Control of the annulus pressure during drilling of oil and gas wells can be a challenging task, due to the complex dynamics of the multiphase flow. Since well kicks and fluid losses are potentially dangerous, it is important to improve the performance and the capabilities of estimation and control and to initiate an automatic well control system. Novel adaptive observers for estimation the flow rates through the well are developed for kick and loss detection, and asymptotic convergence properties are established. A switched control algorithm for feedback control of the choke and the back-pressure pump is proposed for pressure control and kick attenuation and asymptotic convergence is achieved. A new observer is developed to estimate the reservoir pore pressure for improved kick management. Simulation results obtained with a high fidelity drilling simulator are presented to demonstrate the effectiveness of the proposed observer and control scheme. The results show that the proposed observers effectively detect kicks in the early phase and that the automatic control scheme improves the kick handling.