Seminarios

This work presents a control framework for continuous-time stochastic optimal control problems with
discrete-time, partial, noisy, and potentially controllable measurements. The approach uses a probability
measure-valued state and Bayesian updates to incorporate noisy data into control decisions. Control
optimality is characterized by interlaced Hamilton-Jacobi-Bellman (HJB) equations with controlled
impulse steps at measurement times. For Gaussian-controlled processes, an equivalent finite-dimensional
HJB equation based on the state’s mean and covariance is derived. Numerical examples demonstrate the
method’s effectiveness under perfect, none, and noisy (possibly controllable) observations, highlighting the
impact of observation uncertainty on control strategies and performance.