fuzzy and ode system

I have a system of ordinary differential equations (ODE) with some parameters (coefficients). I want to make fuzzy some of these coefficients.

What is the best way to do this in MATLAB?

[Walter Roberson]

Fuzzy systems are typically piecewise defined, and might be differentiable between the breakpoints, but typically have discontinuous first or second derivatives.

As such, most fuzzy systems are not suitable for use with any of the ode*() routines, all of which require continuous first and second derivatives within any one call.

The way to approach it with ode45() or similar would be to use an event function to terminate the integration each time you passed between fuzzy sub-domains.

[Torsten]

Maybe of interest:

https://www.researchgate.net/publication/329058957_Numerical_Solution_of_Fuzzy_Differential_Equation_FDE

[fateme zrbd]

🙏🏻🙏🏻

Answer 1

[Sam Chak]

Hi @fateme zrbd

Say the ODE is given by

where A and B are the coefficients of the state x and the input u, respectively.

From your description of the problem, if you want to fuzzifyA and B, perhaps you want to look up for the Takagi–Sugeno Fuzzy modeling approach.

[fateme zrbd]

🙏🏻🙏🏻

[Sam Chak]

You are welcome, @fateme zrbd. For a deeper treatment of the topic, considering reading "Fuzzy Control Systems Design and Analysis: A Linear Matrix Inequality Approach" by Kazuo Tanaka, and Hua O. Wang.

If you like my suggestions, please consider accepting ✔ and voting 👍 the Answer as a closure. Thanks!