Nonlinear input design as optimal control of a Hamiltonian system
This work addresses input design for parameter estimation in probabilistic models, which is incremental as it builds on existing methods by reformulating the problem as optimal control.
The authors tackled the problem of designing inputs for parametric probabilistic models, such as nonlinear dynamical systems with noise, to concentrate the parameter posterior distribution around true values, and they transformed this into an optimal control problem using a Hamiltonian system representation, demonstrating the method with numerical examples including MRI pulse sequence design.
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.