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The issue at hand is how the additional stabilizing terms affect the resulting controller.
Numerical tests assess the suitability of the approach, the influence of the parameters, and the effectiveness of the new stabilizing terms.
This is because the results are largely insensitive to the definition of the residual, to CFD errors, and to the CFD method itself, which may contain artificial stabilizing terms.
Indeed, a strong action of dissipative terms could make the existence of global solutions easier, since they play the role of stabilizing terms and their smoothing effect makes the blow-up more difficult [21, 26].
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Then, a critic network is constructed to solve the Hamilton Jacobi Bellman equation corresponding to the nominal system, where an additional stabilizing term is introduced to verify the stability.
With introducing two additional terms, namely, the stabilizing term and the robustifying term to update the critic NN, the initial stabilizing control is no longer required.
By employing a stabilizing term in the critic NN weight updating law, there is no requirement for adopting initial admissible control in the proposed algorithm.
Experimental simulations are also conducted to verify the efficient performance of the present design method, especially the major role that the stabilizing term performed.
So we add as a stabilizing term diffusion parallel to the characteristics, which turns out to be the Lax Wendroff diffusion rate.
The main objective lies in that establishing an additional stabilizing term to reinforce the traditional training process of the critic neural network, so that to reduce the requirement with respect to the initial stabilizing control, and therefore, bring in an obvious convenience to the adaptive-critic-based learning control implementation.
These involve either additional stabilizing force terms, or a fully implicit coupling of the Navier Stokes and Cahn Hilliard equation.
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