ubiccari
commented
5 years ago This class is able to solve optimal control problems.
Optimal control refers to the problem of finding a control law for a given system such that a certain optimality criterion is achieved. The essential features of an optimal control problem are: \begin{itemize} \item a cost functional to be minimized; \item an initial/boundary value problem for a differential equation describing the motion, in order to determine the state of the system; \item a control function; \item eventual constraints that have to be obeyed. \end{itemize}
The control may be freely chosen within the given constraints, while the state is uniquely determined by the differential equation and the initial conditions. We have to choose the control in such a way that the cost function is minimized.
This class allows treating general optimal control problems in the form \begin{equation} \min_{u\in\mathcal{U}} J, \end{equation} in which the objective functional $J$ is defined as \begin{equation} J=\Psi (x(T))+\int _{0}^{T}\mathcal{L}(x(t),u(t))\,dt \end{equation} and where $x$ is the state of a dynamical system with input $u\in\mathcal{U}$, the set of admissible controls: \begin{equation} \dot {x}=f(x,u),\quad x(0)=x_{0},\quad u(t)\in\mathcal {U},\quad t\in [0,T]. \end{equation}
Moreover, the class permits to choose among different methods for solving the minimization problem. At the present stage, the methods available are:
\begin{itemize} \item gradient method; \item gradient method with adaptive descend step; \item conjugate gradient method. \end{itemize}
https://deustotech.github.io/dycon-platform-documentation/projects/01-documentation