scholarly journals Stability and Analytic Solutions of an Optimal Control Problem on the Schrödinger Lie Group

Open Physics ◽  
2016 ◽  
Vol 14 (1) ◽  
pp. 549-558
Author(s):  
Remus-Daniel Ene ◽  
Camelia Pop ◽  
Camelia Petrişor
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Numerical Simulations ◽  
Periodic Solutions ◽  
Nonlinear Stability ◽  
Lie Group ◽  
Asymptotic Method ◽  
Analytic Solutions ◽  
Optimal Homotopy Asymptotic Method

AbstractThe nonlinear stability and the existence of the periodic solutions for an optimal control problem on the Schrödinger Lie group are discussed. The analytic solutions via optimal homotopy asymptotic method of the dynamics and numerical simulations are presented, too.

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>

scholarly journals Intrinsic Optimal Control for Mechanical Systems on Lie Group

2017 ◽  
Vol 2017 ◽  
pp. 1-8
Author(s):  
Chao Liu ◽  
Shengjing Tang ◽  
Jie Guo
Keyword(s):  
Optimal Control ◽  
Analytical Solution ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Lie Group ◽  
Control Method ◽  
Geodesic Distance ◽  
Infinite Horizon ◽  
Mechanical Systems ◽  
Programming Approach

The intrinsic infinite horizon optimal control problem of mechanical systems on Lie group is investigated. The geometric optimal control problem is built on the intrinsic coordinate-free model, which is provided with Levi-Civita connection. In order to obtain an analytical solution of the optimal problem in the geometric viewpoint, a simplified nominal system on Lie group with an extra feedback loop is presented. With geodesic distance and Riemann metric on Lie group integrated into the cost function, a dynamic programming approach is employed and an analytical solution of the optimal problem on Lie group is obtained via the Hamilton-Jacobi-Bellman equation. For a special case on SO(3), the intrinsic optimal control method is used for a quadrotor rotation control problem and simulation results are provided to show the control performance.

scholarly journals Dynamic Analysis of a Two-Language Competitive Model with Control Strategies

2013 ◽  
Vol 2013 ◽  
pp. 1-13 ◽  
Author(s):  
Lin-Fei Nie ◽  
Zhi-Dong Teng ◽  
Juan J. Nieto ◽  
Il Hyo Jung
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Numerical Simulations ◽  
Control Strategy ◽  
Sufficient Conditions ◽  
Positive Order ◽  
State Dependent ◽  
Competitive Model ◽  
The Impact

The dynamic behavior of a two-language competitive model is analyzed systemically in this paper. By the linearization and the Bendixson-Dulac theorem on dynamical system, some sufficient conditions on the globally asymptotical stability of the trivial equilibria and the existence and the stability of the positive equilibrium of this model are presented. Nextly, in order to protect the endangered language, an optimal control problem relative to this model is explored. We derive some necessary conditions to solve the optimal control problem and present some numerical simulations using a Runge-Kutta fourth-order method. Finally, the languages competitive model is extended to this model assessing the impact of state-dependent pulse control strategy. Using the Poincaré map, differential inequality, and method of qualitative analysis, we prove the existence and stability of positive order-1 periodic solution for this control model. Numerical simulations are carried out to illustrate the main results and the feasibility of state-dependent impulsive control strategy.

scholarly journals An Underactuated Drift-Free Left Invariant Control System on a Specific Lie Group

2012 ◽  
Vol 2012 ◽  
pp. 1-14
Author(s):  
Camelia Pop Arieşanu
Keyword(s):  
Optimal Control ◽  
Control System ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Lie Group ◽  
Point Of View ◽  
Free Left ◽  
Invariant Control

The paper presents a geometrical overview on an optimal control problem on a special Lie group. The Hamilton-Poisson realization of the dynamics offers us the possibility to study the system from mechanical geometry point of view.

AN OPTIMAL CONTROL PROBLEM ON THE LIE GROUP SO(4)

2008 ◽  
Vol 05 (03) ◽  
pp. 319-327 ◽  
Author(s):  
ANANIA ARON ◽  
IONEL MOŞ ◽  
ANIKO CSAKY ◽  
MIRCEA PUTA
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Lie Group ◽  
Controllable System ◽  
Geometrical Properties

An optimal control problem for a drift-free controllable system on the Lie group SO(4) is discussed and some of its dynamical and geometrical properties are pointed out.

The Tensor Product Based Analytic Solutions of Nonlinear Optimal Control Problem

2014 ◽  
Vol 511-512 ◽  
pp. 1063-1067 ◽  
Author(s):  
Hajer Bouzaouache ◽  
Naceur Benhadj Braiek
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Tensor Product ◽  
Control Problem ◽  
State Feedback ◽  
Numerical Procedure ◽  
Analytic Solutions ◽  
Linear Solution ◽  
Algebraic Laws ◽  
Feedback Optimal Control

In this paper, the attention is focused on the optimization of a particular class of nonlinear systems. The optimum linear solution is not the best one so the problem of determining a nonlinear state feedback optimal control law with quadratic performance index over infinite time horizon is considered. It isn't an easy task and the most discouraging obstacle is the resolution of the Hamilton-Jacobi equation. Thus our contribution, based on the use of the tensor product and its algebraic laws, provide analytic solutions of the studied optimal control problem. The polynomial state feedback solution is computed through a numerical procedure. A numerical example is treated to illustrate the proposed solutions and some conclusions are drawn.

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 Stability problems and numerical integration on the Lie group SO(3) × R3 × R3

2018 ◽  
Vol 16 (1) ◽  
pp. 219-234
Author(s):  
Camelia Pop ◽  
Remus-Daniel Ene
Keyword(s):  
Nonlinear System ◽  
Numerical Integration ◽  
Lie Group ◽  
Asymptotic Method ◽  
Analytic Solutions ◽  
Stability Problems ◽  
Optimal Homotopy Asymptotic Method

AbstractThe paper is dealing with stability problems for a nonlinear system on the Lie group SO(3) × R3 × R3. The approximate analytic solutions of the considered system via Optimal Homotopy Asymptotic Method are presented, too.

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