control-to-facet

Piecewise affine control to facet feedback controller

This source code implements a control-to-facet controller on a polytope.

Problem statement:

Given an affine system $\dot{x} = Ax + Bu + c$ on a full dimensional polytope $P$ with a certain facet $F_{i}$, find a feedback control law $u = f(x)$ such that for any initial state $x(0) \in P$, there is a finite time $T$, where the system $x(T)$ reaches or exits the facet $F_{i}$. For the theory and the math, please refer the literature in the doc/literature.

Solution:

The problem is worked out here and the source code is available here.

Results:

The visual representation of the polytope facets (including normals) and the trajectory exiting the desired facet can be seen in the picture.

Steps to run:

1. Open control2facet.m.
2. Set the vertices of the polytopes (triangle in this example).
3. Set the normal vectors to the facets.
4. Run control2facet.m.