# Optimal control

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 $J(u) := \int_{t_0}^{t_f}L(t, x(t), u(t))dt + K(t_f, x_f).$