Contracting Nonlinear Observers: Convex Optimization and Learning from Data
This work addresses state estimation in nonlinear systems, which is incremental as it builds on existing observer design methods using convex optimization and learning from data.
The authors tackled the problem of designing nonlinear observers by constructing convex sets of contracting observers and optimizing over them to minimize state-estimation error bounds on simulated noisy data, with verification through numerical simulation.
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.