Introduction

Multi-stage optimal control problems are characterized by the fact that a change in the operating scenario (e.g., in the dynamics) and/or in the optimization criterion occurs, at one or more time moments of the process under study. Formally, this means that the optimal control problem is defined by state equations and/or objective functions that are specifically defined over a number of subintervals. The literature on multi-stage optimal control is extensive, of interest to many disciplines, and considers both deterministic and stochastic perspectives (see e.g., [1–11]). Multi-stage optimal control problems are very common in the space domain when the mission consists of different phases, such as orbital insertion, coasting, flyby exploitation, rendezvous, re-entry, and landing. Hence, not surprisingly, multi-stage optimal control in space has long been a fundamental topic. A historical example is the first two-stage liquid-fueled rocket launch on May 13, 1948, at the White Sands Proving Ground (WSPG) in New Mexico (see https://www.nasa.gov/history/75-years-ago-first-launch-of-a-two-stage-rocket/ ). This was a precursor to the actual missions into space.