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Hankel-Norm-Based Model Reduction for Stochastic Discrete-Time Nonlinear Systems in Interval Type-2 T-S Fuzzy
IEEE Transactions on Cybernetics
|January 25, 2020
Summary
This study introduces a novel Hankel-norm model reduction method for uncertain nonlinear systems using interval type-2 fuzzy logic. The approach simplifies complex systems while preserving crucial system dynamics and reducing conservativeness.
Area of Science:
- Control Systems Engineering
- Fuzzy Logic Systems
- Nonlinear System Analysis
Background:
- High-order nonlinear systems present significant modeling and control challenges.
- Interval type-2 (IT2) Takagi-Sugeno (T-S) fuzzy models effectively represent systems with uncertainty.
- Model reduction aims to simplify complex systems by decreasing their order.
Purpose of the Study:
- To develop a Hankel-norm-based model reduction technique for stochastic discrete-time IT2 T-S fuzzy systems.
- To reduce system order while accounting for the influence of IT2 membership functions.
- To minimize conservativeness in the model reduction process.
Main Methods:
- Analysis of Hankel-norm performance for stochastic discrete-time IT2 fuzzy models.
- Application of projection theorem and cone complementary linearization.
- Formulation of a convex model reduction approach using linear matrix inequalities (LMIs).
- Implementation of a membership-functions-dependent (MFD) technique.
Main Results:
- A novel convex Hankel-norm-based model reduction method is proposed.
- The method effectively reduces the order of stochastic discrete-time IT2 T-S fuzzy systems.
- The MFD technique successfully captures IT2 membership function information, reducing conservativeness.
- A numerical example validates the effectiveness of the proposed approach.
Conclusions:
- The developed Hankel-norm model reduction technique is effective for stochastic discrete-time IT2 T-S fuzzy systems.
- The proposed method offers a less conservative approach to model reduction by considering IT2 membership functions.
- This work provides a valuable tool for simplifying complex uncertain nonlinear systems.
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