Catalog of contractors for dynamical systems

We now focus on time-related constraints. The following contractors provide a way to apply them on various domains including tubes, intervals and boxes.

• CtcDeriv: \(\dot{x}(t)=v(t)\)
  • Definition
  • Theoretical illustration
  • Localization example
  • Related content
• CtcEval: \(y_i=x(t_i)\)
  • Definition
  • 1d theoretical presentation
  • 2d localization example
  • Related content
• CtcLohner: \(\dot{\mathbf{x}}(t)=\mathbf{f}\big(\mathbf{x}(t)\big)\)
  • Definition
  • Simple example of use
  • Related content
• CtcPicard: \(\dot{\mathbf{x}}(t)=\mathbf{f}\big(\mathbf{x}(t)\big)\)
  • Definition
• CtcDelay: \(x(t)=y(t+a)\)
  • Definition
• CtcLinobs: \(\dot{\mathbf{x}}=\mathbf{Ax+Bu}\)
  • Definition
• CtcChain: \(\dot{x_1}=x_2,~\dot{x_2}=x_3\)
  • Definition

See also: codac-unsupported.

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How a contractor is implemented

Contractors are C++/Python objects. Some of them can be instantiated according to the problem to deal with. All of them will contract domains with the .contract() method.

Pre-defined contractors

For ease of use, some contractor objects that do not require parameters are predefined in the namespace ctc. They can be used directly without instantiation.

Contractor	Type	Code	Doc
\(\mathcal{C}_{\textrm{polar}}\)	Static	ctc::polar for C++ ctc.polar for Python	Link
\(\mathcal{C}_{\textrm{dist}}\)	Static	ctc::dist for C++ ctc.dist for Python	Link
\(\mathcal{C}_{\frac{d}{dt}}\)	Dynam.	ctc::deriv for C++ ctc.deriv for Python	Link
\(\mathcal{C}_{\textrm{eval}}\)	Dynam.	ctc::eval for C++ ctc.eval for Python	Link
\(\mathcal{C}_{\textrm{delay}}\)	Dynam.	ctc::delay for C++ ctc.delay for Python	–

Methods common to dynamic contractor objects

In the following table, ctc is an instantiation of a Ctc class.

Code	Meaning
ctc.preserve_slicing()	Specifies whether the contractor can impact the tube’s slicing or not
ctc.restrict_tdomain(tdomain)	Limits the temporal domain of the contractions