On partial<i>S</i>-controllability of semilinear partially observable systems

Bashirov, Agamirza E.; Ghahramanlou, Noushin

doi:10.1080/00207179.2014.986763

Cited by 12 publications

(11 citation statements)

References 42 publications

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“…Some invariant results for wide band noise driven systems have already been obtained. In invariant maximum principle in the Pontryagin's form and controllability results for linear and nonlinear systems are established. Invariant Kalman filter is also obtained in the special cases when the signal noise is wide band but the observation noise is non‐degenerate white , and when the signal noise is white but the observations are corrupted by the sum of wide band and non‐degenerate white noises .…”

Section: Invariancementioning

confidence: 99%

Invariant Kalman Filter for Correlated Wide Band Noises

Bashirov

Abuassba

2018

Asian Journal of Control

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Kalman filtering is a powerful estimation method. One of its weaknesses is related to the white or coloured nature of the disturbing noises in the Kalman filtering model. At the same time, real noises are rarely white or coloured. They are mostly wide band. In this regard, white or coloured noise Kalman filtering makes concessions on adequacy. This pushes system scientists to develop mathematical methods of estimation for systems corrupted by wide band noises. In applications, wide band noises are detected by their autocovariance and cross‐covariance functions, which do not allow to model them uniquely. Therefore, it becomes important to develop estimation methods which are independent of a class of wide band noises, but dependent on the unique autocovariance and cross‐covariance functions. Such results are called invariant results. In this paper, we prove a complete set of invariant equations for Kalman type filter for a linear signal‐observation system corrupted by correlated wide band noises. This filter has a ready form to be used in applications, just respective numerical methods must be developed.

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Section: Invariancementioning

confidence: 99%

Invariant Kalman Filter for Correlated Wide Band Noises

Bashirov

Abuassba

2018

Asian Journal of Control

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“…Since, real systems are nonlinear by nature, in recent years numerous controllability problems for different types of nonlinear or semilinear dynamical systems have been considered in many publications. In this regard, using the new techniques avoiding fixed point theorems, Bashirov and Ghahramanlou [] and Bashirov, Mahmudov, Semi and Etikan [] studied the controllability of semilinear ordinary differential equations in Banach spaces.…”

Section: Introductionmentioning

confidence: 99%

Impulsive semilinear heat equation with delay in control and in state

Camacho

Leiva

2019

Asian Journal of Control

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In this paper, we prove the interior approximate controllability of the impulsive semilinear heat equation with delay in control and in state by proving first that the linear heat equation with delay in control is approximately controllable.After that, we add impulses and a nonlinear perturbation with delay in state, and using Rothe's fixed point theorem, we prove that the interior approximate controllability of the impulsive semilinear system. Finally, we present some open problems and a possible general framework to study the controllability of impulsive semilinear diffusion process in Hilbert spaces with delay in control and in state.

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“…where 1 2 ≤ η < 1. The controllability of semilinear control evolution equations has been studied recently by Bashirov and Ghahramanlou [5], Bashirov and Ghahramanlou [6] and Bashirov et al [7] using the new techniques that avoid fixed point theorems. The approximate controllability of semilinear evolution equation is also studied in [1,8,9,10,11,12] recently.…”

Section: Introductionmentioning

confidence: 99%

Solvability of semilinear equations in Hilbert spaces

2018

J. Nonlinear Funct. Anal.

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In this paper, we study the existence of solutions for a broad class of semilinear equations in Hilbert spaces. This is done by applying the Rothe's fixed point theorem and a characterization of dense range linear operators in Hilbert spaces. As an application, we study the approximate controllability of a semilinear control system governed by a semilinear evolution equation, and a particular case of this is a control system given by a semilinear heat equation with interior control.

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On partialS-controllability of semilinear partially observable systems

Cited by 12 publications

References 42 publications

Invariant Kalman Filter for Correlated Wide Band Noises

Invariant Kalman Filter for Correlated Wide Band Noises

Impulsive semilinear heat equation with delay in control and in state

Solvability of semilinear equations in Hilbert spaces

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