New results on minimum-time control of linear systems between arbitrary states with applicability to space flight

A new solution method, recently developed by the authors, is presented which is solving for the first time to the best knowledge of the authors the general problem of minimum-time control of a linear time-invariant normal system evolving from an arbitrary initial state to an arbitrary desired final state subjected to cubic-constrained controls (no-rest to no-rest minimum time control problem). The method and its demonstration are here summarized. Furthermore, new solutions found by using that method are illustrated for the double integrator system and the undamped harmonic oscillator system. These models are applicable to several problems encountered in space-flight dynamics.