Add Docs

Author: Dutto

docs/make.jl

@@ -13,7 +13,7 @@ makedocs(
     ),
     pages = [
         "Introduction" => "index.md",
-        "2D example"   => "2D-example.md",
+        "Indirect shooting"   => "2D-example.md",
     ]
 )
 

docs/src/2D-example.md

@@ -1,3 +1,14 @@
-# Geometric preconditioner for indirect shooting
+# Optimal control problem
 
-blabla
+We consider the following optimal control problem 
+
+```math
+    \left\{ \begin{array}{ll}
+    \displaystyle \min_{x,u} \int_{t_0}^{t_f} x(t) ~\mathrm dt \\[1em]
+    \text{s.c.}~\dot x(t) = u(t), & t\in [t_0, t_f]~\mathrm{a.e.}, \\[0.5em]
+    \phantom{\mathrm{s.c.}~} u(t) \in [-1,1], & t\in [t_0, t_f], \\[0.5em]
+    \phantom{\mathrm{s.c.}~} x(t_0) = x_0, \quad x(t_f) = x_f,
+    \end{array} \right.
+```
+
+with $x_0$, $t_0$, $x_f$ and $t_f$ fixed. This problem is simple, and can be analytically solve without the use of numerical method. However, the goal is to solve this problem by indirect shooting.