A simplification of computation for optimal control problems using fixed-point theorem

1989 ◽  
Vol 72 (10) ◽  
pp. 14-26
Author(s):  
Yasunari Shidama ◽  
Toyomi Ohta ◽  
Hiroo Yamaura
Keyword(s):  
Optimal Control ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Optimal Control Problems ◽  
Control Problems

Numerical solutions for solving a class of fractional optimal control problems via fixed-point approach

SeMA Journal ◽  
2017 ◽  
Vol 74 (4) ◽  
pp. 585-603 ◽  
Author(s):  
Samaneh Soradi Zeid ◽  
Ali Vahidian Kamyad ◽  
Sohrab Effati ◽  
Seyed Ali Rakhshan ◽  
Soleiman Hosseinpour
Keyword(s):  
Optimal Control ◽  
Fixed Point ◽  
Optimal Control Problems ◽  
Numerical Solutions ◽  
Control Problems ◽  
Fractional Optimal Control ◽  
Fixed Point Approach ◽  
Fractional Optimal Control Problems

scholarly journals Optimal Control of Insect Populations

Mathematics ◽  
2021 ◽  
Vol 9 (15) ◽  
pp. 1762
Author(s):  
Anderson L. Albuquerque de Araujo ◽  
José L. Boldrini ◽  
Roberto C. Cabrales ◽  
Enrique Fernández-Cara ◽  
Milton L. Oliveira
Keyword(s):  
Optimal Control ◽  
Fixed Point ◽  
Numerical Experiments ◽  
Optimal Control Problems ◽  
Necessary Optimality Conditions ◽  
Control Problems ◽  
Parabolic Pdes ◽  
First Order ◽  
Optimal Paths ◽  
Insect Populations

We consider some optimal control problems for systems governed by linear parabolic PDEs with local controls that can move along the domain region Ω of the plane. We prove the existence of optimal paths and also deduce the first order necessary optimality conditions, using the Dubovitskii–Milyutin’s formalism, which leads to an iterative algorithm of the fixed-point kind. This problem may be considered as a model for the control of a mosquito population existing in a given region by using moving insecticide spreading devices. In this situation, an optimal control is any trajectory or path that must follow such spreading device in order to reduce the population as much as possible with a reasonable not too expensive strategy. We illustrate our results by presenting some numerical experiments.

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.

Solution of Volterra integral inclusion in b-metric spaces via new fixed point theorem

2016 ◽  
Vol 2017 (1) ◽  
pp. 17-30 ◽  
Author(s):  
Muhammad Usman Ali ◽  
◽  
Tayyab Kamran ◽  
Mihai Postolache ◽  
◽  
...  
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Metric Spaces ◽  
Integral Inclusion
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