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IEEE Transactions on Fuzzy Systems ~ Volume 17, Number 2, April 2009 pp253-484by: IEEEen |
Piecewise Fuzzy Anti-Windup Dynamic Output
Feedback Control of Nonlinear Processes With
Amplitude and Rate Actuator Saturations
Tiejun Zhang, Member, IEEE, Gang Feng, Fellow, IEEE, Huaping Liu, Member, IEEE,
and Jianhong Lu
Abstract—In this paper, a novel anti-windup dynamic output
compensator is developed to deal with the robust H∞ output
feedback control problem of nonlinear processes with amplitude
and rate actuator saturations and external disturbances. Via fuzzy
modeling of nonlinear systems, the proposed piecewise fuzzy antiwindup
dynamic output feedback controller is designed based on
piecewise quadratic Lyapunov functions. It is shown that with sector
conditions, robust output feedback stabilization of an inputconstrained
nonlinear process can be formulated as a convex optimization
problem subject to linear matrix inequalities. Simulation
study on a strongly nonlinear continuously stirred tank reactor
(CSTR) benchmark plant is given to show the performance of the
proposed anti-windup dynamic compensator.
Unreliable Communication Links
Huijun Gao, Member, IEEE, Yan Zhao, and Tongwen Chen, Fellow, IEEE
Abstract—This paper investigates the problem ofH∞ fuzzy control
of nonlinear systems under unreliable communication links.
The nonlinear plant is represented by a Takagi–Sugeno (T–S) fuzzy
model, and the control strategy takes the form of parallel distributed
compensation. The communication links existing between
the plant and controller are assumed to be imperfect (that is, data
packet dropouts occur intermittently, which appear typically in
a network environment), and stochastic variables satisfying the
Bernoulli random binary distribution are utilized to model the unreliable
communication links. Attention is focused on the design
of H∞ controllers such that the closed-loop system is stochastically
stable and preserves a guaranteed H∞ performance. Two
approaches are developed to solve this problem, based on the
quadratic Lyapunov function and the basis-dependent Lyapunov
function, respectively. Several examples are pred to illustrate
the usefulness and applicability of the developed theoretical results.
Index Terms—Basis-dependentLyapunov function,H∞ control,
nonlinear systems, Takagi–Sugeno (T–S) fuzzy systems, unreliable
communication links.
An Adaptive Consensus Support Model for Group
Decision-Making Problems in a Multigranular Fuzzy
Linguistic Context
Francisco Mata, Luis Mart´ınez, and Enrique Herrera-Viedma
Abstract—Different consensus models for group decisionmaking
(GDM) problems have been proposed in the literature.
However, all of them consider the consensus reaching process a
rigid or inflexible one because its behavior remains fixed in all
rounds of the consensus process. The aim of this paper is to improve
the consensus reaching process in GDM problems defined in
multigranular linguistic contexts, i.e., by using linguistic term sets
with different cardinality to represent experts’ preferences. To do
that, we propose an adaptive consensus support system model for
this type of decision-making problem, i.e., a process that adapts
its behavior to the agreement achieved in each round. This adaptive
model increases the convergence toward the consensus and,
therefore, reduces the number of rounds to reach it.
H∞ Fuzzy Filtering of Nonlinear Systems
With Intermittent Measurements
Huijun Gao, Member, IEEE, Yan Zhao, James Lam, Senior Member, IEEE, and Ke Chen
Abstract—This paper is concerned with the problem of H∞
fuzzy filtering of nonlinear systems with intermittent measurements.
The nonlinear plant is represented by a Takagi–Sugeno
(T–S) fuzzy model. The measurements transmission from the plant
to the filter is assumed to be imperfect, and a stochastic variable
satisfying the Bernoulli random binary distribution is utilized to
model the phenomenon of the missing measurements. Attention
is focused on the design of an H∞ filter such that the filter error
system is stochastically stable and preserves a guaranteedH∞
performance. A basis-dependent Lyapunov function approach is
developed to design the H∞ filter. By introducing some slack matrix
variables, the coupling between the Lyapunov matrix and the
system matrices is eliminated, which greatly facilitates the filterdesign
procedure. The developed theoretical results are in the form
of linear matrix inequalities (LMIs). Finally, an illustrative example
is pred to show the effectiveness of the proposed approach.
