Addressing Adaptation and Learning in the Context of MPC with MHE

This paper considers the estimation and control of systems with parametric uncertainty. An approach that combines moving horizon estimation and model predictive control into a single min-max optimization is employed to estimate past and current values of the state, compute a sequence of optimal future control inputs, predict future values of the state, as well as estimate current values of uncertain parameters. This is done by including the state, inputs, and uncertain parameters as optimization variables. Learning the true values of the uncertain parameters requires a sufficiently large number of past measurements and that the system is persistently excited. The true values of the uncertain parameters may change over time, and the optimization computes future control inputs that adapt to changing estimates of the uncertain parameters in order to better control the uncertain system. Several linear and nonlinear examples with parametric uncertainty are discussed and effectively controlled using this combined moving horizon estimation and model predictive control approach.