State-Constrained Control Under Higher Impulses
In these sections, we deal with additional constraints on the solutions to equations of Sects. 7.1 and 7.4, related to control under generalized (higher) impulses . These restrictions are an analogy of state constraints for systems controlled by ordinary impulses of Chap. 5 (see also [1, 7]). Discussing the problem of optimal control under higher impulses and state constraints we describe it first in terms of the theory of distributions [12, 13]. indicating conditions for its solvability. Then, in order to formulate conditions of optimality, we use a reduction of the system to the first-order form under vector measures, as shown in Sect. 7.3.
- 4.Ioffe, A.D., Tikhomirov, V.M.: Theory of Extremal Problems. Nort-Holland, Amsterdam (1979)Google Scholar
- 7.Kurzhanski, A.B., Filippova, T.F.: On the theory of trajectory tubes: a mathematical formalism for uncertain dynamics, viability and control. In: Advances in Nonlinear Dynamics and Control. Progress in Systems and Control Theory, vol. 41, pp. 122–188 (1993)Google Scholar
- 8.Kurzhanski, A.B., Osipov, Yu.S.: On controlling linear systems through generalized controls. Differ. Uravn. 5(8), 1360–1370 (1969)Google Scholar
- 9.Leitman, G.: Optimality and reachability with feedback controls. Dynamical Systems and Microphysics: Control Theory and Mechanics. Academic, Orlando (1982)Google Scholar
- 10.Liapounoff, A.A.: Sur les fonctions-vecteurs completement additives. Bulletin de l’académie des sciences de l’URSS. Série mathématique 4, 465–478 (1940)Google Scholar
- 14.Zavalischin, S.T.: On the question of the general form of a linear equation, I, II. Differ. Equ. 7(5), 791–797; 7(6), 981–989Google Scholar