comparaison test between JuMP and OptimalControl Models

available_problems_cache.txt

@@ -0,0 +1 @@
+dielectrophoretic_particle

ext/JuMPModels/cart_pendulum.jl

@@ -21,13 +21,13 @@ function OptimalControlProblems.cart_pendulum(::JuMPBackend; nh::Int64=100)
     @variables(
         model,
         begin
-            0.0 <= tf
-            ddx
-            -max_x <= x[0:nh] <= max_x
-            -max_v <= dx[0:nh] <= max_v
-            theta[0:nh]
-            omega[0:nh]
-            -max_f <= Fex[0:nh] <= max_f
+            0.0 <= tf, (start = 0.1)
+            ddx, (start = 0.1)
+            -max_x <= x[0:nh] <= max_x, (start = 0.1)
+            -max_v <= dx[0:nh] <= max_v, (start = 0.1)
+            theta[0:nh], (start = 0.1)
+            omega[0:nh], (start = 0.1)
+            -max_f <= Fex[0:nh] <= max_f, (start = 0.1)
         end
     )
 

ext/JuMPModels/double_oscillator.jl

@@ -19,11 +19,11 @@ function OptimalControlProblems.double_oscillator(::JuMPBackend; nh::Int=100)
     @variables(
         model,
         begin
-            x1[0:nh]
-            x2[0:nh]
-            x3[0:nh]
-            x4[0:nh]
-            -1.0 <= u[0:nh] <= 1.0
+            x1[0:nh], (start = 0.1)
+            x2[0:nh], (start = 0.1)
+            x3[0:nh], (start = 0.1)
+            x4[0:nh], (start = 0.1)
+            -1.0 <= u[0:nh] <= 1.0, (start = 0.1)
         end
     )
 

ext/JuMPModels/ducted_fan.jl

@@ -14,14 +14,14 @@ function OptimalControlProblems.ducted_fan(::JuMPBackend; nh::Int=100)
 
     model = Model()
 
-    @variable(model, x1[0:nh])
-    @variable(model, v1[0:nh])
-    @variable(model, x2[0:nh])
-    @variable(model, v2[0:nh])
-    @variable(model, -deg2rad(30.0) <= α[0:nh] <= deg2rad(30.0)) # radian
-    @variable(model, vα[0:nh])
-    @variable(model, -5.0 <= u1[0:nh] <= 5.0) # [nh]
-    @variable(model, 0.0 <= u2[0:nh] <= 17.0) # [nh]
+    @variable(model, x1[0:nh], start = 0.1)
+    @variable(model, v1[0:nh], start = 0.1)
+    @variable(model, x2[0:nh], start = 0.1)
+    @variable(model, v2[0:nh], start = 0.1)
+    @variable(model, -deg2rad(30.0) <= α[0:nh] <= deg2rad(30.0), start = 0.1) # radian
+    @variable(model, vα[0:nh], start = 0.1)
+    @variable(model, -5.0 <= u1[0:nh] <= 5.0, start = 0.1) # [nh]
+    @variable(model, 0.0 <= u2[0:nh] <= 17.0, start = 0.1) # [nh]
     @variable(model, 0 <= tf, start = 1.0)
 
     @objective(model, Min, tf / nh * sum(2 * u1[t]^2 + u2[t]^2 for t in 0:nh) + μ * tf)

ext/JuMPModels/electrical_vehicle.jl

@@ -18,9 +18,9 @@ function OptimalControlProblems.electrical_vehicle(::JuMPBackend; nh::Int=100)
 
     model = Model()
 
-    @variable(model, x[0:nh])
-    @variable(model, v[0:nh])
-    @variable(model, u[0:nh])
+    @variable(model, x[0:nh], start = 0.1)
+    @variable(model, v[0:nh], start = 0.1)
+    @variable(model, u[0:nh], start = 0.1)
 
     @objective(model, Min, sum(b1 * u[t] * v[t] + b2 * u[t]^2 for t in 0:nh))
 

ext/JuMPModels/glider.jl

@@ -30,7 +30,7 @@ function OptimalControlProblems.glider(::JuMPBackend; nh::Int64=100)
     @variables(
         model,
         begin
-            0 <= t_f, (start = 1.0)
+            0 <= tf, (start = 1.0)
             0.0 <= x[k=0:nh], (start = x_0 + vx_0 * (k / nh))
             y[k=0:nh], (start = y_0 + (k / nh) * (y_f - y_0))
             0.0 <= vx[k=0:nh], (start = vx_0)
@@ -44,7 +44,7 @@ function OptimalControlProblems.glider(::JuMPBackend; nh::Int64=100)
     @expressions(
         model,
         begin
-            step, t_f / nh
+            step, tf / nh
             r[i=0:nh], (x[i] / r_0 - 2.5)^2
             u[i=0:nh], u_c * (1 - r[i]) * exp(-r[i])
             w[i=0:nh], vy[i] - u[i]

