Train automatic stopping control with quantized throttle and braking

A method for controlling a movement of a train to a stop, at a stopping position between a first position and a second position over a finite horizon of time, comprising:

• determining constraints of a velocity of the train with respect to a position of the train forming a feasible region for a state of the train during the movement, such that a lower curve bounding the feasible region has a zero velocity only at the first position, and an upper curve bounding the feasible region has a zero velocity only at the second position;
• determining a control invariant subset of the feasible region, wherein for each state within the control invariant subset there is at least one control action having a value selected from a finite set of values that maintains the state of the train within the control invariant subset;
• and
• controlling the movement of the train subject to the constraints by selecting a control action maintaining the state of the train within the control invariant subset of the feasible region over the finite horizon of time, wherein the steps of the method are performed by a processor.

A system for controlling a movement of a train to a stop at a stopping position between a first position and a second position, comprising:

• a set of sensors that monitor and collect data relating to operation of the train;
• a memory having stored therein train data;
• at least one processor, coupled to the memory, and instructions stored therein, for execution by the at least one processor to:
• determine constraints of a velocity of the train with respect to a position of the train forming a feasible region for a state of the train during the movement, such that a lower curve bounding the feasible region has a zero velocity only at the first position, and an upper curve bounding the feasible region has a zero velocity only at the second position;
• determine a control invariant subset of the feasible region, wherein for each state within the control invariant subset there is at least one control action having a value selected from a finite set of values that maintains the state of the train within the control invariant subset;
• and
• control the movement of the train subject to the constraints by selecting a control action maintaining the state of the train within the control invariant subset of the feasible region.