TY - JOUR

T1 - Solution for the continuous-time infinite-horizon linear quadratic regulator subject to scalar state constraints

AU - van Keulen, Thijs

PY - 2020/1/1

Y1 - 2020/1/1

N2 - 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.

AB - 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.

KW - Optimal control

KW - predictive control for linear systems

UR - http://www.scopus.com/inward/record.url?scp=85068240860&partnerID=8YFLogxK

U2 - 10.1109/LCSYS.2019.2922193

DO - 10.1109/LCSYS.2019.2922193

M3 - Article

AN - SCOPUS:85068240860

VL - 4

SP - 133

EP - 138

JO - IEEE Control Systems Letters

JF - IEEE Control Systems Letters

SN - 2475-1456

IS - 1

M1 - 8734848

ER -