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Self-adaptive software systems monitor their operation and adapt when their requirements fail due to unexpected phenomena in their environment. This paper examines the case where the environment changes dynamically over time and the chosen adaptation has to take into account such changes. In control theory, this type of adaptation is known as Model Predictive Control and comes with a well-developed theory and myriads of successful applications. The paper focuses on modelling the dynamic relationship between requirements and possible adaptations. It then proposes a controller that exploits this relationship to optimize the satisfaction of requirements relative to a cost-function. This is accomplished through a model-based framework for designing self-adaptive software systems that can guarantee a certain level of requirements satisfaction over time, by dynamically composing adaptation strategies when …