On Minimax Optimal Dual Control for Fully Actuated Systems - Rantzer, Anders ; 0000-0001-7118-2786 (2025 American Control Conference, ACC 2025, Denver, United States, 2025-07-08 - 2025-07-10, 2025)
A multi-variable adaptive controller is derived as the explicit solution to a minimax dynamic game. The minimizing player selects the control action as a function of past state measurements and inputs. The maximizing player selects disturbances and model parameters for the underlying linear time-invariant dynamics. This leads to a Bellman equation that can be solved explicitly for the case with unitary B-matrix known up to a sign and no input penalty. The minimizing policy is a dual controller that optimizes the tradeoff between exploration and exploitation.