On Minimax Optimal Dual Control for Fully Actuated Systems

Abstract: 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.