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

Research output: Contribution to journalArticleAcademicpeer-review

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.
LanguageEnglish
Article number8734848
Pages133-138
Number of pages6
JournalIEEE Control Systems Letters
Volume4
Issue number1
DOIs
StatePublished - 1 Jan 2020

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State Constraints
Infinite Horizon
Regulator
Continuous Time
Scalar
Finite Horizon
Horizon
Computational complexity
Dichotomy
Boundary conditions
Sampling
Optimality
Computational Complexity
Discretization
Unknown
Interval
Costs
Simulation

Keywords

  • Optimal control
  • predictive control for linear systems

Cite this

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Solution for the continuous-time infinite-horizon linear quadratic regulator subject to scalar state constraints. / van Keulen, Thijs.

In: IEEE Control Systems Letters, Vol. 4, No. 1, 8734848, 01.01.2020, p. 133-138.

Research output: Contribution to journalArticleAcademicpeer-review

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