Merge pull request #3220 from SciML/infiniteopt

add capability to trace MTK dynamics with InfiniteOpt

Project.toml

@@ -64,6 +64,7 @@ BifurcationKit = "0f109fa4-8a5d-4b75-95aa-f515264e7665"
 ChainRulesCore = "d360d2e6-b24c-11e9-a2a3-2a2ae2dbcce4"
 DeepDiffs = "ab62b9b5-e342-54a8-a765-a90f495de1a6"
 HomotopyContinuation = "f213a82b-91d6-5c5d-acf7-10f1c761b327"
+InfiniteOpt = "20393b10-9daf-11e9-18c9-8db751c92c57"
 LabelledArrays = "2ee39098-c373-598a-b85f-a56591580800"
 
 [extensions]
@@ -72,6 +73,7 @@ MTKChainRulesCoreExt = "ChainRulesCore"
 MTKDeepDiffsExt = "DeepDiffs"
 MTKHomotopyContinuationExt = "HomotopyContinuation"
 MTKLabelledArraysExt = "LabelledArrays"
+MTKInfiniteOptExt = "InfiniteOpt"
 
 [compat]
 AbstractTrees = "0.3, 0.4"
@@ -104,6 +106,7 @@ FunctionWrappers = "1.1"
 FunctionWrappersWrappers = "0.1"
 Graphs = "1.5.2"
 HomotopyContinuation = "2.11"
+InfiniteOpt = "0.5"
 InteractiveUtils = "1"
 JuliaFormatter = "1.0.47"
 JumpProcesses = "9.13.1"

ext/MTKInfiniteOptExt.jl

@@ -0,0 +1,26 @@
+module MTKInfiniteOptExt
+import ModelingToolkit
+import SymbolicUtils
+import NaNMath
+import InfiniteOpt
+import InfiniteOpt: JuMP, GeneralVariableRef
+
+# This file contains method definitions to make it possible to trace through functions generated by MTK using JuMP variables
+
+for ff in [acos, log1p, acosh, log2, asin, tan, atanh, cos, log, sin, log10, sqrt]
+    f = nameof(ff)
+    # These need to be defined so that JuMP can trace through functions built by Symbolics
+    @eval NaNMath.$f(x::GeneralVariableRef) = Base.$f(x)
+end
+
+# JuMP variables and Symbolics variables never compare equal. When tracing through dynamics, a function argument can be either a JuMP variable or A Symbolics variable, it can never be both.
+function Base.isequal(::SymbolicUtils.Symbolic,
+        ::Union{JuMP.GenericAffExpr, JuMP.GenericQuadExpr, InfiniteOpt.AbstractInfOptExpr})
+    false
+end
+function Base.isequal(
+        ::Union{JuMP.GenericAffExpr, JuMP.GenericQuadExpr, InfiniteOpt.AbstractInfOptExpr},
+        ::SymbolicUtils.Symbolic)
+    false
+end
+end

test/extensions/Project.toml

@@ -4,6 +4,9 @@ ChainRulesCore = "d360d2e6-b24c-11e9-a2a3-2a2ae2dbcce4"
 ChainRulesTestUtils = "cdddcdb0-9152-4a09-a978-84456f9df70a"
 ForwardDiff = "f6369f11-7733-5829-9624-2563aa707210"
 HomotopyContinuation = "f213a82b-91d6-5c5d-acf7-10f1c761b327"
+InfiniteOpt = "20393b10-9daf-11e9-18c9-8db751c92c57"
+Ipopt = "b6b21f68-93f8-5de0-b562-5493be1d77c9"
+JuMP = "4076af6c-e467-56ae-b986-b466b2749572"
 LabelledArrays = "2ee39098-c373-598a-b85f-a56591580800"
 ModelingToolkit = "961ee093-0014-501f-94e3-6117800e7a78"
 Nemo = "2edaba10-b0f1-5616-af89-8c11ac63239a"

