## 3 Results
### Control Performance under Nominal Conditions  
In the first scenario the control performance subject to network influences is evaluated to establish a baseline for the results once controller failure occur in scenario two. The satellite under observation is satellite 3 represented by two SKITH nodes, an exclusive controller which runs the MPC control task and a combined actuator/sensor node. Initially all satellites are in an along-track formation on the same orbit, except Satellite 3 which has an initial state \(\mathbf{x}_{0,53}\) with a deviation of 10 m in in-plane (\(\hat{X}\)), along-track (\(\hat{Y}\)) and out-of-plane (\(\hat{Z}\)) direction from its desired reference position which is also the origin of the moving Hill coordinate frame. This is visualized in Figure 14. The along-track separation between two adjacent satellites is less than \(d_{cmax}\) and bigger than \(d_{cmax}\) for all satellites that not direct neighbours along the orbit. This leads to communication hop-counts of one for direct satellite neighbours and bigger than one for non-direct neighbours.  
The control goal is therefore to drive satellite 3 to it reference, the moving coordinate system origin \([0,0,0]^{T}\). The networked control loop is run subject to a Markovian network loss, following the network model introduced in Section 2.3 with \(p_{l}=0.3\). In addition the minimal control horizon length \(N_{min}\) is set to 15, the horizon threshold \(N_{th}\) is set to 10 at a control cycle duration of \(T_{S}=6s\). The control input buffer size on the actuator side during the maneuver is shown in Figure 15 where multiple network losses of the control command sequence from the controller to the actuator are visible. Whenever a successful transmission is achieved the control input buffer on the actuator is replenished. In addition an increase of the control input horizon length is visible as a result of the adaption to the network losses, keeping the remaining control input buffer at the actuator well above \(26>N_{min}+N_{th}\) remaining control inputs. The position state evolution of satellite 3 subject to the actuated control inputs is shown in Figure 16. The networked predictive controller drives the system to the desired state \([0,0,0]^{T}\) and exhibits stable performance. During a prolonged open-loop execution with multiple successive packet-losses and while the system is still away from its equilibrium condition a set-point deviation can be seen (t = 80 s until t = 110 s) which is corrected once new command trajectories reach the actuator (t = 110 s until t = 130 s).  
Figure 13: Hardware testbed used for the experiments: Two cube units each containing one or more connected hardware nodes which are associated with one of four satellites. The units are stacked on an electrical test interface board used for external monitoring.  
Figure 14: Initial state of all four satellites with the moving Hill coordinate frame centered at the desired position of satellite 3 in the formation.  
Figure 15: Command buffer state on actuator side under the influence of packet losses. The adaption of the control horizon length as reaction to the measured losses prevents the remaining control input buffer size to fall below \(N_{min}+N_{th}=25\).