Robust Dynamic Average Consensus (RoDAC)

Consider a connected and bidirectional network of agents (e.g., sensors), where each agent in a network has access to its own local input signal, but it must compute and track the average of all such inputs. Each agent communicates only with neighbors in the network, and local computation and memory requirements should be independent of the number of the agents in the network. The RoDAC is defined as the local output of each agent tracking the exact average of the inputs regardless of the initial values of the internal states and the estimates. This robustness feature becomes important when there are agents joining/leaving the network, changes in the network topology, computation faults, and communication faults (i.e., dropped packets), all of which introduce new nonzero initial conditions into the estimator dynamics. While each such event introduces a transient, if the network is constant and connected after these events, robust dynamic average consensus implies convergence to the correct average value. Examples of such inputs are distance measurements between a static sensor and a moving target, or sensor measurements of a time-varying environment.

We developed a class of average consensus estimators to achieve robust dynamic average consensus of time-varying inputs, given partial linear model information of the inputs. These estimators make use of the celebrated internal model principle (IMP), and thus called the internal model average consensus estimator (IMACE). The block diagram form of the estimator is shown below, where L is the graph Laplacian matrix that represents the communication topology of the network, h(s) and g(s) are transfer functions that represent the internal filtering at each agent, \phi(s) is the Laplace transform of the time-varying inputs, and \xi^1(s) and \xi^2(s) are the initial conditions of the h(s) and g(s).