Kalman Filter based Newton Extremum Seeking Control for Maximum Gases Production Rates of Anaerobic Digestion Process

This paper proposes a Kalman filter (KF) based Newton extremum seeking control (NESC) to maximize production rates of hydrogen and methane in anaerobic digestion process. The Kalman filtering algorithm is used to obtain more accurate gradient and Hessian estimates which makes possible to increase the convergence speed to the extremum and to eliminate input and output steady-state oscillations. The simulation examples demonstrate the performances of the proposed approach.

GRADIENT AND HESSIAN ESTIMATES FOR DIRICHLET AND NEUMANN EIGENFUNCTIONS

We establish integral formulas and sharp two-sided bounds for the Ricci curvature, mean curvature and second fundamental form on a Riemannian manifold with boundary. As applications, sharp gradient and Hessian estimates are derived for the Dirichlet and Neumann eigenfunctions.