scholarly journals Solving Linear Optimal Control Problems Using Cubic B-spline Quasi-interpolation

MATEMATIKA ◽  
2018 ◽  
Vol 34 (2) ◽  
pp. 313-324
Author(s):  
M. Matinfar ◽  
M. Dosti
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Main Idea ◽  
Absolute Error ◽  
Analytic Solutions ◽  
Linear Optimal Control ◽  
B Spline ◽  
Linear Optimal Control Problems ◽  
Made In

In this article, we apply an impressive method for solving linear optimal control problem based on cubic B-spline quasi-interpolation. Hamilton-Jacobi equation are applied to linear optimal control problem convert to systems of first-order equations. The main idea of our scheme is approximation derivative with cubic B-spline quasi-interpolation. This method is straightforward, without restrictive assumptions.The results of scheme are made in pleasant agreement with analytic solutions. The accuracy of the proposed method is demonstrated by absolute error. Our scheme is simple to implement because its algorithm is easy and it's one of the advantages of the proposed method.

scholarly journals Optimal control problem of variable-order delay system of advertising procedure: Numerical treatment

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Nasser H. Sweilam ◽  
Taghreed A. Assiri ◽  
Muner M. Abou Hasan
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Analytic Solutions ◽  
Delay System ◽  
Variable Order ◽  
Delay Model ◽  
Standard Difference ◽  
New Formulation ◽  
Number Of Customers

<p style='text-indent:20px;'>This paper presents an optimal control problem of the general variable-order fractional delay model of advertising procedure. The problem describes the flow of the clients from the unaware people group to the conscious or bought band. The new formulation generalizes the model that proposed by Muller. Two control variables are considered to increase the number of customers who purchased the products. An efficient nonstandard difference approach is used to study numerically the behavior of the solution of the mentioned problem. Properties of the proposed system were introduced analytically and numerically. The proposed difference schema maintains the properties of the analytic solutions as boundedness and the positivity. Numerical examples, for testing the applicability of the utilized method and to show the simplicity, accuracy and efficiency of this approximation approach, are presented with some comprising with standard difference methods.</p>

Optimal control of a hyperbolic system that describes Slutsky demand

2021 ◽  
pp. 58-59
Author(s):  
Olha Milchenko
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Hyperbolic System ◽  
Method Of Characteristics ◽  
Social Processes ◽  
Computational Algorithms ◽  
Initial Condition ◽  
Linear Optimal Control ◽  
First Order

A non-linear optimal control problem for a hyperbolic system of first order equations on a line in the case of degeneracy of the initial condition line is considered. This problem describes many natural, economic and social processes, in particular, the optimality of the Slutsky demand, the theory of bio-population, etc. The research is based on the method of characteristics and the use of nonstandard variations of the increment of target functional, which leads to the construction of efficient computational algorithms.

An efficient stochastic approach for robust time-optimal trajectory planning of robotic manipulators under limited actuation

Robotica ◽  
2017 ◽  
Vol 35 (12) ◽  
pp. 2400-2417 ◽  
Author(s):  
Ming-Yong Zhao ◽  
Xiao-Shan Gao ◽  
Qiang Zhang
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Trajectory Planning ◽  
Optimal Trajectory ◽  
Original Problem ◽  
Robotic Manipulators ◽  
Linear Optimal Control ◽  
Time Optimal ◽  
Optimal Trajectory Planning

SUMMARYThis paper focuses on the problem of robust time-optimal trajectory planning of robotic manipulators to track a given path under a probabilistic limited actuation, that is, the probability for the actuation to be limited is no less than a given bound κ. We give a general and practical method to reduce the probabilistic constraints to a set of deterministic constraints and show that the deterministic constraints are equivalent to a set of linear constraints under certain conditions. As a result, the original problem is reduced to a linear optimal control problem which can be solved with linear programming in polynomial time. In the case of κ = 1, the original problem is proved to be equivalent to the linear optimal control problem. Overall, a very general, practical, and efficient algorithm is given to solve the above problem and numerical simulation results are used to show the effectiveness of the method.

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