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Feedback control for damping a system of linear oscillators

Ovseevich, Alexander; Fedorov, Aleksey
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
36.71%
The paper is devoted to a design of a common bounded feedback control steering a system of an arbitrary number of linear oscillators to the equilibrium. At high energies, the control is based on the asymptotic theory of reachable sets of linear systems. With decreasing of the energy, a similar control with a reduced upper bound is used. On the final stage, the control is constructed by using the method of common Lyapunov functions. Special attention is paid to the cases of one and two oscillators.; Comment: 12 pages, 4 figures; presented at the 37th Conference and School on Information Technologies and Systems (Kaliningrad, September 1-6, 2013); the subject of the present paper has grown out of study arXiv:1308.6090 (see Appendix III); published version

Asymptotic control theory for a system of linear oscillators

Fedorov, Aleksey; Ovseevich, Alexander
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
36.71%
We present asymptotical control theory for a system of an arbitrary number of linear oscillators under common bounded control. We suggest a method for a design of a feedback control for the system. We prove by using the DiPerna-Lions theory of singular ODE that the suggested control law correctly defines a motion of the system. The obtained control is asymptotically optimal: the ratio of motion time to zero with this control to the minimum one is close to 1, if the initial energy of the system is large. Some of the results are based on a new lemma about observability of perturbed autonomous linear systems.; Comment: 32 pages; v. 2: substantially revised