## 5 Networked Control Systems with Minimal Attention  
As highlighted in the previous section, the clock-ensemble Kalman filter operates on a discrete time interval of \(\delta\) seconds. Every \(\delta\) seconds, the clock-to-clock difference data between the onboard OCXO platform \(i\) and the IEM is recorded and transmitted to all participating platforms \(i\) (where \(i=1,\ldots,N\)). The onboard steering control value is then calculated and applied to the MPS as soon as the user-defined control interval is achieved. In this framework, reducing bandwidth is essential, particularly by leveraging existing inter-satellite radio links in the fully connected pLEO constellation. This method facilitates the efficient transfer of clock estimates from the clock-ensemble Kalman filter on the anchor platform \(j\) to all other participating platforms. This research critically examines how diminishing the number of data packet exchanges, represented as \(\hat{x}_{i}(t_{k})\), between the remote sensor (the clock-ensemble Kalman filter on the anchor platform \(j\)) and the steering controller or actuator linked to the local IEM realization on platform \(i\), can enhance overall performance. The local IEM realization aboard orbital platform \(i\) applies its model knowledge in its steering controller or actuator to effectively approximate the OCXO's behavior concerning the IEM, particularly during intervals when clock estimates from the remote sensor are not available. The core goal is to ensure feedback by updating the state \(s_{i}(t_{k})\) of the local IEM model, as governed by Equation (77), using the actual state \(x_{i}(t_{k})\) of the ensemble clock \(i\). This crucial state information comes from the remote sensor, which is the clock-ensemble Kalman filter operating on anchor orbital platform \(j\). \[x_{i}(t_{k})=\hat{x}_{i}(t_{k})+z_{i,OCXO}(t_{k})\,, \tag{80}\]  
which, in accordance with (73), leads to  
\[x_{i}(t_{k})=x_{i,OCXO}(t_{k})-x_{0}(t_{k})-e_{i}(t_{k})+v_{i}(t_{k})\,. \tag{81}\]  
During the remainder of the control interval, the steering action relies on the local IEM realization model onboard orbital platform \(i\). The dynamics of this local IEM model are integrated into the steering controller or actuator, resulting in an open-loop operation for a duration of \(h\) seconds. This research presents an initial step toward developing onboard timing architectures in AltPNT. The analysis explores the trade-off between open-loop and closed-loop steering controls, which could facilitate local pLEOT formation across a pLEO constellation, thereby offering potential resilient navigation services. Interestingly, networked control systems have proven to be invaluable for designing control systems that manage steering frequency standards with minimal oversight and resource allocation. Consider a feedback networked control system in Figure 10, where the actual behavior of the IEM estimate is described by  
\[\hat{x}_{i}(t_{k+1})=A_{i}(\delta)\hat{x}_{i}(t_{k})+B_{i}(\delta)u_{i}(t_{k})+ w_{i}(t_{k}))\,, \tag{82}\]  
where \(B_{i}(\delta)=0\) and the update time \(t_{k}\) with \(t_{k+1}-t_{k}=h\) for all \(k\). Also, the local IEM realization model is given by  
\[s_{i}(t_{k+1})=A_{i}(h)s_{i}(t_{k})+B_{i}(h)u_{i}(t_{k})+v_{i}(t_{k})\,. \tag{83}\]  
As shown in Figure 10, the remote sensor onboard platform \(j\) has the full state, \(\hat{x}_{i}(t_{k})\) available. It will send the state information through the inter-satellite radio links every \(h\) seconds. Finally, the onboard controller, \(u_{i}(t_{k})\) for clock steering by  
\[u_{i}(t_{k})=K_{i}\,s_{i}(t_{k})\,, \tag{84}\]  
where one further observes that the gain matrix, \(K_{i}\) affects how quickly the signal transitions from the free-running behavior of the local OCXO clock to the IEM estimate. The state error, \(e_{i}(t_{k})\) is defined as  
\[e_{i}(t_{k})=\hat{x}_{i}(t_{k})-s_{i}(t_{k})\,. \tag{85}\]  
The following analysis is motivated by the work [25].