Optimal value functions for weakly coupled systems: a posteriori estimates

Details Optimal value functions for weakly coupled systems: a posteriori estimates Optimal value functions for weakly coupled systems: a posteriori estimates

2011-10-17

arxiv.org/abs/1110.3616v1

Mathematics

Optimization and Control

Scientific paper

We consider weakly coupled LQ optimal control problems and derive estimates on the sensitivity of the optimal value function in dependence of the coupling strength. Our main result is that if a weak coupling suffices to destabilize the closed loop system with the optimal feedback of the uncoupled system then the value function might change drastically with the coupling. As a consequence, it is not reasonable to expect that a weakly coupled system possesses a weakly coupled optimal value function.

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