Original scientific paper

Polytopic Computations in Constrained Optimal Control

Mato Baotić orcid.org/0000-0002-3186-8887 ; University of Zagreb, Faculty of Electrical Engineering and Computing, Zagreb, Croatia

Abstract

In the last decade a lot of research has focused on the explicit solution of optimal and robust control problems for the class of constrained discrete-time systems. Many newly developed control algorithms for such control problems internally use operations on polytopic sets. We review basic polytopic manipulations and analyze them in the context of the computational effort. We especially consider the so-called regiondiff problem where the set difference between a polyhedron and union of polyhedra needs to be computed. Regiondiff problem and related polycover problem – checking if a polytope is covered by the union of other polytopes – are utilized very often in derivation of the explicit solutions to the constrained finite time optimal control problems for piecewise affine systems. Similar observation holds for the computation of the (positive) controlled invariant sets, infinite time optimal control solution and/or controllers with reduced complexity for piecewise affine systems. We describe an in-place depth-first exploration algorithm that solves the regiondiff problem in an efficient manner. We derive strict upper bound for the computational complexity of the described algorithm. In extensive testing we show that our algorithm is superior to the mixed integer linear programming approach when solving the polycover problem.

Keywords

Polytope; Set difference; Set cover; Constrained optimal control; Discrete-time systems

Hrčak ID:

46543

URI

https://hrcak.srce.hr/46543

Publication date:

22.12.2009.

Article data in other languages: croatian

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