An Interval Type-2 Fuzzy Rough Set Model
for Attribute Reduction
Haoyang Wu, Yuyuan Wu, and Jinping Luo
Abstract—Rough set theory is a very useful tool for describing
and modeling vagueness in ill-defined environments. Traditional
rough set theory is restricted to crisp environments. However,
nowadays, it has been extended to fuzzy environments, resulting in
the development of the so-called fuzzy rough sets. Type-2 fuzzy sets
possess many advantages over type-1 fuzzy sets, but for the general
type-2 fuzzy sets, the computational complexity is severe. On
the other hand, set-theoretic and arithmetic computations for the
interval type-2 fuzzy sets are very simple. Motivated by the aforementioned
accomplishments, in this paper, the concept of fuzzy
rough sets is generalized to interval type-2 fuzzy environments.
Subsequently, a method of attribute reduction within the interval
type-2 fuzzy rough set framework is proposed. Lastly, the properties
of the interval type-2 fuzzy rough sets are presented.
Theory of Extended Fuzzy Discrete-Event Systems
for Handling Ranges of Knowledge Uncertainties
and Subjectivity
Xinyu Du, Student Member, IEEE, Hao Ying, Senior Member, IEEE, and Feng Lin, Senior Member, IEEE
Abstract—In 2001, we originated a theory of fuzzy discreteevent
systems (FDESs) that generalized the conventional/crisp
discrete-event systems (DESs). Vagueness and imprecision concerning
states and event transitions of DESs were represented by
membership grades and computed via fuzzy logic. Our application
of the FDES theory to computerized human immunodeficiency
virus/acquired immune deficiency syndrome treatment regimen
selection, although preliminarily successful, suggests that a more
comprehensive FDES theory is needed to address two general issues
critically important not only to biomedical applications, but
also to real-world problems in other industries. First, domain experts
should have means other than point estimates and type-1
fuzzy sets mandated in the current framework to describe uncertainties,
subjectivity, and imprecision in their (complex) knowledge
and experience. Second, when a group of expertswith distinct opinions
is involved, they should not be forced to reach consensus for
the sake of system development. This is because collective consensus
may not be achievable, which is often the case in medicine,
where individual experts’ opinions should be equally respected
since the underlying ground truth is unknown most of the time. The
theory of extended FDESpresented in this paper addresses both the
problems and contains the FDES theory as a special case. Experts
are now allowed to use interval numbers and type-1 and type-2
fuzzy sets to intuitively and quantitatively ex their diverse
knowledge and experience, whichwill then be processed by the new
theory to form fuzzy state vectors and fuzzy event transition matrices.
Accordingly, we have established mathematical operations
that cover the computations of fuzzy states, fuzzy event transitions,
and parallel composition. Numerical examples are pred.
A Hybrid Approach for Design of Stable Adaptive
Fuzzy Controllers Employing Lyapunov Theory and
Particle Swarm Optimization
Kaushik Das Sharma, Amitava Chatterjee, and Anjan Rakshit
Abstract—This paper proposes a new approach for designing
stable adaptive fuzzy controllers, which employs a hybridization
of a conventional Lyapunov-theory-based approach and a particle
swarm optimization (PSO) based stochastic optimization approach.
The objective is to design a self-adaptive fuzzy controller,
optimizing both its structures and free parameters, such that the
designed controller can guarantee desired stability and can simultaneously
pre satisfactory performance. The design methodology
for the controller simultaneously utilizes the good features of
PSO (capable of pring good global search capability, required
to pre a high degree of automation) and Lyapunov-based tuning
(pring fast adaptation utilizing a local search method).
Three different variants of the hybrid controller are proposed in
this paper. These variants are implemented for benchmark simulation
case studies and real-life experimentation, and their results
demonstrate the usefulness of the proposed approach.
Fuzzy Control for Nonlinear Uncertain
Electrohydraulic Active Suspensions
With Input Constraint
Haiping Du and Nong Zhang
Abstract—This paper presents a Takagi–Sugeno (T–S) modelbased
fuzzy control design approach for electrohydraulic active
vehicle suspensions considering nonlinear dynamics of the actuator,
sprung mass variation, and constraints on the control input.
The T–S fuzzy model is first applied to represent the nonlinear
uncertain electrohydraulic suspension. Then, a fuzzy state feedback
controller is designed for the obtained T–S fuzzy model with
optimizedH∞ performance for ride comfort by using the paralleldistributed
compensation (PDC) scheme. The sufficient conditions
for the existence of such a controller are derived in terms of linear
matrix inequalities (LMIs). Numerical simulations on a full-car
suspension model are performed to validate the effectiveness of the
proposed approach. The obtained results show that the designed
controller can achieve good suspension performance despite the
existence of nonlinear actuator dynamics, sprung mass variation,
and control input constraints.
