Skip to content

Latest commit

 

History

History
73 lines (59 loc) · 5.06 KB

problems-list.md

File metadata and controls

73 lines (59 loc) · 5.06 KB
Raw

[List of problems](@id problems-list)

Pages = ["problems-list.md"]
Depth = 2

Characteristics of the problems

In the following table, we give some characteristics about the problems and their solutions.

Problem (x, u) dims Objective Constraint arc Singular arc Differentiable Time dependence
[Double integrator consumption](@ref DIC) (2, 1) Lagrange ✅ u ❌ ❌ u autonomous
[Double integrator energy](@ref DIE) (2, 1) Lagrange ❌ ❌ ✅  autonomous
[Double integrator energy cc](@ref DIECC) (2, 1) Lagrange ✅ u ❌ ✅ autonomous
[Double integrator energy distance](@ref DIED) (2, 1) Bolza ❌ ❌ ✅  autonomous
[Double integrator energy sc](@ref DIESC) (2, 1) Lagrange ✅ x ❌ ✅ autonomous
[Double integrator time](@ref DIT) (2, 1) Mayer ✅ u ❌ ✅ autonomous
[Goddard](@ref Godda) (3, 1) Mayer ✅ x, u ✅ ✅  autonomous
[LQR](@ref LQR) (2, 1) Lagrange ❌ ❌ ✅  autonomous
[Orbital transfert consumption](@ref OTC) (4, 2) Lagrange ✅ u ❌ ❌ u  autonomous
[Orbital transfert energy](@ref OTE) (4, 2) Lagrange ❌ ❌ ✅  autonomous
[Orbital transfert time](@ref OTT) (4, 2) Mayer ✅ u ❌ ✅  autonomous
[Simple exponential consumption](@ref SEC) (1, 1) Lagrange ✅ u ❌ ❌ u  autonomous
[Simple exponential energy](@ref SEE) (1, 1) Lagrange ❌ ❌ ✅  autonomous
[Simple exponential time](@ref SET) (1, 1) Mayer ✅ u ❌ ✅  autonomous
[Simple integrator energy](@ref SIEM) (1, 1) Lagrange ❌ ❌ ✅  autonomous
[Simple integrator lqr](@ref SILM) (1, 1) Bolza ❌ ❌ ✅  autonomous
[Simple integrator mixed constraint](@ref SICMMC) (1, 1) Lagrange ✅ (x,u) ❌ ✅  autonomous
[Simple integrator turnpike](@ref SISE) (1, 1) Lagrange ✅ u ✅ ✅  autonomous
[Simple integrator non autonomous](@ref SINA) (1, 1) Lagrange ✅ x ❌ ✅  non autonomous

Legend:

  • Problem: a name with a link to the problem page
  • (x, u) dims: dimension of the state and the control
  • Objective: Lagrange, Mayer or Bolza
  • Constraint arc (active on the solution):
    • ❌ (no)
    • ✅ x(pure state constraints)
    • ✅ u (pure control constraints)
    • ✅ (x,u) (mixed state/control constraints)
  • Singular arc: in the case of affine problems, we tell if the solution has a singular arc, that is a non-empty arc along which the switching function vanishes.
    • ❌ (no)
    • ✅ (yes)
  • Differentiable:
    • ✅ (yes)
    • ❌ x (the dynamics and/or other data from the model is non differentiable wrt to the state)
    • ❌ u (the dynamics and/or other data from the model is non differentiable wrt to the control)
  • Time dependence: autonomous or non autonomous

Get some problems for tests

To get all the problems as a Tuple of OptimalControlProblem, simply

Problems()

To get all the problems with one dimensional state and Lagrange cost:

Problems(:x_dim_1, :lagrange)

You can use more sophisticated rules to filter. You simply have to define a logical condition with the combination of symbols and the three operators: !, | and &, respectively for the negation, the disjunction and the conjunction.

Here is an example to get the problems, as a Tuple of OptimalControlProblem, whom description does not contain :lagrange, or contains :time (the or is not exclusive):

@Problems !:lagrange | :time