Regret-Optimal Estimation and Control

We consider estimation and control in linear dynamical systems from the perspective of regret minimization. Unlike most prior work this area, we focus on problem designing causal state estimators controllers which compete against a clairvoyant noncausal policy, instead best policy selected hindsight some fixed parametric class. show that regret-optimal filters can be derived state-space form using operator-theoretic techniques robust control. Our results viewed as extending traditional control, focuses minimizing worst-case cost, to regret. propose analogs Model-Predictive Control (MPC) Extended Kalman Filter (EKF) for with nonlinear dynamics present numerical experiments these algorithms significantly outperform standard approaches