Time-optimal trajectories for a trolley-like system with state constraint

Abstract

Abstract We consider a time-optimal problem for trolley-like system (matherial point with inertia) passage from start to zero position (i.e. origin) under bounded control (acceleration) and linear state constraint. We solve it with Pontryagin maximum principle for state-constrained problems usage. We construct optimal trajectories synthesis and show that it is not simple “cut” of classical trolleyplike problem synthesis. State constraint generates “forbidden zone” bounded by state constraint boundary and half of parabola. We also shows that optimal trajectory (for selected range of state constraint line coefficient) has no more than three switching points (for the classical case, there is no more than one switching point). We analyse synthesis for different cases of parameters and demonstrates its evolution.