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

Thijs van Keulen (Corresponding author)

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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.
Originele taal-2Engels
Artikelnummer8734848
Pagina's (van-tot)133-138
Aantal pagina's6
TijdschriftIEEE Control Systems Letters
Volume4
Nummer van het tijdschrift1
DOI's
StatusGepubliceerd - 1 jan 2020

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