“…Among the existing literature on the minimal time control problem for the evolution system, the control inputs are usually distributed in the whole time interval, i.e., they may affect the control system at each instant of time (see, for instance, [8], [16], [17], [20], [21], [24] and [28]). We also refer the readers to the minimal time sampled control problem of the heat equation (see, for instance, [1], [7], [9], [10], [13] and [22]). However, in many practical applications, it is much more convenient to use impulse controls (see, for instance, [4], [19], [26] and [27]).…”