## 3 Results
### Controller Failure with reassignment  
Now a similar scenario to the previous one is considered. Satellite 3 starts now at position \([20,-10,15]\,m\) and should be driven again to \([0,0,0]\,m\). During the control process the controller node belonging to satellite 3 fails at \(t=35\) s leading to a continuing depletion of the control input buffer at the actuator of satellite 3 which is shown in Figure 17. Once the remaining stored commands fall below \(N_{min}=25\), the controller failure is detected by the actuator and a control task re-assignment is initiated by the actuator node via the described auction procedure at \(t=50\) s.  
For the bid calculation the upper control horizon length is set to 40, resulting in a maximum MPC task execution time of \(\hat{T}_{ctrl}=2.5\) s and together with the desired control frequency \(f_{ctrl}=\frac{1}{75}=\frac{1}{6\,s}\) leads to a maximum estimated task load of \(L_{ctrl}=42\%\). In addition inter-satellite proximity expressed in hops is not expected to be changing during the maneuver, therefore the distance cost \(Cd_{0:m}\) is assumed to be constant and is treated as a scalar value \(Cd\) of dimension one. The scaling factors for the distance cost \(Cd\) are \(\alpha_{d}=0.5\) and \(\beta_{d}=2\). This results in the submission of task bids of combined node 2 of satellite 2 and combined node 4 of satellite 4. The combined node of satellite 1 did not submit a bid,  
Figure 16: Control performance of the networked formation control of satellite 3 over a network with Markovian network characteristics without controller failures.  
Figure 17: Command buffer state on actuator side under the influence of packet losses. In addition at \(t=35\) s the currently assigned controller node fails and a control task reassignment is initiated once the remaining control input buffer size to falls below \(N_{min}\). After the task is reassigned the control input buffer at the actuator is filled again.  
because its expected load after the task acquisition exceeds its capacity. The individual costs and bids are summarized in Table 1.  
After multiple auction re-announcements the actuator node of satellite 3 closes the auction at \(t=60\) s and selects the node with the smallest bid, the combined node of satellite 2, to take over the control task. After one loss event during the winner announcement the assignment is re-transmitted by the actuator and is acknowledged by the winner node. At time \(t=61\) s the control input sequence calculation is resumed and the control input buffer at the actuator is filled again. For the remaining time of the scenario the remaining control input buffer length is mainly influenced by the data loss in the network. The overall control performance is shown in Figure 18. Like before the controller manages to drive the system to its set-point and exhibits stable closed-loop behavior even under the effect of the failure of the initial controller and a necessary control task reassignment. This is smooth control task handover is realized because the remaining control input buffer of length \(N_{min}\) successfully bridges the time until the control task is assigned to a new controller.