Maps with constraints

[mforets]

The src/maps.jl defines a bunch of structures that subtype AbstractMap. As you can see in the table below, we are missing several combinations.

Type	Constrains state	Constrains inputs	Is defined?
IdentityMap			x D
ConstrainedIdentityMap	x		D
LinearMap			x D
AffineMap			x D
LinearControlMap			x D
ConstrainedLinearMap	x		D
ConstrainedAffineMap	x		D
AffineControlMap			x D
ConstrainedAffineControlMap	x	x	x (needs update)
ConstrainedLinearControlMap	x	x	x (needs update)

---

Here are two approaches to complete the table:

1. Add all the missing combinations one by one, e.g. ConstrainedLinearMap for x -> Ax with constraints on x, etc.

2. Add a new struct by composition, defining maps with constraints, like:

struct ConstrainedMap{C, M<:AbstractMap}
    constraint::C
    map::M
end

For ...ContinuousSytem and ...DiscreteSystem we've been implementing approach 1.

I like approach 2 because it is more general. At the same time, it has less structure, because it does not speak about "constraint on what" (state or input).

[schillic]

I prefer 2.

[mforets]

And how about

At the same time, it has less structure, because it does not speak about "constraint on what" (state or input).

?

[schillic]

Add ConstrainedControlMap which can also constrain the input.