Generalized Controls

1978 ◽  
pp. 21-35 ◽  
Author(s):  
R. V. Gamkrelidze
Keyword(s):  
Generalized Controls

scholarly journals Relaxation of the attainability problem for a linear control system of neutral type

2021 ◽  
Vol 31 (1) ◽  
pp. 70-88
Author(s):  
A.G. Chentsov ◽  
A.N. Sesekin
Keyword(s):  
Control System ◽  
Linear System ◽  
Neutral Type ◽  
Fixed Time ◽  
Linear Control System ◽  
Linear Control ◽  
Attraction Set ◽  
Attainability Domain ◽  
Generalized Controls

The problem of control of a linear system of neutral type with impulse constraints is developed. In addition, a given system of intermediate conditions is assumed. A setting is investigated in which a vanishingly small relaxation of the mentioned restrictions is allowed. In this regard, the attainability domain (AD) at a fixed time of the end of the process is replaced by a natural asymptotic analog, the attraction set (AS). To construct the latter, we use the construction of an extension in the class of finitely additive (f.-a.) measures used as generalized controls. It is shown that the AS coincides with the AD of the system in the class of generalized controls – f.-a. measures. The structure of the mentioned AS is investigated.

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