Abstract
The statement of the Hybrid Minimum Principle is presented for time optimal control problems where autonomous and controlled state jumps at the switching instants are accompanied by changes in the dimension of the state space. A key aspect of the analysis is the relationship between the Hamiltonians and the adjoint processes before and after the switching instants. As an example application, an electric vehicle equipped with a two-speed seamless transmission, that augments an additional degree of freedom during the transition period, is modelled within this framework. The state-dependant motor torque constraints are converted to state-independent control input constraints via a change of variable and the introduction of auxiliary discrete states. The problem of the minimum acceleration time required for reaching the speed of 100km/hr is formulated within the presented framework and the Time Optimal Hybrid Minimum Principle is employed in order to find the optimal control inputs and the optimal gear changing instants.
Published Version
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