Necessary and sufficient conditions for the vibrations of a bounded string with directional derivatives in the boundary conditions

Lomovtsev, F. E.; Novikov, E. N.

doi:10.1134/s0012266114010170

Cited by 4 publications

(1 citation statement)

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“…In recent years, feedback control theory has made great progress due to its wide applications in science, engineering, and other real world. Feedback control systems are everywhere around us, including trajectory planning of robotic manipulators, guidance of moving targets by tactical missiles, and control of room temperature and chord vibration; see, e.g., [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15] and the references therein for more details.…”

Section: Introductionmentioning

confidence: 99%

Optimal feedback control for a class of second-order evolution differential inclusions with Clarke’s subdifferential

2022

J. Nonlinear Var. Anal.

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The goal of this paper is to study optimal feedback control for a class of non-autonomous second-order evolution inclusions with Clarke's subdifferential in a separable reflexive Banach space. We only assume that the second order evolution operator involved satisfies the strong continuity condition instead of the compactness, which was used in previous literature. By using the properties of multimaps and Clarke's subdifferential, we assume some sufficient conditions to ensure the existence of feasible pairs of the feedback control systems. Furthermore, we also prove the existence of optimal control pairs.

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Section: Introductionmentioning

confidence: 99%

Optimal feedback control for a class of second-order evolution differential inclusions with Clarke’s subdifferential

2022

J. Nonlinear Var. Anal.

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Directional Derivative Problem for the Telegraph Equation with a Dirac Potential

2018

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Classical solution of the mixed problem for the Klein – Gordon – Fock type equation in the half-strip with curve derivatives at boundary conditions

Korzyuk

Stolyarchuk

2019

Vescì Akademìì navuk Belarusì. Seryâ fizika-matematyčnyh navuk

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The mixed problem for the one-dimensional Klein – Gordon – Fock type equation with curve derivatives at boundary conditions is considered in the half-strip. The solution of this problem is reduced to solving the second-type Volterra integral equations. Theorems of existence and uniqueness of the solution in the class of twice continuously differentiable functions were proven for these equations when initial functions are smooth enough. It is proven that the fulfillment of the matching conditions on the given functions is necessary and sufficient for the existence of the unique smooth solution when initial functions are smooth enough. The method of characteristics is used for the problem analysis. This method is reduced to splitting the original area of definition to the subdomains. The solution of the subproblem can be constructed in each subdomain with the help of the initial and boundary conditions. Then, the obtained solutions are glued in common points, and the obtained glued conditions are the matching conditions. This approach can be used in constructing as an analytical solution when a solution of the integral equation can be found in an explicit way, so an approximate solution. Moreover, approximate solutions can be constructed in numerical or analytical form. When a numerical solution is built, the matching conditions are essential and they need to be considered while developing numerical methods.

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Necessary and sufficient conditions for the vibrations of a bounded string with directional derivatives in the boundary conditions

Cited by 4 publications

References 1 publication

Optimal feedback control for a class of second-order evolution differential inclusions with Clarke’s subdifferential

Optimal feedback control for a class of second-order evolution differential inclusions with Clarke’s subdifferential

Directional Derivative Problem for the Telegraph Equation with a Dirac Potential

Classical solution of the mixed problem for the Klein – Gordon – Fock type equation in the half-strip with curve derivatives at boundary conditions

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