On Polyhedral Estimates of Reachable Sets of Discrete-Time Systems with Uncertain Matrices and Integral Bounds on Additive Terms
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We consider discrete-time systems of bilinear type for the case when interval bounds on the coefficients of the system are imposed, additive input terms are restricted by integral non-quadratic constraints, and initial states belong to given sets, which are assumed to be parallelepipeds. An approach for estimating the reachable sets is presented. It is based on considering reachable sets in the “extended” space and constructing external and internal estimates of them in the form of polytopes of some special shape. The specific cross-sections of these polytopes provide the parallelepiped-valued or parallelotope-valued estimates of the reachable sets in the “initial” space. Evolution of the estimates in the “extended” space is determined by recurrence relations. All the estimates can be calculated by explicit formulas. The main attention is paid to internal estimates. Illustrative examples are presented.
KeywordsDiscrete-time systems Reachable sets Integral constraints Uncertain matrices Polyhedral estimates Parallelepipeds Parallelotopes
The research was supported by the Russian Foundation for Basic Research (RFBR) under Project 18-01-00544a.
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