scholarly journals Approximate controllability and approximate null controllability of semilinear systems

2006 ◽  
Vol 5 (4) ◽  
pp. 953-962 ◽  
Author(s):  
Lianwen Wang ◽  
Keyword(s):  
Approximate Controllability ◽  
Null Controllability ◽  
Semilinear Systems

Lack of null controllability of viscoelastic flows

2019 ◽  
Vol 25 ◽  
pp. 60
Author(s):  
Debayan Maity ◽  
Debanjana Mitra ◽  
Michael Renardy
Keyword(s):  
Approximate Controllability ◽  
Momentum Equation ◽  
Null Controllability ◽  
Viscoelastic Flow ◽  
Viscoelastic Flows ◽  
Relaxation Mode ◽  
Maxwell Fluids ◽  
Linear Viscoelastic ◽  
Exact Null Controllability

We consider controllability of linear viscoelastic flow with a localized control in the momentum equation. We show that, for Jeffreys fluids or for Maxwell fluids with more than one relaxation mode, exact null controllability does not hold. This contrasts with known results on approximate controllability.

scholarly journals Boundary Controllability of a Pseudoparabolic Equation

2013 ◽  
Vol 2013 ◽  
pp. 1-6
Author(s):  
Qiang Tao ◽  
Hang Gao ◽  
Zheng-an Yao
Keyword(s):  
Explicit Solution ◽  
Approximate Controllability ◽  
Null Controllability ◽  
Pseudoparabolic Equation ◽  
Controllability Problem ◽  
Boundary Controllability ◽  
Boundary Controls ◽  
Controllability Property

We deal with the controllability problem for the pseudoparabolic equation by means of boundary controls. Due to the unusual spectrum of this kind of equations, we prove that the null controllability property is false. Furthermore, by the explicit solution, we show that the approximate controllability holds.

scholarly journals Exact Null Controllability, Stabilizability, and Detectability of Linear Nonautonomous Control Systems: A Quasisemigroup Approach

2018 ◽  
Vol 2018 ◽  
pp. 1-12
Author(s):  
Sutrima Sutrima ◽  
Christiana Rini Indrati ◽  
Lina Aryati
Keyword(s):  
Control Systems ◽  
Approximate Controllability ◽  
Null Controllability ◽  
Control Problems ◽  
Output Stability ◽  
Sturm Liouville ◽  
Exact Null Controllability ◽  
Analysis Of Stability ◽  
The Stability ◽  
Controllability And Observability

In the theory control systems, there are many various qualitative control problems that can be considered. In our previous work, we have analyzed the approximate controllability and observability of the nonautonomous Riesz-spectral systems including the nonautonomous Sturm-Liouville systems. As a continuation of the work, we are concerned with the analysis of stability, stabilizability, detectability, exact null controllability, and complete stabilizability of linear non-autonomous control systems in Banach spaces. The used analysis is a quasisemigroup approach. In this paper, the stability is identified by uniform exponential stability of the associated C0-quasisemigroup. The results show that, in the linear nonautonomous control systems, there are equivalences among internal stability, stabizability, detectability, and input-output stability. Moreover, in the systems, exact null controllability implies complete stabilizability.

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