- tags
- Applied maths
- resources
- Book by Daniel Liberzon

## Optimal control problem

An typical optimal control problem starts with a control system \[ \dot{x} = f(t, x, u), \quad x(t_0) = x_0 \] where \(x\) is the state of the system, \(t\) represents time and \(u\) is the control input.

The goal of an OC problem is to minimize a cost functional of the form \[ J(u) := \int_{t_0}^{t_f}L(t, x(t), u(t))dt + K(t_f, x_f). \]