Contracting Nonlinear Observers: Convex Optimization and Learning from Data

Ian R. Manchester

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arXiv · 1711.08135

Contracting Nonlinear Observers: Convex Optimization and Learning from Data

Ian R. Manchester

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Abstract

A new approach to design of nonlinear observers (state estimators) is proposed. The main idea is to (i) construct a convex set of dynamical systems which are contracting observers for a particular system, and (ii) optimize over this set for one which minimizes a bound on state-estimation error on a simulated noisy data set. We construct convex sets of continuous-time and discrete-time observers, as well as contracting sampled-data observers for continuous-time systems. Convex bounds for learning are constructed using Lagrangian relaxation. The utility of the proposed methods are verified using numerical simulation.

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Ian R. Manchester. 2017-11-22. Contracting Nonlinear Observers: Convex Optimization and Learning from Data. https://arxiv.org/abs/1711.08135

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