The Bang–Bang Property of Time-Varying Optimal Time Control for Null Controllable Heat Equation

In this paper, we consider bang–bang property for a kind of time-varying time optimal control problem of null controllable heat equation. The study is a continuation of a recent work (Chen et al. in Syst Control Lett 112:18–23, 2018), where an approximate null controllable heat equation was considered. We first establish the equivalence between optimal norm control and optimal time control and then prove the existence of the optimal norm control and of the optimal time control. The time-varying bang–bang property for the optimal time control is finally established.

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