On generalized terminal state constraints for model predictive control

TL;DR

This paper introduces a generalized terminal state constraint for Model Predictive Control that enhances feasibility and convergence properties, applicable to both tracking and economic MPC, with proven theoretical guarantees and practical illustrations.

Contribution

It proposes a novel generalized terminal state constraint for MPC that increases the feasible set and guarantees finite-time convergence to an optimal control law.

Findings

Larger feasibility set compared to existing methods

Finite-time convergence with arbitrarily good accuracy

Validated through three illustrative examples

Abstract

This manuscript contains technical results related to a particular approach for the design of Model Predictive Control (MPC) laws. The approach, named "generalized" terminal state constraint, induces the recursive feasibility of the underlying optimization problem and recursive satisfaction of state and input constraints, and it can be used for both tracking MPC (i.e. when the objective is to track a given steady state) and economic MPC (i.e. when the objective is to minimize a cost function which does not necessarily attains its minimum at a steady state). It is shown that the proposed technique provides, in general, a larger feasibility set with respect to existing approaches, given the same computational complexity. Moreover, a new receding horizon strategy is introduced, exploiting the generalized terminal state constraint. Under mild assumptions, the new strategy is guaranteed to converge in finite time, with arbitrarily good accuracy, to an MPC law with an optimally-chosen terminal state constraint, while still enjoying a larger feasibility set. The features of the new technique are illustrated by three examples.