Adaptive Observers For Time-Series Fuzzy Systems With Unknown Polynomial Inputs.pdf

This technical report by Zs. Lendek et al. (2010) explores adaptive observer design for Takagi-Sugeno (TS) fuzzy systems affected by unknown polynomial inputs, such as biases or ramp inputs. The primary goal is to simultaneously estimate both the system state and these unknown inputs from available input and output data.

Key Points:

Problem Formulation: Focuses on TS fuzzy models with linear or affine consequents, commonly used to approximate nonlinear systems. Introduces polynomial unknown inputs (e.g., biases, ramp inputs) and unmodeled dynamics.
Observer Design: Proposes an observer designed based on the known part of the fuzzy model.
Stability Analysis: Derives conditions for asymptotic convergence of the observer, ensuring an ultimate bound on the error signal.
Simulation Validation: Demonstrates the effectiveness of the proposed approach through a simulation example.

Novelty:

Addresses a gap in existing literature by providing a method to estimate both states and unknown polynomial inputs simultaneously.
Incorporates prior knowledge of the fuzzy model into the observer design, leading to more efficient and accurate results.

Limitations:

Assumes SISO (Single Input Single Output) systems for simplicity; extension to MIMO (Multi-Input Multi-Output) systems is left as future work.
Focuses on polynomial inputs; other types of unknown inputs may require different approaches.

Applications:

The study has implications for various fields where state and input estimation are crucial, including:

Control and Monitoring: Machine tool control, manipulator applications, electricity distribution networks, wind turbines, biomechanics, traffic control.
Fault Detection and Identification: Estimating the effect of actuator failures or other unknown disturbances in dynamic systems.
* Chaotic Systems: Synchronization and secure communication in chaotic systems.