pyomo-cvp

Control vector parameterization for pyomo.dae.

pyomo.dae makes control profiles piecewise-constant by adding linking equality constraints (reduce_collocation_points), which keeps every collocation-point copy of the control in the model plus one equation per tied copy. pyomo-cvp does it by elimination: after any DAE discretization, each declared control keeps only its profile's free values, every other copy is substituted out of the model, and the component is replaced under its own name. The model you solve is the model you meant: no extra variables, no linking constraints.

On the classic race car problem (nfe=15, ncp=3, Lagrange-Radau):

Install

pip install pyomo-cvp

Usage

import pyomo.environ as pyo
from pyomo_cvp import declare_profile, control_value

# ... build a pyomo.dae model with control m.u over ContinuousSet m.tau ...
declare_profile(m.u, wrt=m.tau, profile="piecewise_constant")

pyo.TransformationFactory("dae.collocation").apply_to(
    m, nfe=15, ncp=3, scheme="LAGRANGE-RADAU")
pyo.TransformationFactory("cvp.parameterize").apply_to(m)

# m.u now has exactly nfe members, one per finite element
pyo.SolverFactory("ipopt").solve(m)
control_value(m.u, 0.5)   # evaluate the profile at any time

The explicit form (no declaration) is equivalent:

pyo.TransformationFactory("cvp.parameterize").apply_to(
    m, var=m.u, contset=m.tau, profile="piecewise_constant")

Works with any pyomo.dae discretization: Lagrange-Radau, Lagrange-Legendre (where it also eliminates the dangling element-boundary copies the constraint-based approach leaves unconstrained), or finite difference. Controls may carry additional (non-time) indices.

Profiles

• 'piecewise_constant' --- one free value per finite element, indexed by the element's start time (u[t0] exists; the final time carries no control).
• 'piecewise_linear' --- one free value per element boundary, continuous, interior points interpolated.
• ('reduced_collocation', k) --- k free values per element (the last k collocation points), Lagrange interpolation elsewhere; the elimination form of reduce_collocation_points(ncp=k).

Examples

Worked notebooks under examples/:

• racecar_cvp.ipynb: minimum-time race car, both invocation forms and all three profiles.
• hicks_cvp.ipynb: the Hicks-Ray CSTR.
• Quad_tank_cvp.ipynb: the quadruple-tank process.

Install their dependencies with pip install pyomo-cvp[examples].

Citing

If you use this package, please also cite the pyomo.dae framework it builds on:

Nicholson, B., Siirola, J.D., Watson, J.-P., Zavala, V.M., Biegler, L.T. (2018). pyomo.dae: a modeling and automatic discretization framework for optimization with differential and algebraic equations. Mathematical Programming Computation 10(2), 187-223. doi:10.1007/s12532-017-0127-0

@article{nicholson2018pyomodae,
  author  = {Nicholson, Bethany and Siirola, John D. and Watson, Jean-Paul
             and Zavala, Victor M. and Biegler, Lorenz T.},
  title   = {pyomo.dae: a modeling and automatic discretization framework
             for optimization with differential and algebraic equations},
  journal = {Mathematical Programming Computation},
  volume  = {10},
  number  = {2},
  pages   = {187--223},
  year    = {2018},
  doi     = {10.1007/s12532-017-0127-0}
}

Maintainer

Maintained by @devin-griff. Issues and pull requests welcome.

License

BSD 3-Clause License. See LICENSE.