On the modelling and exact controllability of networks of vibrating strings
SIAM Journal on Control and Optimization
SIAM Journal on Control and Optimization
Modeling, Analysis and Control of Dynamic Elastic Multi-Link Structures
Modeling, Analysis and Control of Dynamic Elastic Multi-Link Structures
Mathematics and Computers in Simulation
Stabilization and Riesz basis of a star-shaped network of Timoshenko beams
Journal of Dynamical and Control Systems
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We consider optimal control problems related to exact- and approximate controllability of dynamic networks of elastic strings. In this note we concentrate on problems with linear dynamics, no state and no control constraints. The emphasis is on approximating target states and velocities in part of the network using a dynamic domain decomposition method (d^3m) for the optimality system on the network. The decomposition is established via a Uzawa-type saddle-point iteration associated with an augmented Lagrangian relaxation of the transmission conditions at multiple joints. We consider various cost functions and prove convergence of the infinite dimensional scheme for an exemplaric choice of the cost. We also give numerical evidence in the case of simple exemplaric networks.