Affiliation:
1. Institute of Mathematics and Mechanics of Russian Academy of Sciences and Ural Federal University, Ekaterinburg, Russia
Abstract
The dynamics and properties of set-valued states of differential control systems with uncertainties in initial data are studied. It is assumed that the dynamical system has a special structure, in which nonlinear terms in the right-hand sides of related differential equations are quadratic in state coordinates. 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.
Publisher
World Scientific Pub Co Pte Lt
Subject
Condensed Matter Physics,Statistical and Nonlinear Physics
Cited by
16 articles.
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1. Interacting Populations: Dynamics and Viability in Bounded Domains Under Uncertainty;13th Chaotic Modeling and Simulation International Conference;2021
2. On Ellipsoidal Estimates for Reachable Sets of the Control System;Mathematical Optimization Theory and Operations Research;2019
3. An algorithm for estimating reachable set of control system under uncertainties;APPLICATION OF MATHEMATICS IN TECHNICAL AND NATURAL SCIENCES: 11th International Conference for Promoting the Application of Mathematics in Technical and Natural Sciences - AMiTaNS’19;2019
4. External Estimates for Reachable Sets of a Control System with Uncertainty and Combined Nonlinearity;Proceedings of the Steklov Institute of Mathematics;2018-07
5. Estimation Techniques for Bilinear Control Systems;IFAC-PapersOnLine;2018