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An increasing number of distributed real-time systems face the critical challenge of providing quality of service guarantees in open and unpredictable environments. In particular, such systems often need to enforce utilization bounds on multiple processors in order to avoid overload and meet end-to-end deadlines even when task execution times are unpredictable. While recent feedback control real-time scheduling algorithms have shown promise, they cannot handle the common end-to-end task model where each task is comprised of a chain of subtasks distributed on multiple processors. This paper presents the end-to-end utilization control (EUCON) algorithm that adaptively maintains desired CPU utilization through performance feedbacks loops. EUCON is based on a model predictive control approach that models utilization control on a distributed platform as a multivariable constrained optimization problem. A multi-input-multi-output model predictive controller is designed based on a difference equation model that describes the dynamic behavior of distributed real-time systems. Both control theoretic analysis and simulations demonstrate that EUCON can provide robust utilization guarantees when task execution times deviate from estimation or vary significantly at runtime.