sustainable Power Plant Control Strategy Based on Fuzzy Extended State Observer and Predictive Control

Natural Resource Management for Nonlinear Stochastic Biotic-Abiotic Ecosystems: Robust Reference Tracking Control Strategy Using Limited Set of Controllers

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