# Nonlinear input design as optimal control of a Hamiltonian system

## TL;DR

This paper introduces a novel input design approach for nonlinear dynamical systems by transforming the problem into an optimal control task using Hamiltonian systems, aiming to improve parameter estimation accuracy.

## Contribution

It presents a new method that leverages Hamiltonian system representations to optimize input signals for better parameter inference in complex probabilistic models.

## Key findings

- Effective in nonlinear systems with process noise
- Demonstrated via MRI pulse sequence design
- Transforms input design into optimal control problem

## Abstract

We propose an input design method for a general class of parametric probabilistic models, including nonlinear dynamical systems with process noise. The goal of the procedure is to select inputs such that the parameter posterior distribution concentrates about the true value of the parameters; however, exact computation of the posterior is intractable. By representing (samples from) the posterior as trajectories from a certain Hamiltonian system, we transform the input design task into an optimal control problem. The method is illustrated via numerical examples, including MRI pulse sequence design.