Speed-gradient approach to torque and air-to-fuel ratio control in DISC engines

Applies a Lyapunov design technique, the so-called speed-gradient approach, to coordinated air-to-fuel ratio and torque control in direct injection stratified charge gasoline engines. The technique is based on dynamic minimization of a performance function. It is demonstrated how the closed-loop response of this nonlinear and strongly coupled system can be shaped via the adjustment of the weights in the performance function and how the constraints that protect the operating envelope of the engine can be included through the augmentation of a barrier function. A practical numerical procedure is proposed and used to check the closed-loop stability conditions in this application