Convert polytope to intersection of zonotopes

[mforets]

In [1] a method is proposed to convert (exactly) an arbitrary polytope to the intersection of zonotopes.

It would be interesting to add this method. One application is to make a convenient overapproximation of the nonlinear map of a polytope; note that

f(P) = f(Z1 ∩ Z1 ∩ ... ∩ Zk) ⊆ f(Z1) ∩ f(Z2) ∩ ... ∩ f(Zk)

and one can compute f over zonotopes using affine arithmetic.

[1] Wan, J., Sharma, S., & Sutton, R. (2018). Guaranteed state estimation for nonlinear discrete-time systems via indirectly implemented polytopic set computation. IEEE Transactions on Automatic Control, 63(12), 4317-4322. PDF.

[2] dit Sandretto, J. A., & Wan, J. (2018, September). Reachability analysis of nonlinear odes using polytopic based validated runge-kutta. In International Conference on Reachability Problems (pp. 1-14). Springer, Cham.

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