Rapid Load Following of an SOFC Power System via
Stable Fuzzy Predictive Tracking Controller
Tiejun Zhang, Member, IEEE, and Gang Feng, Fellow, IEEE
Abstract—The solid oxide fuel cell (SOFC) is widely accepted
for clean and distributed power generation use, but critical operation
problems often occur when the stand-alone fuel cell is directly
connected to the electricity grid or the dc electric user. In order to
address these problems, in this paper, a data-driven fuzzy modeling
method is employed to identify the dynamic model of an integrated
SOFC/capacitor system. A novel offset-free input-to-state stable
fuzzy predictive controller is developed based on the obtained fuzzy
model. Both the rapid power load following and safe SOFC operation
requirements are taken into account in the design of the
closed-loop control system. Simulations are also given to demonstrate
the load following control performance of the proposed
fuzzy predictive control strategy for the SOFC/capacitor power
system.
Diagnosability of Fuzzy Discrete-Event Systems:
A Fuzzy Approach
Fuchun Liu and Daowen Qiu
Abstract—In order to more effectively cope with the real-world
problems of vagueness, fuzzy discrete-event systems (FDESs) were
proposed by Lin and Ying recently. Then we and Cao and Ying investigated
the supervisory control of FDESs independently. In this
paper, we are concerned with another important issue of FDESs,
the failure diagnosis. More specifically: 1) we propose a “fuzzy
diagnosability” approach by introducing a fuzzy diagnosability
function to characterize the diagnosability degree, which takes
values in the interval [0, 1] rather than {0, 1}; 2) based on the
observability of events, we formalize the construction of the diagnosers
that are used to perform fuzzy diagnosis; 3) a number of
basic properties of the diagnosers are investigated. In particular, we
present a necessary and sufficient condition for failure diagnosis of
FDESs. Our results generalize the important consequences of the
diagnosability for crisp discrete-event systems (DESs) introduced
by Sampath et al. The newly proposed approach allows us to deal
with the problem of diagnosability for both crisp DESs and FDESs;
4) in addition, a method for checking the fuzzy diagnosability for
FDESs is proposed. Also, some examples are pred to illustrate
the application of the diagnosability of FDESs.
On Generalized Fuzzy Belief Functions
in Infinite Spaces
Wei-Zhi Wu, Yee Leung, and Ju-Sheng Mi
Abstract—Determined by a fuzzy implication operator, a general
type of fuzzy belief structure and its induced dual pair of fuzzy
belief and plausibility functions in infinite universes of discourse
are first defined. Relationship between the belief-structure-based
and the belief-space-based fuzzy Dempster–Shafer models is then
established. It is shown that the lower and upper fuzzy probabilities
induced by the fuzzy belief space yield a dual pair of fuzzy
belief and plausibility functions. For any fuzzy belief structure,
there must exist a fuzzy belief space such that the fuzzy belief
and plausibility functions defined by the given fuzzy belief structure
are just the lower and upper fuzzy probabilities induced by
the fuzzy belief space, respectively. Essential properties of the fuzzy
belief and plausibility functions are also examined. The fuzzy belief
and plausibility functions are, respectively, a fuzzy monotone Choquet
capacity and a fuzzy alternating Choquet capacity of infinite
order.
Index Terms—Belief functions, fuzzy implication operators,
fuzzy rough sets, monotone capacity, rough sets.
Fault Detection for Fuzzy Systems With Intermittent
Measurements
Yan Zhao, James Lam, Senior Member, IEEE, and Huijun Gao, Member, IEEE
Abstract—This paper investigates the problem of fault detection
for Takagi–Sugeno (T–S) fuzzy systems with intermittent measurements.
The communication links between the plant and the fault detection
filter are assumed to be imperfect (i.e., data packet dropouts
occur intermittently, which appear typically in a network environment),
and a stochastic variable satisfying the Bernoulli random
binary distribution is utilized to model the unreliable communication
links. The aim is to design a fuzzy fault detection filter such
that, for all data missing conditions, the residual system is stochastically
stable and preserves a guaranteed performance. The problem
is solved through a basis-dependent Lyapunov function method,
which is less conservative than the quadratic approach. The results
are also extended to T–S fuzzy systems with time-varying
parameter uncertainties. All the results are formulated in the form
of linear matrix inequalities, which can be readily solved via standard
numerical software. Two examples are pred to illustrate
the usefulness and applicability of the developed theoretical results.
