Strict Dissipativity and turnpike for LQ Optimal Control Problems with Possibly Boundary Reference

TL;DR

This paper explores the turnpike property in constrained linear-quadratic optimal control problems, linking it to system dissipativity, especially when the optimal trajectory's reference point is on the boundary of state constraints.

Contribution

It establishes sufficient conditions for the turnpike property in boundary-reference cases, extending previous results to more general constrained scenarios.

Findings

Turnpike property holds under new dissipativity conditions.

Boundary reference points can be incorporated into turnpike analysis.

Conditions ensure stability and optimality in constrained LQ problems.

Abstract

In this paper we investigate the turnpike property for constrained LQ optimal control problem in connection with dissipativity of the control system. We determine sufficient conditions to ensure the turnpike property in the case of a turnpike reference possibly occurring on the boundary of the state constraint set.