Primal or Dual Terminal Constraints in Economic MPC? -- Comparison and Insights

TL;DR

This paper compares primal and dual terminal constraint formulations in Economic MPC, analyzing their feasibility, stability implications, and providing a framework for horizon length approximation, supported by a chemical reactor example.

Contribution

It offers a comprehensive comparison of primal and dual terminal constraints in EMPC, including new insights on feasibility and a framework for horizon length approximation.

Findings

Dual/adjoint terminal constraints impact feasibility.

Primal and dual constraints have different stability implications.

A conceptual framework for minimal stabilizing horizon length is proposed.

Abstract

This chapter compares different formulations for Economic nonlinear Model Predictive Control (EMPC) which are all based on an established dissipativity assumption on the underlying Optimal Control Problem (OCP). This includes schemes with and without stabilizing terminal constraints, respectively, or with stabilizing terminal costs. We recall that a recently proposed approach based on gradient correcting terminal penalties implies a terminal constraint on the adjoints of the OCP. We analyze the feasibility implications of these dual/adjoint terminal constraints and we compare our findings to approaches with and without primal terminal constraints. Moreover, we suggest a conceptual framework for approximation of the minimal stabilizing horizon length. Finally, we illustrate our findings considering a chemical reactor as an example.