Robust Output Feedback Stabilization for Uncertain
Discrete-Time Fuzzy Markovian Jump Systems
With Time-Varying Delays
Yashun Zhang, Shengyuan Xu, and Baoyong Zhang
Abstract—This paper pres a delay-dependent approach to
the design of fuzzy dynamic output feedback controllers for uncertain
discrete-time fuzzy Markovian jump systems with interval
time-varying delays. First, by a fuzzy-basis-dependent and modedependent
Lyapunov functional, a stochastic stability condition is
derived by using the Finsler’s lemma. Second, in terms of linear
matrix inequalities (LMIs), a delay-dependent sufficient condition
is presented, under which there exists a fuzzy output feedback
controller such that the resulting closed-loop system is robustly
stochastically stable. A desired controller can be constructed when
these LMIs are feasible. Finally, the effectiveness of the proposed
design method is demonstrated by a simulation example.
Representation of Uncertain Multichannel Digital
Signal Spaces and Study of Pattern Recognition
Based on Metrics and Difference Values on Fuzzy
n-Cell Number Spaces
Guixiang Wang, Peng Shi, Senior Member, IEEE, and Paul Messenger
Abstract—In this paper, we discuss the problem of characterization
for uncertain multichannel digital signal spaces, propose
using fuzzy n-cell number space to represent uncertain n-channel
digital signal space, and put forward amethod of constructing such
fuzzy n-cell numbers.We introduce two new metrics and concepts
of certain types of difference values on fuzzy n-cell number space
and study their properties. Further, based on the metrics or difference
values appropriately defined, we put forward an algorithmic
version of pattern recognition in an imprecise or uncertain environment,
and we also give practical examples to show the application
and rationality of the proposed techniques.
H∞ Fuzzy Control for SystemsWith Repeated Scalar
Nonlinearities and Random Packet Losses
Hongli Dong, Zidong Wang, Senior Member, IEEE, and Huijun Gao, Member, IEEE
Abstract—This paper is concerned with the H∞ fuzzy control
problem for a class of systems with repeated scalar nonlinearities
and random packet losses. A modified Takagi–Sugeno (T–S) fuzzy
model is proposed in which the consequent parts are composed of
a set of discrete-time state equations containing a repeated scalar
nonlinearity. Such a model can describe some well-known nonlinear
systems such as recurrent neural networks. The measurement
transmission between the plant and controller is assumed to be imperfect
and a stochastic variable satisfying the Bernoulli random
binary distribution is utilized to represent the phenomenon of random
packet losses. Attention is focused on the analysis and design of
H∞ fuzzy controllers with the same repeated scalar nonlinearities
such that the closed-loop T–S fuzzy control system is stochastically
stable and preserves a guaranteed H∞ performance. Sufficient
conditions are obtained for the existence of admissible controllers,
and the cone complementarity linearization procedure is employed
to cast the controller design problem into a sequential minimization
one subject to linear matrix inequalities, which can be readily
solved by using standard numerical software. Two examples are
given to illustrate the effectiveness of the proposed design method.
The Model of Fuzzy Variable Precision Rough Sets
Suyun Zhao, Student Member, IEEE, Eric C. C. Tsang, Member, IEEE, and Degang Chen
Abstract—The fuzzy rough set (FRS) model has been introduced
to handle databases with real values. However, FRS was sensitive
to misclassification and perturbation (heremisclassificationmeans
error or missing values in classification, and perturbation means
small changes of numerical data). The variable precision rough sets
(VPRSs) model was introduced to handle databases with misclassification.
However, it could not effectively handle the real-valued
datasets. Now, it is valuable from theoretical and practical aspects
to combine FRS and VPRS so that a powerful tool, which not only
can handle numerical data but also is less sensitive to misclassification
and perturbation, can be developed. In this paper, we set
up a model named fuzzy VPRSs (FVPRSs) by combining FRS and
VPRS with the goal of making FRS a special case. First, we study
the knowledge representation ways of FRS and VPRS, and then,
propose the set approximation operators of FVPRS. Second, we
employ the discernibility matrix approach to investigate the structure
of attribute reductions in FVPRS and develop an algorithm to
find all reductions. Third, in order to overcome the NP-complete
problem of finding all reductions, we develop some fast heuristic
algorithms to obtain one near-optimal attribute reduction. Finally,
we compare FVPRS with RS, FRS, and several flexible RS-based
approaches with respect to misclassification and perturbation. The
experimental comparisons show the feasibility and effectiveness of
FVPRS
Short Papers
Intermediate Variable Normalization for Gradient Descent
Learning for Hierarchical Fuzzy System