State Estimation for Repetitive Processes Using Iteratively Improving Moving Horizon Observers

This paper considers the problem of state estimation for repetitive nonlinear systems. Taking the repetitive nature of the process into account a new state estimation scheme is proposed, which from repetition to repetition iteratively improves the estimate. The scheme combines ideas from iterative learning control and moving horizon state estimation. The state estimate during every repetition is based on approximately minimizing the deviation between the measured and estimated output. Stability and iterative improvements of the state estimates are ensured by enforcing a sufficient contraction of the deviation between the measured and estimated output over the considered estimation window. As shown, under the contraction constraints the state estimation scheme ensures asymptotic convergence of the state estimation error in the nominal case, provided that the system satisfies an uniform reconstructability condition.