To provide Quality of Service (QoS) guarantees in open and unpredictable environments, the utilization control problem is defined to keep the processor utilization at the schedulable utilization bound, even in the face of unpredictable and/or varying task execution times. To handle the end-to-end task model where each task is comprised of a chain of subtasks distributed on multiprocessors, researchers have used Model Predictive Control (MPC) to address the Multiple-Input, Multiple-Output (MIMO) control problem. Although MPC can handle a limited range of model uncertainties due to execution time estimation errors, the system may suffer performance deterioration or even become unstable if the actual task execution times are much larger than their estimated values. In this paper, we present an online adaptive optimal control approach using Recursive Least Squares (RLS) based model estimator plus Linear Quadratic (LQ) optimal controller. We use simulation experiments to demonstrate the ef...