Fuzzy Backstepping Control

Author: CislunarSpace
Site: https://cislunarspace.cn

Definition

Fuzzy backstepping control combines fuzzy logic systems with backstepping methodology, leveraging fuzzy logic's ability to handle nonlinear uncertainties within backstepping's recursive design framework.

T-S Fuzzy System

Basic Structure

Rule $i$ : IF $x_1$ is $A_{i1}$ and ... and $x_n$ is $A_{in}$ , THEN $y_i = p_{i0} + p_{i1}x_1 + ... + p_{in}x_n$

Fuzzy Inference

System output is the weighted average of rule outputs:

y = \frac{\sum_{i=1}^{L} \mu_i(x) \cdot y_i}{\sum_{i=1}^{L} \mu_i(x)}

Design Procedure

1. Fuzzy Modeling

Represent nonlinear system as T-S fuzzy model convex combination:

\dot{x} = \sum_{i=1}^{L} h_i(x)(A_i x + B_i u)

2. Backstepping Design

Perform backstepping design for each rule's subsystem.

Applications in Stratospheric Airships

Altitude Control

The stratospheric airship altitude model is affected by:

Buoyancy changes with temperature (thermodynamic coupling)
Aerodynamic parameter variations with altitude
Wind disturbance uncertainties

References

Tanaka K, Wang H O. Fuzzy Control Systems Design and Analysis[M]. Wiley, 2001.
Li H, et al. Fuzzy Backstepping Control for High Altitude Airship[J]. IEEE Transactions on Fuzzy Systems, 2025.