Shrinking horizon parametrized predictive control with application to energy-efficient train operation

A nonlinear model predictive control approach is studied, for problems where a fixed terminal instant and corresponding terminal set to be reached are imposed. The new technique features a shrinking horizon, rather than the most common receding one, and an input parametrization strategy to reduce computational burden. The property of transferability of the parametrization strategy is introduced. Under this property, theoretical convergence guarantees in nominal conditions are obtained by construction. Two relaxed techniques are then proposed to retain recursive feasibility in presence of bounded additive input disturbance. A bound on the constraint violation achieved by these relaxed techniques as a function of the uncertainty bound is derived, too. The developed strategy is applied to the problem of energy-efficient operation of trains, in either a fully autonomous mode (with continuous input values) or a driver assistance mode (with discrete input values, resulting in a nonlinear integer program if no parametrization is used). Realistic simulation results in this context illustrate the effectiveness of the approach.