Solving optimal control problems of the time-delayed systems by Haar wavelet

2014 ◽  
Vol 22 (11) ◽  
pp. 2657-2670 ◽  
Author(s):  
Alireza Nazemi ◽  
Masoomeh Mansoori
Keyword(s):  
Optimal Control ◽  
Optimal Control Problems ◽  
Haar Wavelet ◽  
Control Problems ◽  
Delayed Systems

SOLVING INFINITE-HORIZON OPTIMAL CONTROL PROBLEMS USING THE HAAR WAVELET COLLOCATION METHOD

2014 ◽  
Vol 56 (2) ◽  
pp. 179-191 ◽  
Author(s):  
ALIREZA NAZEMI ◽  
NEDA MAHMOUDY
Keyword(s):  
Optimal Control ◽  
Optimal Control Problems ◽  
Direct Method ◽  
Infinite Horizon ◽  
Main Idea ◽  
Local Property ◽  
Haar Wavelet ◽  
Haar Wavelets ◽  
Control Problems ◽  
Wavelet Collocation Method

AbstractWe consider infinite-horizon optimal control problems. The main idea is to convert the problem into an equivalent finite-horizon nonlinear optimal control problem. The resulting problem is then solved by means of a direct method using Haar wavelets. A local property of Haar wavelets is applied to simplify the calculation process. The accuracy of the present method is demonstrated by two illustrative examples.

scholarly journals Feedback Control Method Using Haar Wavelet Operational Matrices for Solving Optimal Control Problems

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Waleeda Swaidan ◽  
Amran Hussin
Keyword(s):  
Optimal Control ◽  
Feedback Control ◽  
Optimal Control Problems ◽  
Control Method ◽  
Numerical Technique ◽  
Direct Methods ◽  
Haar Wavelet ◽  
Control Problems ◽  
Operational Matrices ◽  
Feedback Control Method

Most of the direct methods solve optimal control problems with nonlinear programming solver. In this paper we propose a novel feedback control method for solving for solving affine control system, with quadratic cost functional, which makes use of only linear systems. This method is a numerical technique, which is based on the combination of Haar wavelet collocation method and successive Generalized Hamilton-Jacobi-Bellman equation. We formulate some new Haar wavelet operational matrices in order to manipulate Haar wavelet series. The proposed method has been applied to solve linear and nonlinear optimal control problems with infinite time horizon. The simulation results indicate that the accuracy of the control and cost can be improved by increasing the wavelet resolution.

On closed-loop equilibrium strategies for mean-field stochastic linear quadratic problems

2020 ◽  
Vol 26 ◽  
pp. 41
Author(s):  
Tianxiao Wang
Keyword(s):  
Optimal Control ◽  
Closed Loop ◽  
Optimal Control Problems ◽  
Mean Field ◽  
Open Loop ◽  
Time Inconsistency ◽  
Control Problems ◽  
Linear Quadratic ◽  
Linear Quadratic Optimal Control ◽  
Equilibrium Strategies

This article is concerned with linear quadratic optimal control problems of mean-field stochastic differential equations (MF-SDE) with deterministic coefficients. To treat the time inconsistency of the optimal control problems, linear closed-loop equilibrium strategies are introduced and characterized by variational approach. Our developed methodology drops the delicate convergence procedures in Yong [Trans. Amer. Math. Soc. 369 (2017) 5467–5523]. When the MF-SDE reduces to SDE, our Riccati system coincides with the analogue in Yong [Trans. Amer. Math. Soc. 369 (2017) 5467–5523]. However, these two systems are in general different from each other due to the conditional mean-field terms in the MF-SDE. Eventually, the comparisons with pre-committed optimal strategies, open-loop equilibrium strategies are given in details.

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