fuzzy and ode system
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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?
3 个评论
Walter Roberson
2022-8-2
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
2022-8-2
fateme zrbd
2022-8-3
采纳的回答
Sam Chak
2022-8-2
1 个投票
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.
2 个评论
fateme zrbd
2022-8-3
Sam Chak
2022-8-3
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!
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