Algorithm 1 The Pseudo Code of VST-MPC.

Step 1: Set the initial sampling time ${\mathrm{T}}_{\mathrm{S}}=0.2$

Step 2: Set the MPC parameter and calculate the optimal input with MPC

Step 3: Predict ${\mathrm{X}}_{\mathrm{a}}\left(\mathrm{K}+1\right)={\mathrm{A}}_{\mathrm{a}}·{\mathrm{X}}_{\mathrm{a}}\left(\mathrm{K}\right)+{\mathrm{B}}_{\mathrm{a}}·\mathrm{u}\left(\mathrm{K}\right)$

Step 4: Update Xpast = Xa (K + 1), upast = u(K)

Step 5: Calculate the next sampling time using the following equation.

${\mathrm{T}}_{\mathrm{S}}\left(\mathrm{K}+1\right)={\mathrm{T}}_{\mathrm{S}}\left(\mathrm{K}\right)+\mathrm{sign}\left(\mathrm{Z}-\mathrm{C}\right)·\min \left(\mathrm{Z}, \mathrm{C}\right)$

where $\mathrm{Z}=-\mathsf{\lambda }·\left|\frac{\partial }{\partial {\mathrm{T}}_{\mathrm{S}}}\left(\mathsf{\delta }\left(\mathrm{K}\right)·\frac{·{\mathrm{V}}_{\mathrm{y}}\left(\mathrm{K}\right)}{{\mathrm{T}}_{\mathrm{S}}\left(\mathrm{K}\right)}\right)\right|, C=-0.01$

Step 6: Set $T_S$ = ${\mathrm{T}}_{\mathrm{S}}\left(\mathrm{K}+1\right)$

Step 7: If     Ts > ${\mathrm{T}}_{\mathrm{S},\mathrm{maximum}}$ ${\mathrm{T}}_{\mathrm{S}}$ = ${\mathrm{T}}_{\mathrm{S},\mathrm{maximum}}$ else if   ${\mathrm{T}}_{\mathrm{S}}$ < ${\mathrm{T}}_{\mathrm{S},\mathrm{minimum}}$ ${\mathrm{T}}_{\mathrm{S}}$ = ${\mathrm{T}}_{\mathrm{S},\mathrm{minimum}}$ end

Step 8: Go to Step 2 until MPC iteration is over.