ext/JuMPModels/moonlander.jl

@@ -23,14 +23,14 @@ function OptimalControlProblems.moonlander(
     @variables(
         model,
         begin
-            0.0 <= step
+            0.0 <= step, (start = 0.1)
             # state variables
-            p1[k=0:nh]
-            p2[k=0:nh]
-            dp1[k=0:nh]
-            dp2[k=0:nh]
-            theta[k=0:nh]
-            dtheta[k=0:nh]
+            p1[k=0:nh], (start = 0.1)
+            p2[k=0:nh], (start = 0.1)
+            dp1[k=0:nh], (start = 0.1)
+            dp2[k=0:nh], (start = 0.1)
+            theta[k=0:nh], (start = 0.1)
+            dtheta[k=0:nh], (start = 0.1)
             # control variables
             0 <= F1[k=0:nh] <= max_thrust, (start = 5.0)
             0 <= F2[k=0:nh] <= max_thrust, (start = 5.0)

ext/JuMPModels/quadrotor.jl

@@ -22,17 +22,17 @@ function OptimalControlProblems.quadrotor(::JuMPBackend; nh::Int64=60)
     @variables(
         model,
         begin
-            0.0 <= tf
-            p1[0:nh]
-            p2[0:nh]
-            p3[0:nh]
-            v1[0:nh]
-            v2[0:nh]
-            v3[0:nh]
+            0.0 <= tf, (start = 0.1)
+            p1[0:nh], (start = 0.1)
+            p2[0:nh], (start = 0.1)
+            p3[0:nh], (start = 0.1)
+            v1[0:nh], (start = 0.1)
+            v2[0:nh], (start = 0.1)
+            v3[0:nh], (start = 0.1)
             atmin <= at[0:nh] <= atmax, (start = 10.0)
-            -pi / 2 <= ϕ[0:nh] <= pi / 2
-            -pi / 2 <= θ[0:nh] <= pi / 2
-            ψ[0:nh]
+            -pi / 2 <= ϕ[0:nh] <= pi / 2, (start = 0.1)
+            -pi / 2 <= θ[0:nh] <= pi / 2, (start = 0.1)
+            ψ[0:nh], (start = 0.1)
         end
     )
 

ext/JuMPModels/steering.jl

@@ -23,8 +23,11 @@ function OptimalControlProblems.steering(::JuMPBackend; nh::Int64=100)
     model = JuMP.Model()
 
     @variable(model, u_min <= u[i=1:(nh + 1)] <= u_max, start = 0.0)   # control
-    @variable(model, x[i=1:(nh + 1), j=1:4], start = gen_x0(i, j))     # state
-    @variable(model, tf, start = 1.0)                              # final time
+    @variable(model, x1[i=1:(nh + 1)], start = gen_x0(i, 1))           # state x1
+    @variable(model, x2[i=1:(nh + 1)], start = gen_x0(i, 2))           # state x2
+    @variable(model, x3[i=1:(nh + 1)], start = gen_x0(i, 3))           # state x3
+    @variable(model, x4[i=1:(nh + 1)], start = gen_x0(i, 4))           # state x4
+    @variable(model, tf, start = 1.0)                                  # final time
 
     @expression(model, h, tf / nh) # step size
     @objective(model, Min, tf)
@@ -35,18 +38,21 @@ function OptimalControlProblems.steering(::JuMPBackend; nh::Int64=100)
     @constraints(
         model,
         begin
-            con_x1[i=1:nh], x[i + 1, 1] == x[i, 1] + 0.5 * h * (x[i, 3] + x[i + 1, 3])
-            con_x2[i=1:nh], x[i + 1, 2] == x[i, 2] + 0.5 * h * (x[i, 4] + x[i + 1, 4])
-            con_x3[i=1:nh],
-            x[i + 1, 3] == x[i, 3] + 0.5 * h * (a * cos(u[i]) + a * cos(u[i + 1]))
-            con_x4[i=1:nh],
-            x[i + 1, 4] == x[i, 4] + 0.5 * h * (a * sin(u[i]) + a * sin(u[i + 1]))
+            con_x1[i=1:nh], x1[i + 1] == x1[i] + 0.5 * h * (x3[i] + x3[i + 1])
+            con_x2[i=1:nh], x2[i + 1] == x2[i] + 0.5 * h * (x4[i] + x4[i + 1])
+            con_x3[i=1:nh], x3[i + 1] == x3[i] + 0.5 * h * (a * cos(u[i]) + a * cos(u[i + 1]))
+            con_x4[i=1:nh], x4[i + 1] == x4[i] + 0.5 * h * (a * sin(u[i]) + a * sin(u[i + 1]))
         end
     )
 
