optimo

Optimization of Modelica models.

optimo uses OpenModelica for compilation of Modelica models into FMUs. It then relies on CasADi and Rockit to simulate and optimize from those models in Python.

Example

We first define our Modelica model in a .mo script.

model vdp
  "Van der Pol oscillator model."
  
  Real x1(start=0) "The first state";  
  Real x2(start=1) "The second state"; 
  input Real u(start=0) "The control signal"; 
  output Real objectiveIntegrand(start=0) "The objective signal"; 

equation
  der(x1) = (1 - x2^2) * x1 - x2 + u; 
  der(x2) = x1; 
  objectiveIntegrand = x1^2 + x2^2 + u^2;

end vdp;

Now we use this model for simulation and optimization in a Python script:

import matplotlib.pyplot as plt
from optimo.model import OptimoModel

# Compile and transfer the Modelica model
mo = OptimoModel()
mo.transfer_model(model="vdp")

# Simulate
res_sim_df = mo.simulate()

# Optimize 
mo.define_optimization(constraints={"u":(-1, 0.75)}, 
                       objective_terms=["objectiveIntegrand"])
res_ocp_df = mo.optimize()

If no input trajectories are provided, the simulation runs with the initial input values as defined in the model. When plotting these results (see full example) we obtain the following graphs:

Simulation results

Optimization results