An increasing number of distributed real-time systems face the critical challenge of providing end-to-end Quality of Service (QoS) guarantees in open and unpredictable environments. In particular, such systems often need to guarantee the CPU utilization on multiple processors in order to achieve overload protection and meet end-to-end deadlines while task execution times are unpredictable. While the recently developed feedback control real-time scheduling algorithms have shown promise, they cannot handle the common end-to-end task model in distributed systems 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 features a distributed feedback loop that dynamically enforces desired CPU utilization bounds on multiple processors based on online performance measurements EUCON is based on a model predictive control approach that models the utilization control problem on a distributed platform as a multi-variable 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 even when task execution times deviate from the estimation or vary significantly at run-time.