Generalization of Cauchy’s characteristics method to construct smooth solutions to Hamilton-Jacobi-Bellman equations in optimal control problems with singular regimes

2014 ◽  
Vol 38 (3) ◽  
pp. 118-127 ◽  
Author(s):  
I. Ye. Yegorov
Keyword(s):  
Optimal Control ◽  
Optimal Control Problems ◽  
Control Problems ◽  
Smooth Solutions ◽  
Bellman Equations ◽  
Characteristics Method ◽  
Hamilton Jacobi Bellman

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.

A composite pseudospectral method for optimal control problems with piecewise smooth solutions

2017 ◽  
Vol 354 (5) ◽  
pp. 2393-2414 ◽  
Author(s):  
Hamid Reza Tabrizidooz ◽  
Hamid Reza Marzban ◽  
Marzieh Pourbabaee ◽  
Mehrnoosh Hedayati
Keyword(s):  
Optimal Control ◽  
Optimal Control Problems ◽  
Pseudospectral Method ◽  
Piecewise Smooth ◽  
Control Problems ◽  
Smooth Solutions

scholarly journals Application of Optimal HAM for Finding Feedback Control of Optimal Control Problems

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
H. Saberi Nik ◽  
Stanford Shateyi
Keyword(s):  
Optimal Control ◽  
Optimal Control Problems ◽  
Convergent Series ◽  
Residual Error ◽  
Control Problems ◽  
Strong Nonlinearity ◽  
Control Parameters ◽  
Convergence Control ◽  
Hamilton Jacobi Bellman ◽  
Optimal Approach

An optimal homotopy-analysis approach is described for Hamilton-Jacobi-Bellman equation (HJB) arising in nonlinear optimal control problems. This optimal approach contains at most three convergence-control parameters and is computationally rather efficient. A kind of averaged residual error is defined. By minimizing the averaged residual error, the optimal convergence-control parameters can be obtained. This optimal approach has general meanings and can be used to get fast convergent series solutions of different types of equations with strong nonlinearity. The closed-loop optimal control is obtained using the Bellman dynamic programming. Numerical examples are considered aiming to demonstrate the validity and applicability of the proposed techniques and to compare with the existing results.

A class of infinite-horizon stochastic delay optimal control problems and a viscosity solution to the associated HJB equation

2018 ◽  
Vol 24 (2) ◽  
pp. 639-676
Author(s):  
Jianjun Zhou
Keyword(s):  
Optimal Control ◽  
Viscosity Solution ◽  
Optimal Control Problems ◽  
Nonlinear Partial Differential Equation ◽  
Infinite Horizon ◽  
Hjb Equation ◽  
Second Order ◽  
Control Problems ◽  
Stochastic Delay ◽  
Hamilton Jacobi Bellman

In this paper, we investigate a class of infinite-horizon optimal control problems for stochastic differential equations with delays for which the associated second order Hamilton−Jacobi−Bellman (HJB) equation is a nonlinear partial differential equation with delays. We propose a new concept for the viscosity solution including timetand identify the value function of the optimal control problems as a unique viscosity solution to the associated second order HJB equation.

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