Implementation of distributed consensus on an outdoor testbed

Asynchronous Consensus of Continuous-time Multiagent Systems with Minimum Communication

“…Recall from (15) and Lemma 11 that control law (7) gives the maximum inter-update duration under constraint (16). Similarly, it follows from (18) and Lemma 12 that control law (9) gives the maximum inter-update duration under constraint (19).…”

“…Similarly, it follows from (18) and Lemma 12 that control law (9) gives the maximum inter-update duration under constraint (19). Then, as one inter-update duration under Protocol Q is longer than that prescribed by control laws (7) and ( 9), Protocol Q must be violating either constraint (16) or constraint (19). Recall that violation of ( 16) or (19) by Protocol Q results in the violation of necessary condition (11) on feasible protocols.…”

“…It is given that |z i (t k i )| ≤ α. Then, it follows from Lemma 18.2 that control rule ( 7)-( 8) satisfies constraint (16). Let t k+1 i and u * i be as defined in ( 7) and ( 8), respectively.…”

“…Let z i t k i be the local disagreement of a i at its update instant t k i such that z i t k i ≤ α. Then, the control law ( 7)-( 8) is the solution of optimization ( 14)- (16).…”

“…These protocols are either based on discrete synchronous communication or on continuous communication. A global synchronization clock is necessary for the implementation of synchronous protocols, which is often a major practical constraint [16]. On the other hand, the energy consumption of agent's transponder is proportional to the number and duration of transmissions [7].…”