Ellipsoidal Calculus for Estimation and Feedback Control
The emphasis of the present paper is to overview the constructive techniques for modeling and analyzing an array of problems in uncertain dynamics and control, as collected in monograph  and in some further investigations. It deals with problems of guaranteed control synthesis and set-valued estimation for systems that operate under “set-membership uncertainty” - unknown but bounded inputs and disturbances and presents a unified approach to these topics based on descriptions involving the notions of set-valued calculus.
Unable to display preview. Download preview PDF.
- J.S. Baras and A.B. Kurzhanski. Nonlinear filtering: the set-membership (bounding) and the H ∞ approaches. Proc. of the IFAC NOLCOS Conference, 1995.Google Scholar
- F.L. Chernousko. State Estimation for Dynamic Systems. New York: CRC Press, 1994.Google Scholar
- N.N. Krasovskii. In Russian: Game-Theoretic Problems on the Encounter of Motions. Moscow: Nauka, 1970. In English: Rendezvous Game Problems. Springfield, VA: Nat. Tech. Inf. Serv., 1971.Google Scholar
- N.N. Krasovski and A.N. Subbotin. Positional Differential Games. Berlin: Springer-Verlag, 1988.Google Scholar
- A. Krener. Necessary and sufficient conditions for worst-case H ∞ control and estimation. Math. Syst. Estim. and Control 4 (1994).Google Scholar
- A.B. Kurzhanski. Control and Observation Under Uncertainty. Moscow: Nauka, 1977.Google Scholar
- A.B. Kurzhanski and O.I. Nikonov. On the problem of synthesizing control strategies: evolution equations and set-valued integration. Dok-lady Akad. Nauk SSSR 311 (1990), 788–793.Google Scholar
- A. Kurzhanski and O.I. Nikonov. Evolution equations for tubes of trajectories of synthesized control systems. Russ. Acad, of Sci. Math. Dok-lady 48(3) (1994), 606–611.Google Scholar
- A.B. Kurzhanski and I. Vályi. Ellipsoidal Calculus for Estimation and Control. Boston: Birkhäuser, 1996.Google Scholar
- L.S. Pontryagin. Linear differential games of pursuit. Mat. Sbornik 112(154) (1980).Google Scholar
- F.C. Schweppe. Recursive state estimation: unknown but bounded errors and system inputs. IEEE, Trans. Aut. Cont., 13 (1968).Google Scholar
- A.I. Subbotin. Generalized Solutions of First-Order PDE’s. The Dynamic Optimization Perspective. Boston: Birkhäuser, 1995.Google Scholar