Adaptive algorithms with inertia

We introduce a novel Gravity Search adaptive algorithm, which replicates the movement of a ball descending along the inner surface of a bowl filled with liquid. By choosing the appropriate viscosity of the liquid, gravity, and the mass of the ball, the movement of the ball can be controlled to achieve the desired performance. The physical law of conservation of energy makes the algorithm very stable. We also show that the Normalized LMS algorithm is a special form of the proposed Gravity Search adaptive algorithm. Simulation results comparing the performance of Normalized LMS algorithm and the Gravity Search adaptive algorithm are provided. The results show that the Gravity Search adaptive algorithm has superior immunity to the random perturbation of the error signal compared to the Normalized LMS algorithm.