List of problems
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 | (2, 1) | Lagrange | ✅ u | ❌ | ❌ u | autonomous |
Double integrator energy | (2, 1) | Lagrange | ❌ | ❌ | ✅ | autonomous |
Double integrator energy cc | (2, 1) | Lagrange | ✅ u | ❌ | ✅ | autonomous |
Double integrator energy distance | (2, 1) | Bolza | ❌ | ❌ | ✅ | autonomous |
Double integrator energy sc | (2, 1) | Lagrange | ✅ x | ❌ | ✅ | autonomous |
Double integrator time | (2, 1) | Mayer | ✅ u | ❌ | ✅ | autonomous |
Goddard | (3, 1) | Mayer | ✅ x, u | ✅ | ✅ | autonomous |
LQR | (2, 1) | Lagrange | ❌ | ❌ | ✅ | autonomous |
Orbital transfert consumption | (4, 2) | Lagrange | ✅ u | ❌ | ❌ u | autonomous |
Orbital transfert energy | (4, 2) | Lagrange | ❌ | ❌ | ✅ | autonomous |
Orbital transfert time | (4, 2) | Mayer | ✅ u | ❌ | ✅ | autonomous |
Simple exponential consumption | (1, 1) | Lagrange | ✅ u | ❌ | ❌ u | autonomous |
Simple exponential energy | (1, 1) | Lagrange | ❌ | ❌ | ✅ | autonomous |
Simple exponential time | (1, 1) | Mayer | ✅ u | ❌ | ✅ | autonomous |
Simple integrator energy | (1, 1) | Lagrange | ❌ | ❌ | ✅ | autonomous |
Simple integrator lqr | (1, 1) | Bolza | ❌ | ❌ | ✅ | autonomous |
Simple integrator mixed constraint | (1, 1) | Lagrange | ✅ (x,u) | ❌ | ✅ | autonomous |
Simple integrator turnpike | (1, 1) | Lagrange | ✅ u | ✅ | ✅ | autonomous |
Simple integrator non autonomous | (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