What are autonomous and non-autonomous systems and how are they different from each other. What are the differences between the types of systems they are describing? Do both autonomous and non-autonomous system describe dynamical systems or are dynamical systems something different?
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$\begingroup$I assume you refer to dynamical systems; that is, differential equations of the form$$ \dot x = f(x,t,u).$$
These are classified according to which terms appear in $f(x,t,u)$:
- Time invariant if $f(x,t,u)=f(x,u)$ is independent of time,
- Autonomous if $f(x,t,u) = f(x)$ is time invariant and independent of the input.
(These definitions come from Khalil 2001)
What is important is that the evolution of an autonomous system cannot be influenced using an external input and only depends on the initial condition whereas an appropriate controller can change the behavior of non-autonomous systems.
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