Predicting the performance of uncertain multi-agent systems using event-triggering and L ₁ adaptation

This paper studies the impact of communication constraints and uncertainties on the performance of multi-agent systems, while closing the local loops with embedded L ₁ adaptive controllers. We propose a communication and adaptation co-design scheme to guarantee the predictability of the system performance. Under this scheme, an agent locally determines its broadcast time instants using distributed event-triggering. The embedded L ₁ adaptive controller enables each agent to compensate for the local uncertainties and disturbances. We derive performance bounds on the difference between the signals of the ideal model (in the absence of uncertainties and perfect communication) and the real system operating with the proposed co-design scheme. It is shown that these bounds can be arbitrarily reduced to zero by deceasing the thresholds in the local events and increasing the local adaptation gain in each subsystem. The low-pass filter in the L ₁ adaptation structure ensures the robustness of the overall system. The proposed co-design scheme can help to predict the performance of multi-agent system in the presence of uncertainties. The results can be used to design guidelines in safety-critical applications, including air traffic control and collision avoidance in multi-agent systems.