pde control
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Automatica ◽  
2021 ◽  
Vol 129 ◽  
pp. 109637
Author(s):  
Ji Wang ◽  
Miroslav Krstic

Automatica ◽  
2021 ◽  
Vol 127 ◽  
pp. 109538
Author(s):  
Shumon Koga ◽  
Iasson Karafyllis ◽  
Miroslav Krstic

2020 ◽  
Vol 24 (3) ◽  
pp. 393-408
Author(s):  
Georgy Kostin

To model vibrations in flexible structures, a generalized variational formulation of PDE control problems is considered in the frame of the method of integro-differential relations. This approach allows us to estimate a posteriori the quality of finite-dimensional approximations and, as a result, either to refine or coarsen them if necessary. Such estimates also make it possible to correct the related control signals. The procedures for solving optimization problems in dynamics of linear elasticity have been proposed based on the Ritz method and FEM. An original FEM solver for mechanical systems withvarying distributed parameters is described. The resulting control law is regularized via a quadratic cost functional including the discrepancy of the constitutive equations. The verification of optimized control for elastic rod motion involves local and integral error estimates proposed.


2020 ◽  
Vol 53 (2) ◽  
pp. 7623-7628
Author(s):  
Huan Yu ◽  
Jean Auriol ◽  
Miroslav Krstic

2020 ◽  
Author(s):  
Shumon Koga ◽  
Miroslav Krstic
Keyword(s):  

2017 ◽  
Vol 65 (5) ◽  
Author(s):  
Carmen Gräßle ◽  
Martin Gubisch ◽  
Simone Metzdorf ◽  
Sabrina Rogg ◽  
Stefan Volkwein

AbstractIn the present paper a semilinear boundary control problem is considered. For its numerical solution proper orthogonal decomposition (POD) is applied. POD is based on a Galerkin type discretization with basis elements created from the evolution problem itself. In the context of optimal control this approach may suffer from the fact that the basis elements are computed from a reference trajectory containing features which are quite different from those of the optimally controlled trajectory. Therefore, different POD basis update strategies which avoid this problem of unmodelled dynamics are compared numerically.


2015 ◽  
Vol 60 (4) ◽  
pp. 891-906 ◽  
Author(s):  
Jie Qi ◽  
Rafael Vazquez ◽  
Miroslav Krstic
Keyword(s):  

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