Control synthesis via parallelotopes: optimzation and parallel compuations

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Abstract
The constructive schemes based on the parallelotopic estimates of trajectory tubes are presented for solving the feedback terminal target control problems for linear dynamic systems under uncertainty and without that. The families of external and internal parallelotopic estimates for solvability tubes are introduced. Each particular approximate tube satisfies the generalized semigroup property and may be calculated independently of the others. This further allows to parallelize computations. The introduced families ensure exact representations of the tube sections (through intersections and unions) for the case without uncertainty. Locally volume-optimal external and internal estimates are found. The introduced internal estimates are the “parallelotopic solvability tubes”. This fact allows to synthesize a control strategy in an analytical form on the base of a solution of some specific mathematical programming problem. The results of numerical modelling are presented.