## 2 Concept of Operations
### Local Rate Regulators for Communications and Clock Data Services  
What follows is a flexible framework for managing control autonomy to maintain the advantages of spread spectrum technology and the performance of multiple access for a family of physical-layer communication systems and pLEOT integration. In practice, only relevant and locally available information of orbital platform \(i\) is necessary for making adaptive CN0 allocations for communication and pLEOT based on ad hoc, non-dedicated demands. This information includes \(P_{total}^{i}\), \(\gamma_{clk}^{si}\), \(\gamma_{c}^{si}\), and \(CN0^{i}_{total}\). Each local agent \(i\) has a periodic opportunity to compute increment policies concerning the total CN0 for integrated communication and clock data transfer services at orbital platform \(i\). The main value of the difference equations, as governed by Equations (8), (9), (14), (16) and (17), lies in their utility as a physical modeling tool. These equations help develop a discrete-time state-space model where the dynamics to be managed focus on the Quality of Service (QoS) satisfaction for communication and pLEOT services. \[\left[ \begin{array}{c}CN0^{i}_{clk}(k+1)\\ CN0^{i}_{c}(k+1)\\ e_{clk}^{i}(k+1)\\ e_{c}^{i}(k+1)\\ \alpha^{i}_{c}(k+1)\\ CN0^{i}_{total}\end{array} \right] =\left[ \begin{array}{cccccc}1&0&0&0&0&0\\ 0&1&0&0&0&0\\ 0&0&1&0&0&0\\ 0&0&0&1&1&0\\ 0&0&0&0&0&1\end{array} \right]\left[ \begin{array}{c}CN0^{i}_{clk}(k)\\ CN0^{i}_{c}(k)\\ e_{clk}^{i}(k)\\ e_{c}^{i}(k)\\ q_{c}^{i}(k)\\ CN0^{i}_{total}\end{array} \right]\] \[+\left[ \begin{array}{cc}CN0^{i}_{total}&0\\ 0&CN0^{i}_{total}\\ CN0^{i}_{total}&-\frac{\gamma_{clk}^{si}}{B}\\ 0&CN0^{i}_{total}\\ 0&0\\ 0&0\end{array} \right]\left[ \begin{array}{c}CN^{i}_{clk}(k)\\ u_{c}^{i}(k)\\ \end{array} \right]. \tag{18}\]In reference to the developed model, the aggregate state \(x_{i}(k)\) and control input \(u_{i}(k)\) vectors, along with the corresponding matrix coefficients of (18), are defined as follows  
\[x_{i}(k)\triangleq\left[ \begin{array}{c}CN0^{i}_{clk}(k)\\ CN0^{i}_{c}(k)\\ e^{i}_{clk}(k)\\ q^{i}_{c}(k)\\ CN0^{i}_{total}\end{array} \right];\quad A_{i}\triangleq\left[ \begin{array}{ ccccc}1&0&0&0&0&0\\ 0&1&0&0&0&0\\ 0&0&1&0&0&0\\ 0&0&0&1&0&0\\ 0&0&0&1&1&0\\ 0&0&0&0&1\end{array} \right] \tag{19}\] \[B_{i}\triangleq\left[ \begin{array}{c}CN0^{i}_{total}&0\\ 0&CN0^{i}_{total}\\ CN0^{i}_{total}&-\frac{T_{clk}^{i}}{B}\\ 0&CN0^{i}_{total}\\ 0&0\\ 0&0\end{array} \right];\quad u_{i}(k)\triangleq\left[ \begin{array}{c}u^{i}_{clk }(k)\\ u^{i}_{c}(k)\end{array} \right] \tag{20}\]  
then, the linear time-invariant state-space model (18), as shown in Figure 3, provides the advantage of applying the control engineering framework for CN0-based on-demand procedures at local agents  
\[x_{i}(k+1) =A_{i}x_{i}(k)+B_{i}u_{i}(k) \tag{21}\] \[y_{i}(k) =C_{i}x_{i}(k)+D_{i}u_{i}(k)\,, \tag{22}\]  
where, in this case, the output coefficient \(C_{i}\) is an identity matrix of appropriate size and the feedthrough or feedforward \(D_{i}\) is a zero matrix. In CN0-based control protocols, the local agent \(i\) has a vital mission: to optimize the increments of total CN0 to ensure effective regulatory performance and accurate reference tracking. It is important to understand that the total power available for communications and clock data transfers is finite. At times, the total CN0 resource can be excessively provisioned, leading to inefficiencies. Therefore, we must strategically maintain a balance between precision and CN0 margins--these margins indicate the discrepancies between the CN0 levels of our communications and clock data transfers and the standards set by traditional satellite communications and AltPNT. Furthermore, the efficiency of utilization is assessed while respecting established constraints, ensuring optimal performance in our integrated signal system.