Evolution Equations and Control Theory
Latest Publications


TOTAL DOCUMENTS

447
(FIVE YEARS 217)

H-INDEX

14
(FIVE YEARS 5)

Published By American Institute Of Mathematical Sciences

2163-2480

2022 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Jochen Schmid

<p style='text-indent:20px;'>We establish an exponential stabilization result for linear port-Hamiltonian systems of first order with quite general, not necessarily continuous, energy densities. In fact, we have only to require the energy density of the system to be of bounded variation. In particular, and in contrast to the previously known stabilization results, our result applies to vibrating strings or beams with jumps in their mass density and their modulus of elasticity.</p>


2022 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Xilu Wang ◽  
Xiaoliang Cheng

<p style='text-indent:20px;'>In this paper, we consider continuous dependence and optimal control of a dynamic elastic-viscoplastic contact model with Clarke subdifferential boundary conditions. Since the constitutive law of elastic-viscoplastic materials has an implicit expression of the stress field, the weak form of the model is an evolutionary hemivariational inequality coupled with an integral equation. By providing some equivalent weak formulations, we prove the continuous dependence of the solution on external forces and initial conditions in the weak topologies. Finally, the existence of optimal solutions to a boundary optimal control problem is established.</p>


2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Alain Haraux

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Türker Özsarı ◽  
Kemal Cem Yılmaz

<p style='text-indent:20px;'>Backstepping based controller and observer models were designed for higher order linear and nonlinear Schrödinger equations on a finite interval in [<xref ref-type="bibr" rid="b3">3</xref>] where the controller was assumed to be acting from the left endpoint of the medium. In this companion paper, we further the analysis by considering boundary controller(s) acting at the right endpoint of the domain. It turns out that the problem is more challenging in this scenario as the associated boundary value problem for the backstepping kernel becomes overdetermined and lacks a smooth solution. The latter is essential to switch back and forth between the original plant and the so called target system. To overcome this difficulty we rely on the strategy of using an imperfect kernel, namely one of the boundary conditions in kernel PDE model is disregarded. The drawback is that one loses rapid stabilization in comparison with the left endpoint controllability. Nevertheless, the exponential decay of the <inline-formula><tex-math id="M1">\begin{document}$ L^2 $\end{document}</tex-math></inline-formula>-norm with a certain rate still holds. The observer design is associated with new challenges from the point of view of wellposedness and one has to prove smoothing properties for an associated initial boundary value problem with inhomogeneous boundary data. This problem is solved by using Laplace transform in time. However, the Bromwich integral that inverts the transformed solution is associated with certain analyticity issues which are treated through a subtle analysis. Numerical algorithms and simulations verifying the theoretical results are given.</p>


2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Vyacheslav Maksimov

<p style='text-indent:20px;'>The problems of designing feedback control algorithms for parabolic and hyperbolic variational inequalities are considered. These algorithms should preserve given properties of solutions of inequalities under the action of unknown disturbances. Solving algorithms that are stable with respect to informational noises are constructed. The algorithms are based on the method of extremal shift well-known in the theory of guaranteed control.</p>


Sign in / Sign up

Export Citation Format

Share Document