Time-to-go function of double-integrator system with asymmetrical constraints

The paper addresses the problem of searching the time-to-go function of a double-integrator system with asymmetrically constrained state and control and presents its general analytical solution. The paper further discusses application of the solution in the model predictive control where the time-to-go function is utilized as the terminal cost to represent the long-horizon information. The application of the time-to-go function in the model predictive control criterion is illustrated using numerical examples.