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On controllability of second order dynamical systems – a survey

Klamka J., Wyrwał J., Zawiski R.

Bulletin of the Polish Academy of Sciences. Technical Sciences

2017

Vol. 65, nr 3

279--295

The paper presents a survey of recent results in the area of controllability of second order dynamical systems. Controllability problem for finite and infinite dimensional, linear, semilinear, deterministic and stochastic dynamical systems (with delays and undelayed) is taken into consideration. Different types of controllability are discussed.

An output controllability problem for semilinear distributed hyperbolic systems

Zerrik E., Larhrissi R., Bourray H.

International Journal of Applied Mathematics and Computer Science

2007

Vol. 17, no 4

437-446

The paper aims at extending the notion of regional controllability developed for linear systems to the semilinear hyperbolic case. We begin with an asymptotically linear system and the approach is based on an extension of the Hilbert uniqueness method and Schauder’s fixed point theorem. The analytical case is then tackled using generalized inverse techniques and converted to a fixed point problem leading to an algorithm which is successfully implemented numerically and illustrated with examples.