Moving horizon estimation for hybrid systems

We propose a state smoothing algorithm for hybrid systems based on Moving Horizon Estimation (MHE) by exploiting the equivalence between hybrid systems modeled in the Mixed Logic Dynamical form and piecewise affine systems. We provide sufficient conditions on the time horizon and the penalties on the state at the beginning of the estimation horizon to guarantee asymptotic convergence of the MHE scheme. Moreover, we propose two practical algorithms for the computation of such penalties that allow to implement MHE by solving a Mixed-Integer Quadratic Program.