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The problem of resource management in a system of a-priori unknown software components executing on nondeterministic hardware is considered. The approach uses on-line parameter estimation to address uncertainties and combines this with a convex optimization-based control scheme able to handle overload situations. An algorithm to solve the optimization in real-time is presented together with performance analysis through simulations. An implementation of the approach is experimentally compared with a static analysis scheme using worst case a-priori estimates. It is demonstrated that the presented approach outperforms the static scheme in situations with uncertainty and that the advantage increases as uncertainty grows.