In this letter, we propose a new type of recursive least squares (RLS) algorithms without using the initial information of a parameter or a state to be estimated. The proposed RLS algorithm is first obtained for a generic linear model and is then extended to a state estimator for a stochastic state-space model. Compared with the existing algorithms, the proposed RLS algorithms are simpler and more numerically stable. It is shown through simulation that the proposed RLS algorithms have better numerical stability for digital computations than existing algorithms.

We propose a stability-guaranteed horizon size (SgHS) for stabilizing receding horizon control (RHC). It is shown that the proposed SgHS can be represented explicitly in terms of the known parameters of the given system model and is independent of the terminal weighting matrix in the cost function. The proposed SgHS is validated via a numerical example.