Solution for the Continuous-Time Infinite-Horizon Linear Quadratic Regulator Subject to Scalar State Constraints

This letter 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 hori...

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Bibliographic Details
Published in:IEEE control systems letters 2020-01, Vol.4 (1), p.133-138
Main Author: van Keulen, Thijs
Format: Article
Language:English
Subjects:
Boundary conditions
Eigenvalues and eigenfunctions
Optimal control
predictive control for linear systems
Regulators
Trajectory
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Summary:This letter 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.
ISSN:2475-1456
2475-1456
DOI:10.1109/LCSYS.2019.2922193