  Adaptive model predictive control (MPC) methods using set-membership
identification to reduce parameter uncertainty are considered in this work.
Strong duality is used to reformulate the set-membership equations exactly
within the MPC optimization. A predicted worst-case cost is then used to enable
performance-oriented exploration. The proposed approach guarantees robust
constraint satisfaction and recursive feasibility. It is shown that method can
be implemented using homothetic tube and flexible tube parameterizations of
state tubes, and a simulation study demonstrates performance improvement over
state-of-the-art controllers.