     # Boundary conditions
-    @constraint(model, [j = 1:4], x[1, j] == xs[j])
-    @constraint(model, [j = 2:4], x[nh + 1, j] == xf[j])
+    @constraint(model, x1[1] == xs[1])
+    @constraint(model, x2[1] == xs[2])
+    @constraint(model, x3[1] == xs[3])
+    @constraint(model, x4[1] == xs[4])
+    @constraint(model, x2[nh + 1] == xf[2])
+    @constraint(model, x3[nh + 1] == xf[3])
+    @constraint(model, x4[nh + 1] == xf[4])
 
     return model
-end
+end

ext/JuMPModels/truck_trailer.jl

@@ -40,16 +40,16 @@ function OptimalControlProblems.truck_trailer(
         model,
         begin
             # Final time
-            0.0 <= tf
+            0.0 <= tf, (start = 0.1)
             # State variables
-            x2[0:nh]
-            y2[0:nh]
+            x2[0:nh], (start = 0.1)
+            y2[0:nh], (start = 0.1)
             -pi / 2 <= theta0[0:nh] <= pi / 2, (start = 0.1)
             -pi / 2 <= theta1[0:nh] <= pi / 2, (start = 0.0)
             theta2[0:nh], (start = 0.0)
             # Control variables
             -0.2 * speedf <= v0[0:nh] <= 0.2 * speedf, (start = -0.2)
-            -pi / 6 <= delta0[0:nh] <= pi / 6
+            -pi / 6 <= delta0[0:nh] <= pi / 6, (start = 0.1)
         end
     )
 

ext/JuMPModels/vanderpol.jl

@@ -13,9 +13,9 @@ function OptimalControlProblems.vanderpol(::JuMPBackend; nh::Int=100)
     @variables(
         model,
         begin
-            x1[0:nh]
-            x2[0:nh]
-            u[0:nh]
+            x1[0:nh], (start = 0.1)
+            x2[0:nh], (start = 0.1)
+            u[0:nh], (start = 0.1)
             step[0:nh] == tf / nh
         end
     )

ext/MetaData/beam.jl

@@ -1 +1,11 @@
-beam_meta = Dict(:name => "beam", :nh => 100, :nvar => 404, :ncon => 305, :minimize => true)
+beam_meta = Dict(
+    :name => "beam",
+    :nh => 100,
+    :nvar => 404,
+    :ncon => 305,
+    :minimize => true,
+    :state_name => ["x1", "x2"],
+    :costate_name => ["con_x1", "con_x2"],
+    :control_name => ["u"],
+    :time => ("final_time", "tf", 1.0)
+)

ext/MetaData/bioreactor.jl

@@ -1,3 +1,11 @@
 bioreactor_meta = Dict(
-    :name => "bioreactor", :nh => 100, :nvar => 505, :ncon => 404, :minimize => false
-)
+    :name => "bioreactor",
+    :nh => 100,
+    :nvar => 505,
+    :ncon => 404,
+    :minimize => false,
+    :state_name => ["y", "s", "b"],
+    :costate_name => ["con_y", "con_s", "con_b"],
+    :control_name => ["u"],
+    :time => ("final_time", "T", 300.0) # T = 10 * N where N = 30 by default
+)

ext/MetaData/cart_pendulum.jl

@@ -1,3 +1,11 @@
 cart_pendulum_meta = Dict(
-    :name => "cart_pendulum", :nh => 100, :nvar => 507, :ncon => 405, :minimize => true
-)
+    :name => "cart_pendulum",
+    :nh => 100,
+    :nvar => 507,
+    :ncon => 405,
+    :minimize => true,
+    :state_name => ["x", "dx", "theta", "omega"],
+    :costate_name => ["d_x", "d_dx", "d_theta", "d_omega"],
+    :control_name => "Fex",
+    :time => ("final_time", "tf", nothing)
+)

ext/MetaData/chain.jl

@@ -1,3 +1,11 @@
 chain_meta = Dict(
-    :name => "chain", :nh => 100, :nvar => 404, :ncon => 305, :minimize => true
-)
+    :name => "chain",
+    :nh => 100,
+    :nvar => 404,
+    :ncon => 305,
+    :minimize => true,
+    :state_name => ["x1", "x2", "x3"],
+    :costate_name => ["con_x1", "con_x2", "con_x3"],
+    :control_name => ["u"],
+    :time => ("final_time", "tf", 1.0)
+)

