On polyhedral estimates for trajectory tubes of dynamical discrete-time systems with multiplicative uncertainty
Elena K. Kostousova · AIMS Press eBooks · 2011
The approach for constructing external and internal polyhedral(parallelepiped-valued) estimates of reachable sets and trajectory tubes forthe discrete-time systems with a multiplicative uncertainty (for linear systemswith the uncertainty in initial states, additive controls and system matrices) ispresented. The techniques for set-valued operations using parallelepipeds andparallelotopes as basic sets are described. The solution to an auxiliary problemof finding an internal estimate for the set which is obtained by multiplyingan interval matrix on a parallelotope is presented. Recurrence relations forevolution of estimates of reachable sets (cross-sections of trajectory tubes) aredescribed. All proposed estimates can be calculated by explicit formulas. Theresults of numerical simulations are presented.