TY - JOUR

T1 - Value functional and optimal feedback control in linear-quadratic optimal control problem for fractional-order system

AU - Gomoyunov, Mikhail

N1 - This work is supported by RSF grant 19-11-00105, https://rscf.ru/en/project/19-11-00105/

PY - 2024

Y1 - 2024

N2 - In this paper, a finite-horizon optimal control problem involving a dynamical system described by a linear Caputo fractional differential equation and a quadratic cost functional is considered. An explicit formula for the value functional is given, which includes a solution of a certain Fredholm integral equation. A step-by-step feedback control procedure for constructing -optimal controls with any accuracy is proposed. The basis for obtaining these results is the study of a solution of the associated Hamilton–Jacobi–Bellman equation with so-called fractional coinvariant derivatives.

AB - In this paper, a finite-horizon optimal control problem involving a dynamical system described by a linear Caputo fractional differential equation and a quadratic cost functional is considered. An explicit formula for the value functional is given, which includes a solution of a certain Fredholm integral equation. A step-by-step feedback control procedure for constructing -optimal controls with any accuracy is proposed. The basis for obtaining these results is the study of a solution of the associated Hamilton–Jacobi–Bellman equation with so-called fractional coinvariant derivatives.

UR - http://www.scopus.com/inward/record.url?partnerID=8YFLogxK&scp=85180904756

U2 - 10.3934/mcrf.2023002

DO - 10.3934/mcrf.2023002

M3 - Article

VL - 14

SP - 215

EP - 254

JO - Mathematical Control and Related Fields

JF - Mathematical Control and Related Fields

SN - 2156-8472

IS - 1

ER -