Skip to content

0x202 Optimal Control


The general functino to represent a smooth system is

\[\dot{x} = f(x,u)\]

where \(x\) is the state and \(u\) is the state. In a mechanical system \(x\) can be \((q, v)\) where \(q\) is configuration (might not be a vector) and \(v\) is velocity.

For example of an pendulum, \(x = (\theta, \dot\theta) \in S^1 \times R\) where \(S^1\) is a circle. this is a cylinder

Definitino (control affine systems) Many systems have the following specific structure (can be put into this form)

\[\dot{x} = f_0(x) + B(x) u\]

where \(f_0(x)\) is a drift and \(B(x)\) is the input Jacobian.


CMU 16-745 Optimal control lecture