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Moreover, compared with the relevant research results on structural controllability with minimum driver nodes, the proposed solution methodology may also be applied to other constrained network optimization problems beyond complete controllability with minimum control nodes.
In this paper, based on a given directed weighted network with both state and control nodes, a novel optimization tool with extremal dynamics to generate an optimal network topology with minimum control nodes and complete controllability under Kalman's rank condition has been developed.
In [21], R Sakthivel and Y Ren investigated the complete controllability property of a nonlinear stochastic control system with jumps in a separable Hilbert space.
Even though the concept of the approximate controllability is weaker than the complete controllability, it is prevalent to consider approximate controllable systems which can be adequate in application [5 7].
Wang and Zhou [3] investigated the complete controllability of fractional evolution systems without assuming the compactness of characteristic solution operators.
The necessary and sufficient condition for complete controllability is rank [ Q P Q P 2 Q ] = 3.
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Here, when we put an additional SRR in the x z plane, the metamaterial exhibits 2D optical functions, and adding an SRR in the y z plane, the metamaterial gains complete 3D controllability of light waves.
Uniform complete observability and controllability are key concepts for the design of state observers and controllers for linear time-varying systems.
Related to feedback control, controllability is another pivotal concept in control theory.
An extensive list of these publications focused on the complete and approximate controllability of the fractional dynamical systems can be found (see [1 5, 7, 9 47]).
The authors in [15, 16] considered weak, complete, and exact controllability of semilinear stochastic systems and stochastic functional differential in Hilbert spaces, and the obtained results therein can be applied to the stochastic systems with kinds of delays.
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