G. Ferrari-Trecate, D. Mignone, and M. Morari. Moving horizon estimation for hybrid systems. IEEE Trans. Autom. Contr. , 47(10):1663--1676, 2002.
We propose a state smoothing algorithm for hybrid systems basedon Moving Horizon Estimation (MHE)by exploiting the equivalence between hybrid systems modeled in the Mixed LogicDynamical form and piecewise affine systems.We provide sufficient conditions on the time horizon and the penalties on thestate at the beginning of the estimation horizonto guarantee asymptotic convergence of the MHE scheme.Moreover, we propose two practical algorithms for the computation of such penaltiesthat allow to implement MHE by solving a Mixed-Integer Quadratic Program.