Approximation of Generalized Trajectories of a Linear Control System with Discontinuous Coefficients
A linear control system with resource and phase constraints and discontinuous coefficients at control is considered.The asymptotic of the trajectory bundles of the control system under infinitesimal perturbations of the phase constraints is considered.The obtained limit set is described in terms of a generalized control problem,which is constructed on the basis of extension of the original problem in the class of finitely additive measures.This approach to investigation of unstable control problems with integral constraints was suggested by A.G.Chentsov in the 1990.The limit trajectories in such problems may be discontinuous functions,which forces one to use the topology of pointwise convergence.Since this topology is nonmetrizable,the closure of sets in the general case is realized by means of nets.In this paper it is shown that every generalized trajectory,corresponding to a finitely additive measure,can be approximated by a sequence of usual trajectories.
unstable control problem generalized problem finitely additive measures approximation topology of pointwise convergence.
Svetlana Tarasova
Institute of Mathematics and Mechanics,Ural Branch of the Russian Academy of Sciences,16 S.Kovalevskaya St.,620219 Ekaterinburg Russia
国际会议
International Conference on Modelling,Identification and Control(模拟、鉴定、控制国际会议)
上海
英文
2008-06-29（万方平台首次上网日期，不代表论文的发表时间）