A New Method For Hybrid-fuzzy Identification.pdf

This technical report introduces a novel method for identifying non-linear hybrid systems with mixed continuous and discrete states. Hybrid systems, encompassing both continuous and integer/discrete variables, pose unique challenges in modeling and control. The proposed approach leverages fuzzy clustering and principal component analysis (PCA) to overcome these complexities.

Key Features:

1. Hybrid Identification: The method determines the hybrid nature of the system by inversely applying the merge method for clusters, enabling the identification of unknown switching points based on input-output data alone.

2. Fuzzy Modeling: It employs Takagi-Sugeno (TS) fuzzy models with Gaussian membership functions (MFs) to represent non-linearities within each discrete mode. Binary MFs capture the hard partition between discrete modes and their corresponding continuous behavior.

3. PCA Integration: PCA is used to reduce dimensionality and simplify the identification process, making it more computationally efficient.

Illustrative Experiment:

The report presents a case study on a hybrid-tank system to demonstrate the effectiveness of the proposed method. Results show its ability to accurately capture both continuous and discrete dynamics, outperforming existing methods that rely solely on piecewise ARX (PWARX) models.

Benefits:

- No Prior Knowledge Required: The approach does not demand prior knowledge of discrete modes or system structure.
- Versatility: Suitable for various hybrid systems with different non-linearities.
- Efficiency: Utilizes PCA to streamline the identification process.

Applications:

This method finds applications in control design, system modeling, and predictive control for hybrid systems across diverse industries, including manufacturing, robotics, and power systems.