Digital idle speed control of automotive engines: A safety problem for hybrid systems

We address the idle speed control problem in automotive electronics using hybrid methods to derive a digital control law with guaranteed properties. Associating a switching system with the hybrid system that describes the engine operation is crucial to developing a computationally feasible approach. For switching systems with minimum and maximum dwell times and controlled resets, we are able to derive digital control strategies with guaranteed properties that ensure safety. The proposed methodology, while motivated by the idle control problem, is of general interest for hybrid systems for which minimum and maximum dwell times can be established. In our modeling approach, we do not assume synchronization between sampling time and switching time. This is an important technical aspect in general, and in particular for our application, where there is no reason why sampling and switching should be synchronized. Some simulation results are included to demonstrate the effectiveness of the approach