scholarly journals Connection among Stochastic Hamilton–Jacobi–Bellman Equation, Path-Integral, and Koopman Operator on Nonlinear Stochastic Optimal Control

2021 ◽  
Vol 90 (10) ◽  
pp. 104802
Author(s):  
Jun Ohkubo
Keyword(s):  
Optimal Control ◽  
Path Integral ◽  
Stochastic Optimal Control ◽  
Bellman Equation ◽  
Koopman Operator ◽  
Hamilton Jacobi Bellman Equation ◽  
Hamilton Jacobi Bellman

scholarly journals Optimal Control Strategy of Companies: Inheriting Period and Carbon Emission Reduction

2020 ◽  
Vol 2020 ◽  
pp. 1-11
Author(s):  
Jin Liang ◽  
Wenlin Huang
Keyword(s):  
Optimal Control ◽  
Control Strategy ◽  
Emission Reduction ◽  
Carbon Emission ◽  
Bellman Equation ◽  
Control Model ◽  
Policy Implications ◽  
Optimal Control Strategy ◽  
Hamilton Jacobi Bellman Equation ◽  
Hamilton Jacobi Bellman

In this paper, we develop an optimal control model of companies for the inheriting period, during which interphase banking and borrowing of allowances are allowable. By considering the emission reduction policy and the initial auction amount, we optimize the problem in two steps. The model is then converted into a two-dimensional Hamilton–Jacobi–Bellman equation. The numerical results, analysis, and comparisons are presented. Finally, we highlight several policy implications from the perspectives of companies and governments.

Solving a class of fractional optimal control problems by the Hamilton–Jacobi–Bellman equation

2016 ◽  
Vol 24 (9) ◽  
pp. 1741-1756 ◽  
Author(s):  
Seyed Ali Rakhshan ◽  
Sohrab Effati ◽  
Ali Vahidian Kamyad
Keyword(s):  
Optimal Control ◽  
Fractional Derivative ◽  
Bellman Equation ◽  
Optimal Control Problems ◽  
Control Problems ◽  
Fractional Optimal Control ◽  
Solution Scheme ◽  
Hamilton Jacobi Bellman Equation ◽  
Fractional Optimal Control Problems ◽  
Hamilton Jacobi Bellman

The performance index of both the state and control variables with a constrained dynamic optimization problem of a fractional order system with fixed final Time have been considered here. This paper presents a general formulation and solution scheme of a class of fractional optimal control problems. The method is based upon finding the numerical solution of the Hamilton–Jacobi–Bellman equation, corresponding to this problem, by the Legendre–Gauss collocation method. The main reason for using this technique is its efficiency and simple application. Also, in this work, we use the fractional derivative in the Riemann–Liouville sense and explain our method for a fractional derivative of order of [Formula: see text]. Numerical examples are provided to show the effectiveness of the formulation and solution scheme.

Sign in / Sign up

Export Citation Format

Share Document