A Robust Consensus + Innovations-Based Distributed Parameter Estimator

While distributed parameter estimation has been extensively studied in the literature, little has been achieved in terms of robust analysis and tuning methods in the presence of disturbances. However, disturbances such as measurement noise and model mismatches occur in any real-world setting. Therefore, providing tuning methods with specific robustness guarantees would greatly benefit the practical application. To address these issues, we recast the error dynamics of a continuous-time version of the widely used consensus + innovations-based distributed parameter estimator to reflect the error dynamics induced by the classical gradient descent algorithm. This paves the way for the construction of a strong Lyapunov function. Based on this result, we derive linear matrix inequality-based tools for tuning the algorithm gains such that a guaranteed upper bound on the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathbf {\mathcal {L}_{2}}$</tex-math></inline-formula>-gain with respect to parameter variations, measurement noise, and disturbances in the communication channels is achieved. An application example illustrates the efficiency of the method.