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I have a question about the control of a non-affine system.

Here is my system $\dot{x} = a(u) + b(u) . u$

\begin{equation}\label{a_beta} a(u) = 0.22 \left( \frac{116(u^3 + 1)-4.06 \lambda }{(\lambda + 0.08u)(u^3 + 1)} -5 \right) \exp \left( -\frac{12.5}{\Gamma} \right) \end{equation} and \begin{equation}\label{b_beta} b(u) = 0.22 \left( - 0.4 -\frac{0.3248}{(\lambda + 0.08u)(u^3 + 1)} \right) \exp \left( -\frac{12.5}{\Gamma} \right) \end{equation} also \begin{equation} \Gamma = \frac{1}{\left(\frac{1}{\lambda + 0.08u}\right) - \left(\frac{0.035}{u^3 + 1}\right)} \end{equation} such that $\lambda$ is a positive constant number.

Do you have any idea how to handle this non-affine system?

I would be grateful if someone reply to this question.

Ehsan Aslmostafa
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  • Depends on what you mean by "handle this ... system". You could always try to linearize the system and get a controller for that system. Then if you are lucky and your initial conditions are close enough to the equilibrium it will stabilize it. – dgadjov Aug 18 '24 at 18:32

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