Robustness to Incorrect System Models in Stochastic Control

In stochastic control applications, typically only an ideal model (controlled transition kernel) is assumed and the control design is based on the given model, raising the problem of performance loss due to the mismatch between the assumed model and the actual model. In this talk, I will talk about continuity properties of discrete-time stochastic control problems with respect to system models (i.e., controlled transition kernels) and robustness of optimal control policies designed for incorrect models applied to the true system. Continuity can be established under total variation convergence of the transition kernels under mild assumptions and with further restrictions on the dynamics and observation model under weak and setwise convergence of the transition kernels. Using these continuity properties, we establish convergence results and error bounds due to mismatch that occurs by the application of a control policy that is designed for an incorrectly estimated system model to a true model, thus establishing positive and negative results on robustness.