On Optimal Switches for Energy Efficient Control of a Train Considering Regenerative Braking

In order to make full use of each optimal control mode and the characteristics of the optimal switches and solve the optimal control sequence quickly, a class of train energy-efficient optimal control problems with fixed trip time and regenerative braking energy feedback is set up, and the optimal switching rules and the switching time between optimal control modes are analyzed in this paper. First, 4 types of nonsingular modes and the corresponding state equations are deduced by using the Pontryagin Maximum Principle. The optimal switching set and switching directions are defined. On this basis, 13 types of optimal switches without touching the speed limit and 30 types of optimal switches with touching the speed limit are summarized. By introducing the conception of speed holding section, the problem of solving the optimal control sequence can be transformed into the problem of searching the local optimal linkages among a series of speed holding sections. The solving process can be improved by using the characteristics of 43 types of optimal switching rules and switching time, and the efficiency of solving the local optimal linkages can also be improved.