Update rocket_control.jl

docs/src/tutorials/nonlinear/rocket_control.jl

@@ -38,8 +38,6 @@ import Plots
 
 # * Thrust: $u_t(t)$.
 
-# Our goal is thus to maximize $x_h(T)$.
-
 # There are three equations that control the dynamics of the rocket:
 
 #  * Rate of ascent: $$\frac{d x_h}{dt} = x_v$$
@@ -57,23 +55,25 @@ import Plots
 
 # We use a discretized model of time, with a fixed number of time steps, $T$.
 
-# ## Constants
+# Our goal is thus to maximize $x_h(T)$.
+
+# ## Data
 
 # All parameters in this model have been normalized to be dimensionless, and
 # they are taken from [COPS3](https://www.mcs.anl.gov/~more/cops/cops3.pdf).
 
 h_0 = 1                      # Initial height
 v_0 = 0                      # Initial velocity
 m_0 = 1.0                    # Initial mass
-m_f = 0.6                    # Final mass
+m_T = 0.6                    # Final mass
 g_0 = 1                      # Gravity at the surface
 h_c = 500                    # Used for drag
 c = 0.5 * sqrt(g_0 * h_0)    # Thrust-to-fuel mass
 D_c = 0.5 * 620 * m_0 / g_0  # Drag scaling
 u_t_max = 3.5 * g_0 * m_0    # Maximum thrust
 T_max = 0.2                  # Number of seconds
 T = 1_000                    # Number of time steps
-Δt = 0.2 / T                 # Time per discretized step
+Δt = 0.2 / T;                # Time per discretized step
 
 # ## JuMP formulation
 
@@ -88,10 +88,10 @@ set_silent(model)
 # `t`. It is good practice for nonlinear programs to always provide a starting
 # solution for each variable.
 
-@variable(model, 0 <= x_v[1:T], start = v_0)           # Velocity
-@variable(model, 0 <= x_h[1:T], start = h_0)           # Height
-@variable(model, m_f <= x_m[1:T] <= m_0, start = m_0)  # Mass
-@variable(model, 0 <= u_t[1:T] <= u_t_max, start = 0)  # Thrust
+@variable(model, x_v[1:T] >= 0, start = v_0)           # Velocity
+@variable(model, x_h[1:T] >= 0, start = h_0)           # Height
+@variable(model, x_m[1:T] >= m_T, start = m_0)         # Mass
+@variable(model, 0 <= u_t[1:T] <= u_t_max, start = 0); # Thrust
 
 # We implement boundary conditions by fixing variables to values.
 
@@ -111,7 +111,7 @@ fix(u_t[T], 0.0; force = true)
     D[t = 1:T],
     D_c * x_v[t]^2 * exp(-h_c * (x_h[t] - h_0) / h_0),
 )
-@NLexpression(model, g[t = 1:T], g_0 * (h_0 / x_h[t])^2)
+@NLexpression(model, g[t = 1:T], g_0 * (h_0 / x_h[t])^2);
 
 # The dynamical equations are implemented as constraints.
 
@@ -121,7 +121,7 @@ fix(u_t[T], 0.0; force = true)
     [t in 2:T],
     (x_v[t] - x_v[t-1]) / Δt == (u_t[t-1] - D[t-1]) / x_m[t-1] - g[t-1],
 )
-@NLconstraint(model, [t in 2:T], (x_m[t] - x_m[t-1]) / Δt == -u_t[t-1] / c)
+@NLconstraint(model, [t in 2:T], (x_m[t] - x_m[t-1]) / Δt == -u_t[t-1] / c);
 
 # Now we optimize the model and check that we found a solution: