Solution for the continuous-time infinite-horizon linear quadratic regulator subject to scalar state constraints

Thijs van Keulen (Corresponding author)

Research output: Contribution to journalArticleAcademicpeer-review

3 Downloads (Pure)

Abstract

This article provides a solution for the continuous-time Linear Quadratic Regulator (LQR) subject to a scalar state constraint. Using a dichotomy transformation, novel properties for the finite-horizon LQR are derived; the unknown boundary conditions are explicitly expressed as a function of the horizon length, the initial state, and the final state or, cost of the final state. Practical relevance of these novel properties are demonstrated with an algorithm to compute the continuous-time LQR subject to a scalar state constraint. The proposed algorithm uses the analytical conditions for optimality, without a priori discretization, to find only those sampling time instances that mark the start and end of a constrained interval. Each subinterval consists of a finite-horizon LQR, hence, a solution can be efficiently computed and the computational complexity does not grow with the horizon length. In fact, an infinite horizon can be handled. The algorithm is demonstrated with a simulation example.
Original languageEnglish
Article number8734848
Pages (from-to)133-138
Number of pages6
JournalIEEE Control Systems Letters
Volume4
Issue number1
DOIs
Publication statusPublished - 1 Jan 2020

Keywords

  • Optimal control
  • predictive control for linear systems

Fingerprint Dive into the research topics of 'Solution for the continuous-time infinite-horizon linear quadratic regulator subject to scalar state constraints'. Together they form a unique fingerprint.

Cite this