Spatiotemporal Adaptive Fuzzy Control for State Profile Tracking of Nonlinear Infinite-Dimensional Systems on a Hypercube

In this article, the issue of spatiotemporal adaptive fuzzy state profile tracking control is addressed for parabolic partial differential systems (PPDSs) on a hypercube exposed to unknown nonlinear dynamics. Specifically, a spatiotemporal fuzzy set on a hypercube is first constructed from the 3-D f...

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Published in:IEEE transactions on fuzzy systems Vol. 32; no. 2; pp. 683 - 696
Main Authors: Wang, Jun-Wei, Wei, Yong-Hang, Shi, Peng
Format: Journal Article
Language:English
Published: New York IEEE 01.02.2024
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
3-D fuzzy set
Adaptive control
adaptive fuzzy control
Adaptive systems
Aerospace electronics
Closed loops
Continuity (mathematics)
Dynamical systems
Fuzzy control
Fuzzy sets
Hilbert space
Hypercubes
infinite-dimensional systems
Mathematical models
Nonlinear dynamics
Nonlinear systems
partial differential equation (PDE)
Spatiotemporal phenomena
Stability
state profile tracking
Tracking control
Tracking errors
ISSN:1063-6706, 1941-0034
Online Access:Get full text
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Summary:In this article, the issue of spatiotemporal adaptive fuzzy state profile tracking control is addressed for parabolic partial differential systems (PPDSs) on a hypercube exposed to unknown nonlinear dynamics. Specifically, a spatiotemporal fuzzy set on a hypercube is first constructed from the 3-D fuzzy set on a simple 1-D space domain to completely take into account the spatial-temporal property of the PPDS. Then, a spatiotemporal fuzzy system is developed on an open subset to approximate any real continuous functions in a separable Hilbert space based on the spatiotemporal fuzzy set notion. It is shown that any continuous functions can be approximated by the proposed spatiotemporal fuzzy system in arbitrary precision. Both indirect and direct spatiotemporal adaptive fuzzy state profile tracking control strategies are put forth with the use of the spatiotemporal fuzzy system. The resulting closed-loop tracking error system's stability is thoroughly examined in terms of Lyapunov stability. Finally, the effectiveness and benefit of theoretical results are illustrated by extensive simulation experiments.
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ISSN:1063-6706
1941-0034
DOI:10.1109/TFUZZ.2023.3307619