ext/MetaData/dielectrophoretic_particle.jl

@@ -4,4 +4,8 @@ dielectrophoretic_particle_meta = Dict(
     :nvar => 304,
     :ncon => 203,
     :minimize => true,
-)
+    :state_name => ["x", "y"],
+    :costate_name => ["con_x", "con_y"],
+    :control_name => "u",
+    :time => ("final_time", "tf", nothing)
+)

ext/MetaData/double_oscillator.jl

@@ -1,7 +1,11 @@
 double_oscillator_meta = Dict(
     :name => "double_oscillator",
-    :nh => nothing,
+    :nh => 100, #:nh => nothing,
     :nvar => nothing,
     :ncon => nothing,
     :minimize => true,
-)
+    :state_name => ["x1", "x2", "x3", "x4"],
+    :costate_name => ["con_x1", "con_x2", "con_x3", "con_x4"],
+    :control_name => "u",
+    :time => ("final_time", "tf", 2π)
+)

ext/MetaData/ducted_fan.jl

@@ -1,7 +1,11 @@
 ducted_fan_meta = Dict(
     :name => "ducted_fan",
-    :nh => nothing,
+    :nh => 100, # :nh => nothing,
     :nvar => nothing,
     :ncon => nothing,
     :minimize => true,
-)
+    :state_name => ["x1", "v1", "x2", "v2", "α", "vα"],
+    :costate_name => ["con_x1", "con_v1", "con_x2", "con_v2", "con_α", "con_vα"],
+    :control_name => ["u1", "u2"],
+    :time => ("final_time", "tf", nothing)
+)

ext/MetaData/electrical_vehicle.jl

@@ -1,7 +1,11 @@
 electrical_vehicle_meta = Dict(
     :name => "electrical_vehicle",
-    :nh => nothing,
+    :nh => 100, #:nh => nothing,
     :nvar => nothing,
     :ncon => nothing,
     :minimize => true,
-)
+    :state_name => ["x", "v"],
+    :costate_name => ["cond_x", "cond_v"],
+    :control_name => "u",
+    :time => ("final_time", "tf", 1.0)
+)

ext/MetaData/glider.jl

@@ -1,3 +1,11 @@
 glider_meta = Dict(
-    :name => "glider", :nh => 100, :nvar => 506, :ncon => 407, :minimize => false
-)
+    :name => "glider",
+    :nh => 100,
+    :nvar => 506,
+    :ncon => 407,
+    :minimize => false,
+    :state_name => ["x", "y", "vx", "vy"],
+    :costate_name => ["x_eqn", "y_eqn", "vx_eqn", "vy_eqn"],
+    :control_name => "cL",
+    :time => ("final_time", "tf", nothing)
+)

ext/MetaData/insurance.jl

@@ -1,3 +1,11 @@
 insurance_meta = Dict(
-    :name => "insurance", :nh => 100, :nvar => 910, :ncon => 809, :minimize => false
-)
+    :name => "insurance",
+    :nh => 100, #:nh => nothing,
+    :nvar => nothing,
+    :ncon => nothing,
+    :minimize => false,
+    :state_name => ["I", "m", "x3"],
+    :costate_name => ["con_dI", "con_dm", "con_dx3"],
+    :control_name => ["h", "R", "H", "U", "dUdR"],
+    :time => ("final_time", "tf", 10)
+)

ext/MetaData/jackson.jl

@@ -1,3 +1,11 @@
 jackson_meta = Dict(
-    :name => "jackson", :nh => 100, :nvar => 404, :ncon => 303, :minimize => false
-)
+    :name => "jackson",
+    :nh => 100,
+    :nvar => 404,
+    :ncon => 303,
+    :minimize => false,
+    :state_name => ["a", "b", "x3"],
+    :costate_name => ["con_da", "con_db", "con_dx3"],
+    :control_name => ["u"],
+    :time => ("final_time", "tf", 4.0)
+)

ext/MetaData/moonlander.jl

@@ -1,3 +1,11 @@
 moonlander_meta = Dict(
-    :name => "moonlander", :nh => 100, :nvar => 610, :ncon => 809, :minimize => true
-)
+    :name => "moonlander",
+    :nh => 100,
+    :nvar => 610,
+    :ncon => 809,
+    :minimize => true,
+    :state_name => ["p1", "p2", "dp1", "dp2", "theta", "dtheta"],
+    :costate_name => ["d_p1", "d_p2", "d_dp1", "d_dp2", "d_theta", "d_dtheta"],
+    :control_name => ["F1", "F2"],
+    :time => ("final_time", "tf", nothing)
+)