This paper presents an L1 adaptive controller for pressure control using an engine bleed valve in an aircraft air management system (AMS). The air management system is composed of two pressure-regulating bleed valves, a temperature control valve, a flow control valve, and a heat exchanger/precooler. Valve hysteresis due to backlash and dry friction is included in the system model. The nonlinearities involved in the system cause oscillations under linear controllers, which decrease component life. This paper is the unique in the consideration of these uncertainties for control design. This paper presents simulation results using the adaptive controller and compares them to those using a proportional–integral (PI) controller.