Stochastic model predictive control with active uncertainty learning: A Survey on dual control

This paper provides a review of model predictive control (MPC) methods with active uncertainty learning. System uncertainty poses a key theoretical and practical challenge in MPC, which can be aggravated when system uncertainty increases due to the time-varying nature of system dynamics. For uncertain systems with stochastic uncertainty, this paper presents the stochastic MPC (SMPC) problem in the dual control paradigm, where the control inputs to an uncertain system have a probing effect for active uncertainty learning and a directing effect for controlling the system dynamics. The complexity of the SMPC problem with dual control effect is described in connection to stochastic dynamic programming as well as Bayesian estimation for its output feedback implementation. Further, implicit and explicit dual control methods for approximating the receding-horizon control problem with dual control effect are surveyed and analyzed with the intent to discuss the key challenges and opportunities in SMPC with dual control effect.