Abstract
AbstractIn many applications, uncertainty and imprecision in control systems require the focus on reachable sets instead of single state vectors. Then, closed-loop controls also refer to these attainable sets leading to a class of set evolution problems. We suggest sufficient conditions for its well-posedness and for approximating their solutions by intersections of finitely many time-dependent ellipsoids characterized by solutions to a system of ordinary differential equations.
Funder
Air Force Office of Scientific Research
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Management Science and Operations Research,Control and Optimization
Reference66 articles.
1. Aubin, J.P.: Viability Theory. Systems & Control: Foundations & Applications. Birkhäuser, Boston, MA (1991)
2. Aubin, J.P.: A note on differential calculus in metric spaces and its applications to the evolution of tubes. Bull. Pol. Acad. Sci. Math. 40(2), 151–162 (1992)
3. Aubin, J.P.: Mutational equations in metric spaces. Set-Valued Anal. 1(1), 3–46 (1993). https://doi.org/10.1007/BF01039289
4. Aubin, J.P.: Mutational and Morphological Analysis. Systems & Control: Foundations & Applications. Tools for Shape Evolution and Morphogenesis. Birkhäuser, Boston, MA (1999). https://doi.org/10.1007/978-1-4612-1576-9 (Tools for shape evolution and morphogenesis)
5. Aubin, J.P., Frankowska, H.: Set-Valued Analysis, Systems & Control: Foundations & Applications, vol. 2. Birkhäuser, Boston, MA (1990)
Cited by
1 articles.
订阅此论文施引文献
订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献
1. Invariance of sets under mutational inclusions on metric spaces;Nonlinear Differential Equations and Applications NoDEA;2023-04-20