A New Identification Framework for Off-Line Computation of Moving-Horizon Observers

Abstract

In this paper, a new nonlinear identification framework is proposed to address the issue of off-line computation of moving-horizon observer estimate. The proposed structure merges the advantages of nonlinear approximators with the efficient computation of constrained quadratic programming problems.A bound on the estimation error is proposed and the efficiency of the resulting scheme is illustrated using two state estimation examples.

Approximate Explicit Model Predictive Control via Piecewise Nonlinear System Identification

“…In this section, we briefly recall the identification framework [11] for a class of nonlinear relationships. Several modifications with preliminary analysis are also introduced.…”

“…The strict positivity of this weight is to avoid any drastically loose approximation as well as to guarantee the well-posedness of the formulation. In this paper, we utilize a simple form of the weight indicator ω(q, Z) as (11) where ρ i > 0 are the constant weights corresponding to disjoint subspaces W i ⊂ [q, q] × Z.…”

“…The remainder of this paper is organized as follows. Section 2 recalls the identification of a nonlinear map proposed in [11]. The extension of this framework to the piecewise nonlinear maps is explained in Section 3 where an identification methodology is developed with application to EMPCs.…”

“…In particular, each component of the control vector is identified independently as a PWNL map of the available regressor. A heuristic identification procedure to do so is proposed, which is an extension of the preliminary work [11]. Regarding complexity, the PWNL representations of the identified EMPCs allows to reduce the number of regions with respect to the piecewise affine approaches, especially for constrained NMPCs.…”