State estimation and nonlinear predictive control of autonomous hybrid system using derivative free state estimators

In this work, we develop a state estimation scheme for nonlinear autonomous hybrid systems, which are subjected to stochastic state disturbances and measurement noise, using derivative free state estimators. In particular, we propose the use of ensemble Kalman filters (EnKF), which belong to the class of particle filters, and unscented Kalman filters (UKF) to carry out estimation of state variables of autonomous hybrid system. We then proceed to develop novel nonlinear model predictive control (NMPC) schemes using these derivative free estimators for better control of autonomous hybrid systems. A salient feature of the proposed NMPC schemes is that the future trajectory predictions are based on stochastic simulations, which explicitly account for the uncertainty in predictions arising from the uncertainties in the initial state and the unmeasured disturbances. The efficacy of the proposed state estimation based control scheme is demonstrated by conducting simulation studies on a benchmark three-tank hybrid system. Analysis of the simulation results reveals that EnKF and UKF based NMPC strategies is well suited for effective control of nonlinear autonomous three-tank hybrid system.