Partial controllability concepts

Abstract

The main results in theory of controllability are formulated for deterministic or stochastic control systems given in a standard form. i.e., given as a first order differential equation driven by an infinitesimal generator of strongly continuous semigroup in an abstract Hilbert or Banach space and disturbed by a deterministic function or by a white noise process. At the same time, some deterministic or stochastic linear systems can be written in a standard form if the state space is enlarged. Respectively, the ordinary controllability conditions for them are too strong since they assume extended state space. It is reasonable to introduce partial controllability concepts, which assume original state space. In this paper, we study necessary and sufficient conditions of partial controllability for deterministic and stochastic linear control systems given in a standard form and their implications to particular cases.

Delay structure of wideband noises with application to filtering problems

“…The concepts of controllability for stochastic systems were an intensive research area in the last years . Recently, a developed concept of partial controllability modifies known results on controllability of stochastic systems to wideband and shifted white‐noise‐driven systems.…”

On partialS-controllability of semilinear partially observable systems

“…Proof: This is a restatement of a well-known fact for the case of the interval [T − δ, T] (see Bashirov et al, 2007).…”

“…The concepts of L-partial exact and approximate controllability were initiated in Bashirov, Etikan, and Ş emi (2010) and Bashirov, Mahmudov, Ş emi, and Etikan (2007). These concepts were motivated by the fact that the general results on controllability are obtained for the systems in a standard form: first-order deterministic differential equations (as well as stochastic equations driven by white noises).…”

“…Further discussion are given in Bashirov (1996)and Bashirov and Mahmudov (1999a, 1999b, 1999c. The partial versions are defined in Bashirov et al (2007). To define these concepts, introduce the sets…”

Approximate Controllability of Semilinear Impulsive Evolution Equations

“…This paper has been motivated by the works done in Bashirov and Ghahramanlou [1], Bashirov and Jneid [2], and Bashirov et al [3], where a new technique to prove the controllability of evolution equations without impulses is used avoiding fixed point theorems, and the work done in [4].…”