SET-VALUED DYNAMICS IN PROBLEMS OF MATHEMATICAL THEORY OF CONTROL PROCESSES AND STATE ESTIMATION
We consider some approaches to study the dynamics and properties of set-valued states of differential control systems with uncertainties in initial data. It is assumed that the dynamical system has a special structure, in which the nonlinear terms in the right-hand sides of related differential equations are quadratic in state coordinates.
The model of uncertainty considered here is deterministic, with set-membership description of uncertain items which are taken to be unknown but bounded with given bounds. We construct external and internal ellipsoidal estimates of reachable sets of nonlinear control system and find differential equations of proposed ellipsoidal estimates of reachable sets of nonlinear control system.
The results obtained for quadratic system nonlinearities are extended to other types of control systems under uncertainty. Numerical simulation results are also given.
The research was supported by the Russian Foundation for Basic Researches (RFBR) under Project 09-01-00223, by Integration Project 09-C-1-1010 of Ural Branch (UB) and Siberian Branch (SB) of the Russian Academy of Sciences (RAS), by Fundamental Research Programs "Mathematical Control Theory" (Project 09-P-1-1014) and "Fundamental Problems of Nonlinear Dynamics" (Project 09-P-1-1007) of the Presidium of RAS with the support of UB of RAS.