Abstract
Idle speed control for an automotive engine is formulated as the problem of computing a maximal safe set for a hybrid system modeling an SI engine in idle mode. Since this problem is computationally intractable, we exploit the relations between safe sets for a continuous-time switching system S and an appropriate discrete-time switching system associated with S to reduce drastically its complexity. An algorithm in the discrete-time domain is proposed for the determination of the maximal safe set. The methodology is general enough to be easily extended to different hybrid control problems. In particular, we solved the problem of the computation of the maximal safe set in the case of un-synchronized switching and sampling times for idle control, an open problem for quite some time. Simulation results show the efficiency of the proposed approach.
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