  A finite horizon optimal tracking problem is considered for linear dynamical
systems subject to parametric uncertainties in the state-space matrices and
exogenous disturbances. A suboptimal solution is proposed using a model
predictive control (MPC) based explicit dual control approach which enables
active uncertainty learning. A novel algorithm for the design of robustly
invariant online terminal sets and terminal controllers is presented. Set
membership identification is used to update the parameter uncertainty online. A
predicted worst-case cost is used in the MPC optimization problem to model the
dual effect of the control input. The cost-to-go is estimated using
contractivity of the proposed terminal set and the remaining time horizon, so
that the optimizer can estimate future benefits of exploration. The proposed
dual control algorithm ensures robust constraint satisfaction and recursive
feasibility, and navigates the exploration-exploitation trade-off using a
robust performance metric.
