2,040 research outputs found
Contributions to fuzzy polynomial techniques for stability analysis and control
The present thesis employs fuzzy-polynomial control techniques in order to
improve the stability analysis and control of nonlinear systems. Initially, it
reviews the more extended techniques in the field of Takagi-Sugeno fuzzy systems,
such as the more relevant results about polynomial and fuzzy polynomial
systems. The basic framework uses fuzzy polynomial models by Taylor series
and sum-of-squares techniques (semidefinite programming) in order to obtain
stability guarantees.
The contributions of the thesis are:
¿ Improved domain of attraction estimation of nonlinear systems for both
continuous-time and discrete-time cases. An iterative methodology based
on invariant-set results is presented for obtaining polynomial boundaries
of such domain of attraction.
¿ Extension of the above problem to the case with bounded persistent disturbances
acting. Different characterizations of inescapable sets with
polynomial boundaries are determined.
¿ State estimation: extension of the previous results in literature to the
case of fuzzy observers with polynomial gains, guaranteeing stability of
the estimation error and inescapability in a subset of the zone where the
model is valid.
¿ Proposal of a polynomial Lyapunov function with discrete delay in order
to improve some polynomial control designs from literature. Preliminary
extension to the fuzzy polynomial case.
Last chapters present a preliminary experimental work in order to check
and validate the theoretical results on real platforms in the future.Pitarch Pérez, JL. (2013). Contributions to fuzzy polynomial techniques for stability analysis and control [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/34773TESI
Stability analysis of polynomial fuzzy models via polynomial fuzzy Lyapunov functions
In this paper, the stability of continuous-time polynomial fuzzy models by means of a polynomial generalization of fuzzy Lyapunov functions is studied. Fuzzy Lyapunov functions have been fruitfully used in the literature for local analysis of Takagi-Sugeno models, a particular class of the polynomial fuzzy ones. Based on a recent Taylor-series approach which allows a polynomial fuzzy model to exactly represent a nonlinear model in a compact set of the state space, it is shown that a refinement of the polynomial Lyapunov function so as to make it share the fuzzy structure of the model proves advantageous. Conditions thus obtained are tested via available SOS software. © 2011 Elsevier B.V. All rights reserved.Bernal Reza, MÁ.; Sala, A.; Jaadari, A.; Guerra, T. (2011). Stability analysis of polynomial fuzzy models via polynomial fuzzy Lyapunov functions. Fuzzy Sets and Systems. 185(1):5-14. doi:10.1016/j.fss.2011.07.008S514185
New advances in H∞ control and filtering for nonlinear systems
The main objective of this special issue is to
summarise recent advances in H∞ control and filtering
for nonlinear systems, including time-delay, hybrid and
stochastic systems. The published papers provide new
ideas and approaches, clearly indicating the advances
made in problem statements, methodologies or applications
with respect to the existing results. The special
issue also includes papers focusing on advanced and
non-traditional methods and presenting considerable
novelties in theoretical background or experimental
setup. Some papers present applications to newly
emerging fields, such as network-based control and
estimation
Relaxed stability conditions based on Taylor series membership functions for polynomial fuzzy-model-based control systems
© 2014 IEEE. In this paper, we investigate the stability of polynomial fuzzy-model-based (PFMB) control systems, aiming to relax stability conditions by considering the information of membership functions. To facilitate the stability analysis, we propose a general form of approximated membership functions, which is implemented by Taylor series expansion. Taylor series membership functions (TSMF) can be brought into stability conditions such that the relation between membership grades and system states is expressed. To further reduce the con-servativeness, different types of information are taken into account: the boundary of membership functions, the property of membership functions, and the boundary of operating domain. Stability conditions are obtained from Lyapunov stability theory by sum of squares (SOS) approach. Simulation examples demonstrate the effect of each piece of information
A review of convex approaches for control, observation and safety of linear parameter varying and Takagi-Sugeno systems
This paper provides a review about the concept of convex systems based on Takagi-Sugeno, linear parameter varying (LPV) and quasi-LPV modeling. These paradigms are capable of hiding the nonlinearities by means of an equivalent description which uses a set of linear models interpolated by appropriately defined weighing functions. Convex systems have become very popular since they allow applying extended linear techniques based on linear matrix inequalities (LMIs) to complex nonlinear systems. This survey aims at providing the reader with a significant overview of the existing LMI-based techniques for convex systems in the fields of control, observation and safety. Firstly, a detailed review of stability, feedback, tracking and model predictive control (MPC) convex controllers is considered. Secondly, the problem of state estimation is addressed through the design of proportional, proportional-integral, unknown input and descriptor observers. Finally, safety of convex systems is discussed by describing popular techniques for fault diagnosis and fault tolerant control (FTC).Peer ReviewedPostprint (published version
Closed-form estimates of the domain of attraction for nonlinear systems via fuzzy-polynomial models
In this work, the domain of attraction of the origin of
a nonlinear system is estimated in closed-form via level sets with
polynomial boundary, iteratively computed. In particular, the
domain of attraction is expanded from a previous estimate, such
as, for instance, a classical Lyapunov level set. With the use of
fuzzy-polynomial models, the domain-of-attraction analysis can
be carried out via sum of squares optimization and an iterative
algorithm. The result is a function wich bounds the domain of
attraction, free from the usual restriction of being positive and
decrescent in all the interior of its level sets
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