## 6 Onboard Steering Commands via Minimal-Cost-Variance Control
These innovative control strategies provide a transparent framework for effectively allocating performance robustness and reliability requirements across diverse qualitative performance attributes and their corresponding risks, ensuring enhanced decision-making and risk management. Indeed, the effectiveness of cost-cumulant control algorithms was demonstrated in various applications, such as cable-stayed bridges [26], structures affected by wind [27], and buildings subjected to earthquake vibrations [28]. The results from these implementations were compared to those obtained using Linear-Quadratic-Gaussian (LQG) control, which focuses on minimizing the statistical average of (94). The findings revealed that the cost-cumulant controllers significantly outperformed the results achieved with LQG control. In light of recent advancements and the growing efficiency of edge computing onboard each orbital platform \(i\), it is both prudent and beneficial to reassess a notable member of the cost-cumulant control family: the minimal-cost-variance (MCV) control. This innovative approach prioritizes the reduction of cost variance while ensuring the cost mean remains within established limits [29]. The MCV control technique is particularly relevant in addressing the escalating concerns surrounding clock steering operations, which play a vital role in maintaining precision and reliability in local reference time scales across diverse orbital platforms. Embracing this technique could significantly enhance the operational frameworks and outcomes. A highly effective strategy for designers is to set rigorous metrological requirements that enable the clock to be adjusted just once, eliminating the need for repeated actions. This operational requirement for clock adjustment makes the MCV control paradigm an ideal choice for implementing changes to the clock and time scale. By adopting this framework, designers can focus on minimizing the variance of the performance measure, as highlighted in (94), while ensuring that the expected value of that performance measure remains within specified constraints. This approach not only enhances precision but also streamlines efficiency in time management. As a guide for the reader, this section serves as an important signpost related to the theory of MCV control. It lays the foundation for designing new steering control laws that can achieve the objectives for autonomous, resilient, and remote timing systems. This is accomplished by influencing the probability distribution of the performance measure to accurately estimate IEM parameters in desirable ways. Specifically, the focus on minimizing the variance of \(J_{i}(n_{0})\) while keeping its mean within a defined constraint is relevant to the current context  
\[E\{J_{i}^{2}|Z_{i}(n_{0})\}-E^{2}\{J_{i}(n_{0})|Z_{i}(n_{0})\} \tag{95}\]  
is minimized, while  
\[E\{J_{i}(n_{0})|Z_{i}(n_{0})\}=h_{i}(n_{0},Z_{i}(n_{0})) \tag{96}\]  
where \(E\{\cdot|\cdot\}\) denotes the conditional expectation operator and the actual data \(Z_{i}(k)\triangleq\{z_{i}(n_{0}),z_{i}(n_{0}+1),\ldots,z_{i}(k);u_{i}(n_{0}),u _{i}(n_{0}+1),\ldots,u_{i}(k-1)\}\) measured from local frequency standards onboard separate orbital platforms with \(Z_{i}(n_{0})\triangleq z_{i}(n_{0})\) and \(n_{0}<k\). The primary focus of \(h_{i}(n_{0},Z_{i}(n_{0}))\) involves practical considerations, such as the desired response, acceptable deviations from that response, and the complexity of the clock steering controller. How should we move forward based on this general assessment? It becomes evident that the choice of \(h_{i}(n_{0},Z_{i}(n_{0}))\) is not entirely arbitrary.