engleski

Efficient computation of the one-step robust sets for piecewise affine systems with polytopic additive uncertainties

We propose a modification of the existing algorithm for computing the one-step robust sets for the discrete-time piecewise affine (DTPWA) systems subject to additive polytope-bounded uncertainties. In the old algorithm the Minkowski set difference between a union of polytopes (the so-called P-collection) and a polytope needs to be computed, which in turn calls twice for the computation of the set difference between a polytope and a P-collection. These set operations become computationally very demanding with the increasing number of polytopes in the P-collection and thus limit the practical applicability of the algorithm. In this paper we propose a more efficient procedure that avoids explicit evaluation of the Minkowski set difference. Our algorithm, on average, significantly reduces the complexity of the computation. We illustrate this on several examples of DTPWA systems for which the maximal robust positively invariant set is computed.

one-step robust sets; discrete-time piecewise affine systems; robust invariant sets; polytopes; additive polytope-bounded uncertainty

nije evidentirano