Stabilization of Strictly Pre-Dissipative Receding Horizon Linear Quadratic Control by Terminal Costs

TL;DR

This paper demonstrates that in receding horizon linear quadratic control, terminal costs can replace terminal constraints to ensure asymptotic stability under strict pre-dissipativity, with results specific to the linear-quadratic case.

Contribution

It shows how to replace terminal constraints with terminal costs for stability in linear-quadratic receding horizon control, extending previous methods.

Findings

Terminal costs can substitute terminal constraints for stability.

Results are specific to linear-quadratic systems.

Analysis of nonlinear case is deferred to future work.

Abstract

Asymptotic stability in receding horizon control is obtained under a strict pre-dissipativity assumption, in the presence of suitable state constraints. In this paper we analyze how terminal constraints can be replaced by suitable terminal costs. We restrict to the linear-quadratic setting as that allows us to obtain stronger results, while we analyze the full nonlinear case in a separate contribution.