Merge pull request #569 from control-toolbox/562-doc-relecture-de-la-documentation

Relecture documentation

Author: ocots

docs/src/manual-abstract.md

@@ -257,7 +257,7 @@ In the example below, there are
     ẋ(t) == [x₂(t), u(t)]
     tf ≥ 0 
     x₂(t) ≤ 1
-    u(t)^2 ≤ 1
+    0.1 ≤ u(t)^2 ≤ 1
     ...
 end
 ```
@@ -276,7 +276,7 @@ end
     ẋ(t) == [x₂(t), u(t)]
     tf >= 0 
     x₂(t) <= 1
-    u(t)^2 <= 1
+    0.1 ≤ u(t)^2 <= 1
     ...
 end
 ```

docs/src/manual-flow-ocp.md

@@ -36,7 +36,7 @@ nothing # hide
 The **pseudo-Hamiltonian** of this problem is
 
 ```math
-    H(x, p, u) = p_q\, q + p_v\, v + p^0 u^2 /2,
+    H(x, p, u) = p_q\, v + p_v\, u + p^0 u^2 /2,
 ```
 
 where $p^0 = -1$ since we are in the normal case. From the Pontryagin maximum principle, the maximising control is given in feedback form by

docs/src/manual-flow-others.md

@@ -11,10 +11,10 @@ In this tutorial, we explain the `Flow` function, in particular to compute flows
 Consider the simple optimal control problem from the [basic example page](@ref example-double-integrator-energy). The **pseudo-Hamiltonian** is
 
 ```math
-    H(x, p, u) = p_q\, q + p_v\, v + p^0 u^2 /2,
+    H(x, p, u) = p_q\, v + p_v\, u + p^0 u^2 /2,
 ```
 
-where $p^0 = -1$ since we are in the normal case. From the Pontryagin maximum principle, the maximising control is given in feedback form by
+where $x=(q,v)$, $p=(p_q,p_v)$, $p^0 = -1$ since we are in the normal case. From the Pontryagin maximum principle, the maximising control is given in feedback form by
 
 ```math
 u(x, p) = p_v

docs/src/manual-model.md

@@ -66,7 +66,7 @@ nothing # hide
 You can also compute flows (for more details, see the [flow manual](@ref manual-flow-ocp)) from the optimal control problem, providing a control law in feedback form. The **pseudo-Hamiltonian** of this problem is
 
 ```math
-    H(x, p, u) = p_q\, q + p_v\, v + p^0 u^2 /2,
+    H(x, p, u) = p_q\, v + p_v\, u + p^0 u^2 /2,
 ```
 
 where $p^0 = -1$ since we are in the normal case. From the Pontryagin maximum principle, the maximising control is given in feedback form by