The Algorithm

This part of the user’s guide describes the control to facet algorithms which are the basis for control law synthesis for PAHS.

For detailed descriptions of the theory which the toolbox is based on see the bibliography.

The algorithm implemented in the toolbox consists of a four main tasks:

  1. Compute LMIs describing the constraints

  2. Determine a feasible controllable set of facets

  3. Find a control-law in the feasible set

  4. Make a graphic representation of the results


The prerequisits for the algorithm is that the vertices of the state space simplex are known, the vertices/facets of the polytope describing the input space are known and the dynamics the affine dynamics of the system has been determined.