Optimal control of a class of Caputo fractional systems

被引：0

作者：

Das, Sanjukta ^{[1
]}

Tripathi, Vidushi ^{[1
]}

机构：

[1] Mahindra Univ, Ecole Cent Sch Engn, Hyderabad 500043, India

来源：

JOURNAL OF ANALYSIS | 2024年

关键词：

Fractional calculus; Optimal control; Pontryagin maximum principle; Necessary conditions; HJB equation; PONTRYAGIN MAXIMUM PRINCIPLE; EQUATIONS; CONTROLLABILITY;

D O I：

10.1007/s41478-024-00840-2

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

This article introduces a broad formulation of fractional optimal control issues characterized by a class of Caputo fractional systems within Hilbert spaces. Through a variational method, the Pontryagin maximum principle (PMP) is established as a set of essential conditions for optimality. Following this, the Hamilton-Jacobi-Bellman (HJB) equations are derived based on the derived PMP. In conclusion, it is established that the value function serves as a viscosity solution of the HJB equation. Numerical example is finally provided to exemplify the theory developed.

引用

页数：22

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