Determination of terminal switch curve for time-optimal control of second-order systems via a suboptimal control method

The exact terminal switch curve for time-optimal control of a certain class of second-order systems is derived from a suboptimal control method for nonlinear autonomous systems. The suboptimal control method approximates the necessary conditions for optimal control of the nonlinear system and those of the approximating linear system. The linear approximant is found via the least-squares approximation.