Unconstrained Moving Horizon Estimation and simultaneous Model Predictive Control by multi-parametric programming

We demonstrate how unconstrained Moving Horizon Estimation (MHE) and Model Predictive Control (MPC) can be simultaneously addressed via multi-parametric programming. We show that the estimation error is bounded in an invariant set by first obtaining the error dynamics of unconstrained MHE for linear, time-invariant systems and then using set-theoretical methods to derive bounds on the estimation error. We then use the error dynamics and the error bounds for the design of a robust output feedback explicit/multi-parametric MPC resulting in a simultaneous estimation and control design which we illustrate with an example of robust tube-based output feedback MPC.