test/extensions/test_infiniteopt.jl

@@ -0,0 +1,102 @@
+using ModelingToolkit, InfiniteOpt, JuMP, Ipopt
+using ModelingToolkit: D_nounits as D, t_nounits as t, varmap_to_vars
+
+@mtkmodel Pendulum begin
+    @parameters begin
+        g = 9.8
+        L = 0.4
+        K = 1.2
+        m = 0.3
+    end
+    @variables begin
+        θ(t) # state
+        ω(t) # state
+        τ(t) = 0 # input
+        y(t) # output
+    end
+    @equations begin
+        D(θ) ~ ω
+        D(ω) ~ -g / L * sin(θ) - K / m * ω + τ / m / L^2
+        y ~ θ * 180 / π
+    end
+end
+@named model = Pendulum()
+model = complete(model)
+
+inputs = [model.τ]
+(f_oop, f_ip), dvs, psym, io_sys = ModelingToolkit.generate_control_function(
+    model, inputs, split = false)
+
+outputs = [model.y]
+f_obs = ModelingToolkit.build_explicit_observed_function(io_sys, outputs; inputs = inputs)
+
+expected_state_order = [model.θ, model.ω]
+permutation = [findfirst(isequal(x), expected_state_order) for x in dvs] # This maps our expected state order to the actual state order
+
+##
+
+ub = varmap_to_vars([model.θ => 2pi, model.ω => 10], dvs)
+lb = varmap_to_vars([model.θ => -2pi, model.ω => -10], dvs)
+xf = varmap_to_vars([model.θ => pi, model.ω => 0], dvs)
+nx = length(dvs)
+nu = length(inputs)
+ny = length(outputs)
+
+##
+m = InfiniteModel(optimizer_with_attributes(Ipopt.Optimizer,
+    "print_level" => 0, "acceptable_tol" => 1e-3, "constr_viol_tol" => 1e-5, "max_iter" => 1000,
+    "tol" => 1e-5, "mu_strategy" => "monotone", "nlp_scaling_method" => "gradient-based",
+    "alpha_for_y" => "safer-min-dual-infeas", "bound_mult_init_method" => "mu-based", "print_user_options" => "yes"));
+
+@infinite_parameter(m, τ in [0, 1], num_supports=51,
+    derivative_method=OrthogonalCollocation(4)) # Time variable
+guess_xs = [t -> pi, t -> 0.1][permutation]
+guess_us = [t -> 0.1]
+InfiniteOpt.@variables(m,
+    begin
+        # state variables
+        (lb[i] <= x[i = 1:nx] <= ub[i], Infinite(τ), start = guess_xs[i]) # state variables
+        -10 <= u[i = 1:nu] <= 10, Infinite(τ), (start = guess_us[i]) # control variables
+        0 <= tf <= 10, (start = 5) # Final time
+        0.2 <= L <= 0.6, (start = 0.4) # Length parameter
+    end)
+
+# Trace the dynamics
+x0, p = ModelingToolkit.get_u0_p(io_sys, [model.θ => 0, model.ω => 0], [model.L => L])
+
+xp = f_oop(x, u, p, τ)
+cp = f_obs(x, u, p, τ) # Test that it's possible to trace through an observed function
+
+@objective(m, Min, tf)
+@constraint(m, [i = 1:nx], x[i](0)==x0[i]) # Initial condition
+@constraint(m, [i = 1:nx], x[i](1)==xf[i]) # Terminal state
+
+x_scale = varmap_to_vars([model.θ => 1
+                          model.ω => 1], dvs)
+
+# Add dynamics constraints
+@constraint(m, [i = 1:nx], (∂(x[i], τ) - tf * xp[i]) / x_scale[i]==0)
+
+optimize!(m)
+
+# Extract the optimal solution
+opt_tf = value(tf)
+opt_time = opt_tf * value(τ)
+opt_x = [value(x[i]) for i in permutation]
+opt_u = [value(u[i]) for i in 1:nu]
+opt_L = value(L)
+
+# Plot the results
+# using Plots
+# plot(opt_time, opt_x[1], label = "θ", xlabel = "Time [s]", layout=3)
+# plot!(opt_time, opt_x[2], label = "ω", sp=2)
+# plot!(opt_time, opt_u[1], label = "τ", sp=3)
+
+using Test
+@test opt_x[1][end]≈pi atol=1e-3
+@test opt_x[2][end]≈0 atol=1e-3
+
+@test opt_x[1][1]≈0 atol=1e-3
+@test opt_x[2][1]≈0 atol=1e-3
+
+@test opt_L≈0.2 atol=1e-3 # Smallest permissible length is optimal

test/runtests.jl

@@ -116,5 +116,6 @@ end
         @safetestset "Auto Differentiation Test" include("extensions/ad.jl")
         @safetestset "LabelledArrays Test" include("labelledarrays.jl")
         @safetestset "BifurcationKit Extension Test" include("extensions/bifurcationkit.jl")
+        @safetestset "InfiniteOpt Extension Test" include("extensions/test_infiniteopt.jl")
     end
 end