Fuzzy State-Space Modeling and Robust Observer-Based Control Design for Nonlinear Partial Differential Systems

Chen, Bor‐Sen; Chang, Young Chul

doi:10.1109/tfuzz.2009.2020506

Cited by 114 publications

(19 citation statements)

References 47 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In fact, there are many interpolation schemes for approximating a nonlinear dynamic system with several local linear dynamic systems such as Equation (60); for example, fuzzy interpolation and cubic spline interpolation methods [13]. Then, we get the following result.…”

Section: System Entropy Measurement Of Nspds Via Global Linearizationmentioning

confidence: 86%

“…The biochemical system can be formulated as follows [13] where ypx, tq is the concentration of the substrate in the biomembrane, κ is the substrate diffusion coefficient, V M is the maximum activity in one unit of the biomembrane, K M is the Michaelis constant, and K S is the substrate inhibition constant. The parameters of the biochemical enzyme system are given by κpypx, tqq " e ypx,tq , V M " 0.5, K M " 1, K S " 1 and the output coupling C " 1.…”

Section: Examplementioning

confidence: 99%

“…The boundary conditions used to restrict the concentration are zero at x " 0 and x " 1, i.e., yp0, tq " 0, yp1, tq " 0. A more detailed discussion about the enzyme can be found in [13]. Suppose that the biochemical enzyme system is under the effect of an external signal vpx, tq.…”

Section: Examplementioning

confidence: 99%

“…System entropy describes disorder or uncertainty of a physical system and can be considered to be a significant system property [12]. Real physical systems are always modeled using stochastic partial differential dynamic equation in the spatio-temporal domain [12][13][14][15][16][17]. The entropy of thermodynamic systems has been discussed in [18][19][20].…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

System Entropy Measurement of Stochastic Partial Differential Systems

Chen

Hsieh

2016

Entropy

View full text Add to dashboard Cite

System entropy describes the dispersal of a system's energy and is an indication of the disorder of a physical system. Several system entropy measurement methods have been developed for dynamic systems. However, most real physical systems are always modeled using stochastic partial differential dynamic equations in the spatio-temporal domain. No efficient method currently exists that can calculate the system entropy of stochastic partial differential systems (SPDSs) in consideration of the effects of intrinsic random fluctuation and compartment diffusion. In this study, a novel indirect measurement method is proposed for calculating of system entropy of SPDSs using a Hamilton-Jacobi integral inequality (HJII)-constrained optimization method. In other words, we solve a nonlinear HJII-constrained optimization problem for measuring the system entropy of nonlinear stochastic partial differential systems (NSPDSs). To simplify the system entropy measurement of NSPDSs, the global linearization technique and finite difference scheme were employed to approximate the nonlinear stochastic spatial state space system. This allows the nonlinear HJII-constrained optimization problem for the system entropy measurement to be transformed to an equivalent linear matrix inequalities (LMIs)-constrained optimization problem, which can be easily solved using the MATLAB LMI-toolbox (MATLAB R2014a, version 8.3). Finally, several examples are presented to illustrate the system entropy measurement of SPDSs.

show abstract

Section: System Entropy Measurement Of Nspds Via Global Linearizationmentioning

confidence: 86%

Section: Examplementioning

confidence: 99%

Section: Examplementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

System Entropy Measurement of Stochastic Partial Differential Systems

Chen

Hsieh

2016

Entropy

View full text Add to dashboard Cite

show abstract

“…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. A fuzzy infinite-dimensional state space model based on the Galerkin method has been proposed to represent a nonlinear PDEs system with some truncation error (Chen and Chang, 2009). An alternative method, the finite difference scheme (Strikwerda, 2004), has also been widely applied to obtain the numerical solutions of PDEs, and a fuzzy tracking control for nonlinear PDEs systems with environmental disturbances has been proposed based on this scheme (Chang and Chen, 2010).…”

mentioning

confidence: 99%

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

View full text Add to dashboard Cite

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.

show abstract

Adaptive control and signal processing literature survey (No. 16)

2010

Adaptive Control & Signal

View full text Add to dashboard Cite

In order to keep readers up to date, the journal will contain a list of recently published journal articles relevant to the fields of adaptive control and signal processing six times a year. This list is compiled from a wide range of journals. Please note that even though the list has been broadly categorized these classifications are by no means strict, and are there to assist the reader. Please also note that inclusion in the list is not an endorsement of a paper's quality. If you have any suggestions or comments, please e-mail Erfu Yang at erfu.yang@eee.strath.ac.uk.

show abstract

Fuzzy State-Space Modeling and Robust Observer-Based Control Design for Nonlinear Partial Differential Systems

Cited by 114 publications

References 47 publications

System Entropy Measurement of Stochastic Partial Differential Systems

System Entropy Measurement of Stochastic Partial Differential Systems

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

Adaptive control and signal processing literature survey (No. 16)

Contact Info

Product

Resources

About