Offset-free design principles in the presence of uncertainty: A comprehensive tour from tracking to economic MPC

Abstract

This keynote lecture addresses the design principles of Model Predictive Control (MPC) systems to cope with the presence of structural mismatch between the actual plant dynamics and MPC model. The general goal is to asymptotically reach the optimal behavior for the actual unknown plant dynamics. The talk is structured in three main parts.
We start from the case of tracking, linear and nonlinear, MPC to build a general algorithm that guarantees offset-free tracking of piece-wise constant set-points in the outputs. To this aim the nominal model is augmented with integrating states, referred to as “disturbances”, and a combined state and disturbance observer is consequently designed. We analyze the requirements and opportunities of this disturbance observer, and discuss how other approaches, commonly thought to be different, are indeed particular cases of this general approach.
In the second part, we present recent results on the generalization of Internal Model Control (IMC) systems to handle integrating and unstable plants in the presence of plant-model mismatch. This generalization is based on a general disturbance model, as in offset-free tracking MPC. We analyze the necessary and sufficient conditions that guarantee internal stability and offset-free tracking, and we derive analytical expressions of the sensitivity functions to provide the designer with effective tools for achieving the desired tradeoff between performance and robustness.
Finally, we focus the attention to so-called economic MPC formulations, in which the cost function is not positive definite around the optimal equilibrium. For this novel class of MPC systems, we present the recent results on offset-free design which includes, in addition to an augmented model as in tracking MPC, a suitable modifier necessary to achieve matching of the necessary conditions of optimality. Computation of such modifier requires, in principle, knowledge of plant gradient information, and therefore we discuss implementation strategies based on easily available input-output measurements only. We conclude the lecture by sketching future research directions and open problems.