Dynamic Boundary Fuzzy Control Design of Semilinear Parabolic PDE Systems With Spatially Noncollocated Discrete Observation

The problem of dynamic boundary fuzzy control design is investigated in this paper for nonlinear parabolic partial differential equation (PDE) systems with spatially noncollocated discrete observation. Two cases of noncollocated discrete observation in space (i.e., pointwise observation in space and...

Full description

Saved in:
Bibliographic Details
Published in:IEEE transactions on cybernetics 2019-08, Vol.49 (8), p.3041-3051
Main Author: Wang, Jun-Wei
Format: Article
Language:English
Subjects:
Aerospace electronics
Boundary control
Computer simulation
Control design
Controllers
distributed parameter systems
Feedback control
Fuzzy control
Fuzzy systems
Linear matrix inequalities
Mathematical analysis
Mathematical model
Mathematical models
Matrix methods
noncollocated discrete observation in space
observer-based dynamic feedback control
Observers
Parabolic differential equations
Partial differential equations
Sensors
State observers
Takagi–Sugeno (T-S) fuzzy model
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:The problem of dynamic boundary fuzzy control design is investigated in this paper for nonlinear parabolic partial differential equation (PDE) systems with spatially noncollocated discrete observation. Two cases of noncollocated discrete observation in space (i.e., pointwise observation in space and local piecewise uniform observation in space) are considered, respectively. The spatially noncollocated discrete observation makes the control design very difficult. Such design difficulty can be surmounted by an observer-based feedback control technique. It is assumed that the semilinear PDEs are accurately represented by a Takagi-Sugeno fuzzy PDE model. On the basis of the obtained fuzzy PDE model, a fuzzy Luenberger-type PDE state observer with above two cases of noncollocated discrete observation in space is first proposed for exponential estimation of the PDE system state. An observer-based dynamic fuzzy controller is then constructed such that the resulting closed-loop system is exponentially stable. Sufficient conditions on existence of such fuzzy controller are developed by Lyapunov technique with variations of vector-valued Poincaré-Wirtinger inequality, and presented in terms of linear matrix inequalities. Finally, extensive numerical simulation results of two examples are provided to support the proposed design method.
ISSN:2168-2267
2168-2275
DOI:10.1109/TCYB.2018.2838094