TY - JOUR
T1 - Optimal linear–quadratic control of asymptotically stabilizable systems using approximations
AU - Zwart, Hans
AU - Morris, Kirsten A.
AU - Iftime, Orest V.
PY - 2020/12
Y1 - 2020/12
N2 - In this paper we study approximations to the infinite-horizon quadratic optimal control problem for linear systems that may be only asymptotically stabilizable. For linear systems, this issue only arises with infinite-dimensional systems. We provide sufficient conditions which guarantee when approximations to the optimal feedback result in the cost converging to the optimal cost. One technique for approximate solution of the optimal control problem is to use Newton–Kleinman iterations for the associated Riccati equation. Some new results in this direction are provided. Several important classes of systems, lightly damped second-order systems and a platoon-type system, are shown to be optimizable. Also, finding an initial stabilizing control for the Newton–Kleinman iteration can be non-trivial. The initial iterate for these classes is described.
AB - In this paper we study approximations to the infinite-horizon quadratic optimal control problem for linear systems that may be only asymptotically stabilizable. For linear systems, this issue only arises with infinite-dimensional systems. We provide sufficient conditions which guarantee when approximations to the optimal feedback result in the cost converging to the optimal cost. One technique for approximate solution of the optimal control problem is to use Newton–Kleinman iterations for the associated Riccati equation. Some new results in this direction are provided. Several important classes of systems, lightly damped second-order systems and a platoon-type system, are shown to be optimizable. Also, finding an initial stabilizing control for the Newton–Kleinman iteration can be non-trivial. The initial iterate for these classes is described.
KW - Asymptotic stability
KW - Infinite-dimensional systems
KW - Optimal control
KW - Riccati equations
UR - http://www.scopus.com/inward/record.url?scp=85095915183&partnerID=8YFLogxK
U2 - 10.1016/j.sysconle.2020.104802
DO - 10.1016/j.sysconle.2020.104802
M3 - Article
AN - SCOPUS:85095915183
VL - 146
JO - Systems and control letters
JF - Systems and control letters
SN - 0167-6911
M1 - 104802
ER -