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

Abstract

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.

Active set prediction for nonlinear model predictive control on a shrinking horizon based on the principle of optimality

“…The rendezvous and docking of spacecrafts is described in Reference 26. Further, in Reference 27, a combination of move blocking and switching parametrizations is used on a shrinking horizon for the control of an electric train, while Reference 28 presents a robust, self‐triggered variant of shrinking horizon NMPC. Another robustification approach is proposed in Reference 29, which applies a variant of the well‐known multi‐stage NMPC scheme to the control along a shrinking horizon.…”

Suboptimal nonlinear model predictive control with input move-blocking

“…The present work deals with the stability analysis of online MBMPC with a receding horizon for discrete-time systems. Therefore, the literature review does not cover papers on MBMPC that split the optimization into an offline and an online part (see, e.g., [6,29]), apply a nonuniform time discretization (see, e.g., [30]), use alternative parameterizations (see, e.g., [31]), or implement a shrinking horizon formulation [32].…”