Robust Dual Control MPC with Guaranteed Constraint Satisfaction

We present a robust dual control MPC (RDC-MPC) policy with guaranteed constraint satisfaction for simultaneous closed-loop identification and regulation of state and input-constrained linear systems subject to parametric and additive uncertainty. The uncertain system is modeled as a polytopic Linear Difference Inclusion (pLDI) for which a maximal robust control invariant (RCI) set is calculated. Selecting a control from the associated robust admissible input (RAI) set guarantees constraint satisfaction for all pLDI realizations, and thus guarantees constraint satisfaction during the identification transient when the MPC prediction model is uncertain. The MPC problem is then cast as selecting a control from the RAI set that optimizes the dual objective of identifying the unknown system parameters and regulating the true system, where the tradeoff between the two objectives is adjusted based on the prediction error of the identified system. Numerical examples illustrate the proposed scheme's effectiveness and performance increase, while guaranteeing robust constraint satisfaction.