A Robust and Accelerated Heavy-Ball-Based Algorithm for Parameter Identification

Abstract. This paper contributes to designing a new parameter identification algorithm for linear regression systems with constant unknown parameters and noisy measurements. The proposed algorithm is based on a new accelerated version of the heavy-ball method, which uses a nonlinear extension of Kreisselmeier’s filters. For the noise-free case, the algorithm can identify constant parameters accurately and in finite time, assuming persistence of the regressor’s excitation. A local stability analysis is developed using the Lyapunov function approach. The robustness characterizations for the noisy case are provided in terms of input-to-state stability property for the parameter identification error dynamics. Additionally, the paper considers a classic optimization problem, taking into account prior data collection of measurements. A reduced version of the proposed identification algorithm is introduced for this case, ensuring global finite-time stability for the noise-free case and local input-to-state stability for the noisy scenario. The effectiveness of the proposed parameter identification algorithm is depicted with some simulation results.