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2 Archives of Control Sciences

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On optimal boundary and distributed control of partial integro-differential equations

100%

Khurshudyan A. Z.

Archives of Control Sciences

2014

tom Vol. 24, no. 1

5-25

A method of optimal control problems investigation for linear partial integro-differential equations of convolution type is proposed, when control process is carried out by boundary functions and right hand side of equation. Using Fourier real generalized integral transform control problem solution is reduced to minimization procedure of chosen optimality criterion under constraints of equality type on desired control function. Optimality of control impacts is obtained for two criteria, evaluating their linear momentum and total energy. Necessary and sufficient conditions of control problem solvability are obtained for both criteria. Numerical calculations are done and control functions are plotted for both cases of control process realization.

On adhesive binding optimization of elastic homogeneous rod to a fixed rigid base as a control problem by coefficient

51%

Jilavyan S. H. , Khurshudyan A. Z. , Sarkisyan A. S.

Archives of Control Sciences

2013

tom Vol. 23, no. 4

413--425

The problem of finite, partially glued to a fixed rigid base rod longitudinal vibrations damping by optimizing adhesive structural topology is investigated. Vibrations of the rod are caused by external load, concentrated on free end of the rod, the other end of which is elastically clamped. The problem is mathematically formulated as a boundary-value problem for onedimensional wave equation with attenuation and variable controlled coefficient. The intensity of adhesion distribution function is taken as optimality criterion to be minimized. Structure of adhesion layer, optimal in that sense, is obtained as a piecewise-constant function. Using Fourier real generalized integral transform, the problem of unknown function determination is reduced to determination of certain switching points from a system of nonlinear, in general, complex equations. Some particular cases are considered.