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.

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 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.

scholarly journals Numerical treatment of nonlinear optimal control problems

2017 ◽  
Vol 35 (2) ◽  
pp. 195-208
Author(s):  
Reza Khoshsiar Ghaziani ◽  
Mojtaba Fardi ◽  
Mehdi Ghasemi
Keyword(s):  
Optimal Control ◽  
Iterative Methods ◽  
Optimal Control Problems ◽  
Sufficient Conditions ◽  
Approximate Solutions ◽  
Convergent Series ◽  
Uniqueness Of Solution ◽  
Control Problems ◽  
Numerical Treatment ◽  
The Given

In this paper, we present iterative and non-iterative methods for the solution of nonlinear optimal con-trol problems (NOCPs) and address the sufficient conditions for uniqueness of solution. We also studyconvergence properties of the given techniques. The approximate solutions are calculated in the form ofa convergent series with easily computable components. The efficiency and simplicity of the methods aretested on a numerical example.

Adaptive space-time finite element methods for parabolic optimal control problems

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Ulrich Langer ◽  
Andreas Schafelner
Keyword(s):  
Optimal Control ◽  
Finite Element ◽  
Finite Element Methods ◽  
Optimal Control Problems ◽  
Space Time ◽  
Residual Error ◽  
Control Problems ◽  
Error Estimator ◽  
Parabolic Optimal Control ◽  
Error Indicators

Abstract We present, analyze, and test locally stabilized space-time finite element methods on fully unstructured simplicial space-time meshes for the numerical solution of space-time tracking parabolic optimal control problems with the standard L 2-regularization. We derive a priori discretization error estimates in terms of the local mesh-sizes for shape-regular meshes. The adaptive version is driven by local residual error indicators, or, alternatively, by local error indicators derived from a new functional a posteriori error estimator. The latter provides a guaranteed upper bound of the error, but is more costly than the residual error indicators. We perform numerical tests for benchmark examples having different features. In particular, we consider a discontinuous target in form of a first expanding and then contracting ball in 3d that is fixed in the 4d space-time cylinder.

Sign in / Sign up

Export Citation Format

Share Document