Algorithm 2. Gateway inference and reporting-period command generation

Scope and output: Full-input controller for one target node. Each valid opportunity produces a sequenced period command ${\mathit{T}}_{\mathrm{cmd}}$, the proposed ${\mathit{T}}_{\mathrm{sync}}$. Inputs and state: Delivered SoC telemetry and sampling times; completed uplink deliveries; current trace context; the defined memberships and 27-rule table. Cache $K=\left(S_K,{\tau }_K\right)$ stores usable-energy SoC (%) and its sampling time; $s$ is the sequence. Profile: $t\in {\mathrm{T}}_g=\{\left(300m-1\right)\hspace{0.17em}\mathrm{s}:m=\mathrm{1,2},\dots \}$; $T_{\mathrm{age}}=7200\hspace{0.17em}\mathrm{s}$; $W=3600\hspace{0.17em}\mathrm{s}$, $r_{\mathrm{ref}}=1/60\hspace{0.17em}\mathrm{Hz}$; $T_{\min }=60\hspace{0.17em}\mathrm{s}$, $T_{\mathrm{cap}}=3600\hspace{0.17em}\mathrm{s}$, $q=0.001\hspace{0.17em}\mathrm{s}$; $\Omega =[60,3600]\hspace{0.17em}\mathrm{s}$; $S\in [0,100]$, normalized traffic $N\in [0,1]$, context $C\in [0,1]$. Delivered telemetry 1 Initialize $K\leftarrow \mathrm{missing}$ and $s\leftarrow 0$ 2 On the first successful physical delivery of a target report: 3  $K\leftarrow$(reported SoC, telemetry sampling time) 4  Record this report’s first successful delivery time Scheduled inference 5 At each opportunity $t\in {\mathrm{T}}_g$: 6  Commit completed physical uplink observations through $t$ 7  If the gateway is available and $K$ is present with $t-{\tau }_K\le T_{\mathrm{age}}$: 8   $S\leftarrow S_K$; $C\leftarrow \mathrm{CurrentContext}\left(t\right)$ 9   $N\leftarrow \min \left(1,\mathrm{DeliveredCount}(\left(t-W,t]\right)/\left(W{r}_{\mathrm{ref}}\right)\right)$ 10   Compute membership degrees for $S$, $N$, and $C$ 11   For each rule $r$ in the 27-rule table: 12   ${\alpha }_r\leftarrow$ minimum of its three antecedent membership degrees 13   $g_r\left(u\right)\leftarrow \min \left({\alpha }_r,{\mu }_{D_r}\left(u\right)\right)$, for consequent $D_r$ 14   End for 15   $g\left(u\right)\leftarrow \min \left(1,{\displaystyle {\sum }_{r=1}^{27}}{g}_r\left(u\right)\right)$ 16   $T_{\mathrm{raw}}\leftarrow {\displaystyle \frac{{\int }_{\Omega }u\hspace{0.17em}g\left(u\right)\hspace{0.17em}\mathrm{d}u}{{\int }_{\Omega }g\left(u\right)\hspace{0.17em}\mathrm{d}u}}$ (analytic continuous centroid) Period construction and dissemination 17   $T_0\leftarrow \mathrm{clip}\left(T_{\mathrm{raw}},T_{\min },T_{\mathrm{cap}}\right)$ 18   $T_{\mathrm{env}}\leftarrow T_0+{\mu }_{\mathrm{Low}}\left(S\right)\left(T_{\mathrm{cap}}-T_0\right)$ 19   $T_{\mathrm{cmd}}\leftarrow \mathrm{clip}\left(q\lfloor T_{\mathrm{env}}/q\rfloor ,T_{\min },T_{\mathrm{cap}}\right)$ 20   $s\leftarrow s+1$; create command (identifier, $s$, generation time $t$, $T_{\mathrm{cmd}}$) 21   Offer two $0.04\hspace{0.17em}\mathrm{s}$ blind copies of this command at $t$ and $t+0.05\hspace{0.17em}\mathrm{s}$ 22  Else: generate no command at this opportunity 23  End if 24 End Data contract: Telemetry is sampled at actual target TX start. DeliveredCount includes successful background deliveries and the first successful delivery of each target report. CurrentContext returns the current prescribed trace value. Evaluation contract: Inputs are finite and in the stated domains; the centroid has positive finite area and finite first moment. An invalid evaluation raises FLCError. The Low-SoC envelope follows the centroid and clipping; quantization floors to 1 ms. Node interface: After the matching RX service completes, channel-successful copies reach Algorithm 1 for validation and subsequent application at an operational nominal boundary.