added: support box constraint in LinMPC and NonLinMPC

[franckgaga]

Following discussion at #378, it is a good idea in terms of performances to treat constraints on the decision variable as box constraints, instead of linear inequality constraints, at least for NLP and interior point methods.

In this PR, these constraints:

• limit on slack variable $\epsilon > 0$
• limits on the input increments $\mathbf{\Delta u}$,
• limits on the terminal state $\mathbf{\hat{x}}(k+H_p)$ for non-SingleShooting

are treated as box constraints. It applies to both LinMPC and NonLinMPC. Note that if there is a nonzero value in the associated softness parameters $\mathbf{c_{(\bullet)}}$ it is no longer a box constraint and the associated is treated as a linear inequality constraint, like before.

The default QP solver for LinMPC is OSQP.jl, and it does not support box constraint natively. It is still possible to define box constraints with the bridge mechanism of JuMP.jl. The new default optim argument for LinMPC is optim=JuMP.Model(OSQP.MathOptInterfaceOSQP.Optimizer, add_bridges=true). It should not affect the performances since JuMP will automatically convert them as linear equality constraints, as it was the case before this PR. It's possible that the performances with DAQP.jl will be improved however, since it supports box constraints natively.

Warning

Constructing LinMPC with optim=JuMP.Model(OSQP.MathOptInterfaceOSQP.Optimizer, add_bridges=false) will now throw an error. Please use add_bridges=true (it should not affect performances).

Let's see the benchmarks.

[codecov-commenter]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 98.60%. Comparing base (ed09542) to head (2f2cd11).

Additional details and impacted files

@@            Coverage Diff             @@
##             main     #379      +/-   ##
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+ Coverage   98.58%   98.60%   +0.01%     
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  Files          27       27              
  Lines        5512     5591      +79     
==========================================
+ Hits         5434     5513      +79     
  Misses         78       78              

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