Design of Optimal UKF State Observer–Controller for Stochastic Dynamical Systems

Abstract

"Stochastic noise processes" passed through highly nonlinear systems, always pose a significant threat to the industrial plant's stability. A novel generalized optimal “unscented Kalman filter state observer-controller” (UKFOC) algorithm is presented to control these plants effectively and efficiently. The proposed optimal UKFOC provides state “estimation and control” simultaneously, omitting the system's need for a separate controller. The “trajectory exit probability” from the desired boundaries is minimized based on the large deviation principle with the bounded instantaneous “trajectory tracking error” and the “state tracking error.” These boundaries are rationally computed from the error statistics. The convergence and robustness are realized in terms of the error energy under the influence of the noise and the small parametric uncertainties, respectively. The algorithm's superior performance is demonstrated with respect to Lyapunov control and adaptive Lyapunov control based techniques. Finally, the UKFOC is implemented and tested for the commercially available Phantom Omni robot to demonstrate the potential application on a real-time basis.