Computer Algorithms of Pseudo‐Formal Linearization Based on Chebyshev Interpolation for Nonlinear Time‐Varying Systems and a Nonlinear Filter

In this paper, we design algorithms of a linearization and a nonlinear filter for time‐varying systems using a pseudo‐formal linearization based on Chebyshev interpolation. Presented algorithms make it easy to linearize nonlinear time‐varying systems and to synthesize a nonlinear filter. They can also reduce the computational burden in both linearization and estimation processes by exploiting Chebyshev interpolation. This algorithm applies a Kalman filter to each linearized system, which is obtained in a some subdomain by using pseudo‐formal linearization, to construct a nonlinear filter that is valid for the entire domain. We demonstrate the effectiveness of algorithms through demonstrating numerical experiments with linearizations and a nonlinear filter of an academic bioreactor.