Data to Controller for Nonlinear Systems: An Approximate Solution

TL;DR

This paper develops an approximate data-driven control method for nonlinear systems, modeling uncertainties as random variables conditioned on observed data, and provides finite-dimensional solutions demonstrated through simulations.

Contribution

It introduces a novel approach to nonlinear control that accounts for data-driven uncertainty and offers practical approximation techniques for intractable problems.

Findings

Effective in simulation on nonlinear systems

Handles unknown parameters and disturbances as random variables

Provides finite-dimensional deterministic optimization solutions

Abstract

This paper considers the problem of determining an optimal control action based on observed data. We formulate the problem assuming that the system can be modelled by a nonlinear state-space model, but where the model parameters, state and future disturbances are not known and are treated as random variables. Central to our formulation is that the joint distribution of these unknown objects is conditioned on the observed data. Crucially, as new measurements become available, this joint distribution continues to evolve so that control decisions are made accounting for uncertainty as evidenced in the data. The resulting problem is intractable which we obviate by providing approximations that result in finite dimensional deterministic optimisation problems. The proposed approach is demonstrated in simulation on a nonlinear system.