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2 Archives of Control Sciences

2 2021

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Heating control of a finite rod with a mobile source

Jilavyan Samvel H., Grigoryan Edmon R., Khurshudyan Asatur Zh.

Archives of Control Sciences

2021

Vol. 31, No. 2

417--430

The Green’s function approach is applied for studying the exact and approximate null-controllability of a finite rod in finite time by means of a source moving along the rod with controllable trajectory. The intensity of the source remains constant. Applying the recently developed Green’s function approach, the analysis of the exact null-controllability is reduced to an infinite system of nonlinear constraints with respect to the control function. A sufficient condition for the approximate null-controllability of the rod is obtained. Since the exact solution of the system of constraints is a long-standing open problem, some heuristic solutions are used instead. The efficiency of these solutions is shown on particular cases of approximate controllability.

Approximate controllability of second order infinite dimensional systems

Klamka Jerzy, Khurshudyan Asatur Zh.

Archives of Control Sciences

2021

Vol. 31, No. 1

165--184

In the paper approximate controllability of second order infinite dimensional system with damping is considered. Applying linear operators in Hilbert spaces general mathematical model of second order dynamical systems with damping is presented. Next, using functional analysis methods and concepts, specially spectral methods and theory of unbounded linear operators, necessary and sufficient conditions for approximate controllability are formulated and proved. General result may be used in approximate controllability verification of second order dynamical system using known conditions for approximate controllability of first order system. As illustrative example using Green function approach approximate controllability of distributed dynamical system is also discussed.