Dynamic Programming Principle and Hamilton--Jacobi--Bellman Equations for Fractional-Order Systems

DOI10.1137/19M1279368zbMath1452.49017arXiv1908.01747OpenAlexW3095160273MaRDI QIDQ5136128

Mikhail Gomoyunov

Publication date: 25 November 2020

Published in: SIAM Journal on Control and Optimization (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1908.01747

zbMATH Keywords

optimal controlHamilton-Jacobi-Bellman equationfractional derivativesfeedback controldynamic programming principlecoinvariant derivatives

Mathematics Subject Classification ID

Dynamic programming in optimal control and differential games (49L20) Optimal feedback synthesis (49N35) Dynamic programming (90C39) Hamilton-Jacobi equations (35F21)

Related Items (14)

Minimax solutions of Hamilton–Jacobi equations with fractional coinvariant derivatives ⋮ Optimal feedback in a linear-quadratic optimal control problem for a fractional-order system ⋮ Causal state feedback representation for linear quadratic optimal control problems of singular Volterra integral equations ⋮ Game-theoretical problems for fractional-order nonstationary systems ⋮ On optimal positional strategies in fractional optimal control problems ⋮ On the relationship between the Pontryagin maximum principle and the Hamilton-Jacobi-Bellman equation in optimal control problems for fractional-order systems ⋮ On linear-quadratic differential games for fractional-order systems ⋮ Sensitivity analysis of value functional of fractional optimal control problem with application to feedback construction of near optimal controls ⋮ Unnamed Item ⋮ Path-dependent Hamilton-Jacobi equations: the minimax solutions revised ⋮ Differential games in fractional-order systems: inequalities for directional derivatives of the value functional ⋮ Minimax solutions of homogeneous Hamilton-Jacobi equations with fractional-order coinvariant derivatives ⋮ Global stabilization of uncertain nonlinear systems via fractional-order PID ⋮ On differentiability of solutions of fractional differential equations with respect to initial data

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