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Self-adaptive software systems are designed to support a number of alternative solutions for fulfilling their requirements. These define an adaptation space. During operation, a self-adaptive system monitors its performance and when it finds that its requirements are not fulfilled, searches its adaptation space to select a best adaptation. Two major problems need to be addressed during the selection process: (a) Handling environmental uncertainty in determining the impact of an adaptation; (b) maintain an optimal equilibrium among conflicting requirements. This position paper investigates the application of Adaptive Model Predictive Control ideas from Control Theory to design self-adaptive software that makes decisions by predicting its future performance for alternative adaptations and selects ones that minimize the cost of requirement failures using quantitative information. The technical details of our proposal are …