Constrained State Estimation for Nonlinear Systems: A Redesign Approach Based on Convexity

Abstract

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Oblique Projected Dynamical Systems and Incremental Stability Under State Constraints

“…Next to establishing desirable (incremental) stability properties for oblique PDS, we also demonstrate the use of these results in a recently popular observer re-design problem exploiting state constraint information of the to-be-observed dynamics, see [2], [3]. The objective is to re-design an available unconstrained observer such that its original stability properties for the estimation error dynamics are preserved, while additionally guaranteeing that the estimated state lies in a prescribed constraint set, in which also the observed state lies.…”

“…They are given by x | y P = x Py and |x| 2 P = x Px for x, y ∈ R n . A set-valued mapping 2 for all (x, x * ) ∈ gr(P) and all (y, y * ) ∈ gr(P). We call P strongly monotone, if it is α-strongly monotone for some α > 0.…”

“…The objective is to re-design an available unconstrained observer such that its original stability properties for the estimation error dynamics are preserved, while additionally guaranteeing that the estimated state lies in a prescribed constraint set, in which also the observed state lies. In [3] this problem was considered for discretetime systems, while recently and independently in [2] also continuous-time versions were developed. We provide here an alternative perspective on this problem for a smaller set of nonlinear observers than considered in [2].…”

“…In [3] this problem was considered for discretetime systems, while recently and independently in [2] also continuous-time versions were developed. We provide here an alternative perspective on this problem for a smaller set of nonlinear observers than considered in [2]. However, we do not require inflation of the set K as in [2] and provide a more basic solution.…”

“…We provide here an alternative perspective on this problem for a smaller set of nonlinear observers than considered in [2]. However, we do not require inflation of the set K as in [2] and provide a more basic solution.…”