Posts for: #control

Consider once again an optimal control problem (OCP) in continuous time: $$ \begin{equation} \begin{alignedat}{2} &\min_{x, u}{}&& \int_0^T \ell(x(t), u(t)) dt + h(x(T)) \\ &\suchthat&& \dot{x} = f(x, u), \quad t \in [0, T) \end{alignedat} \end{equation} $$

The Differential Dynamic Programming (DDP) is a nowadays quite popular optimal control algorithm, which was introduced by Jacobson all the way back in the 1970s. Recently, it has made a resurgence following work by Tassa and Todorov.

Most control loops out there used in real-world systems are simple feedback loops proportional to the error, its derivative or integral (this is called PID control). However, this kind of control can exhibit undesirable behavior such as oscillations or failing to converge to a given setpoint quickly if at all. Some more complex systems such robots, satellites or cars can come with precise performance requirements, and more carefully constructed control actions need to be supplied with guarantees about their optimality.