Optimal control and optimality condition of the Camassa–Holm equation

2017 ◽  
Vol 36 ◽  
pp. 18-29 ◽  
Author(s):  
Chunyu Shen ◽  
Lixin Tian
Keyword(s):  
Optimal Control ◽  
Optimality Condition ◽  
Holm Equation

scholarly journals Distributed-Order Non-Local Optimal Control

Axioms ◽  
2020 ◽  
Vol 9 (4) ◽  
pp. 124
Author(s):  
Faïçal Ndaïrou ◽  
Delfim F. M. Torres
Keyword(s):  
Optimal Control ◽  
Maximum Principle ◽  
Control Theory ◽  
Optimality Condition ◽  
Optimal Control Theory ◽  
Sufficient Optimality Condition ◽  
Weak Version ◽  
Fractional Optimal Control ◽  
Non Local ◽  
Distributed Order

Distributed-order fractional non-local operators were introduced and studied by Caputo at the end of the 20th century. They generalize fractional order derivatives/integrals in the sense that such operators are defined by a weighted integral of different orders of differentiation over a certain range. The subject of distributed-order non-local derivatives is currently under strong development due to its applications in modeling some complex real world phenomena. Fractional optimal control theory deals with the optimization of a performance index functional, subject to a fractional control system. One of the most important results in classical and fractional optimal control is the Pontryagin Maximum Principle, which gives a necessary optimality condition that every solution to the optimization problem must verify. In our work, we extend the fractional optimal control theory by considering dynamical system constraints depending on distributed-order fractional derivatives. Precisely, we prove a weak version of Pontryagin’s maximum principle and a sufficient optimality condition under appropriate convexity assumptions.

scholarly journals A global method for some class of optimization and control problems

2000 ◽  
Vol 23 (9) ◽  
pp. 605-616 ◽  
Author(s):  
R. Enkhbat
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Convex Function ◽  
Control Problem ◽  
Optimality Condition ◽  
Optimal Control Problems ◽  
Control Problems ◽  
Global Method ◽  
Optimization And Control ◽  
And Control

The problem of maximizing a nonsmooth convex function over an arbitrary set is considered. Based on the optimality condition obtained by Strekalovsky in 1987 an algorithm for solving the problem is proposed. We show that the algorithm can be applied to the nonconvex optimal control problem as well. We illustrate the method by describing some computational experiments performed on a few nonconvex optimal control problems.

scholarly journals Optimality Condition-Based Sensitivity Analysis of Optimal Control for Hybrid Systems and Its Application

2012 ◽  
Vol 2012 ◽  
pp. 1-22
Author(s):  
Chunyue Song
Keyword(s):  
Optimal Control ◽  
Sensitivity Analysis ◽  
Hybrid Systems ◽  
Optimality Condition ◽  
Optimal Control Problems ◽  
Numerical Solutions ◽  
Equivalent Transformation ◽  
Control Problems ◽  
Continuous Control ◽  
Mode Transition

Gradient-based algorithms are efficient to compute numerical solutions of optimal control problems for hybrid systems (OCPHS), and the key point is how to get the sensitivity analysis of the optimal control problems. In this paper, optimality condition-based sensitivity analysis of optimal control for hybrid systems with mode invariants and control constraints is addressed under a priori fixed mode transition order. The decision variables are the mode transition instant sequence and admissible continuous control functions. After equivalent transformation of the original problem, the derivatives of the objective functional with respect to control variables are established based on optimal necessary conditions. By using the obtained derivatives, a control vector parametrization method is implemented to obtain the numerical solution to the OCPHS. Examples are given to illustrate the results.

scholarly journals KONTROL OPTIMAL MODEL PENYEBARAN VIRUS KOMPUTER DENGAN PENGARUH KOMPUTER EKSTERNAL YANG TERINFEKSI DAN REMOVABLE STORAGE MEDIA

2017 ◽  
Vol 9 (1) ◽  
pp. 113
Author(s):  
Dewi Erla Mahmudah ◽  
Muhammad Zidny Naf’an ◽  
Muh. Sofi’i ◽  
Wika Wika
Keyword(s):  
Optimal Control ◽  
Optimality Condition ◽  
Minimum Principle ◽  
Prevention Strategies ◽  
Optimal Model ◽  
Pontryagin Minimum Principle ◽  
Computer Viruses ◽  
Storage Media ◽  
The Cost

.  In this paper, we discuss an optimal control on the spread of computer viruses under the effects of infected external computers and removable storage media. Prevention Strategies do with ascertaining control prevention to minimize the number of infective computers (Latent and Breakingout) and installing effective antivirus programs in each sub-population. The aim are to derive optimal prevention strategies and minimize the cost associated with the control. The characterization of optimal control is perform analitically by applying Pontryagin Minimum Principle. The obtained optimality system of Hamilton fuction is satistfy the optimality condition.

Optimal control of the viscous Dullin–Gottwalld–Holm equation

2010 ◽  
Vol 11 (1) ◽  
pp. 480-491 ◽  
Author(s):  
Chunyu Shen ◽  
Lixin Tian ◽  
Anna Gao
Keyword(s):  
Optimal Control ◽  
Holm Equation

A Complete Optimality Condition in the Inverse Problem of Optimal Control

1984 ◽  
Vol 22 (2) ◽  
pp. 327-341 ◽  
Author(s):  
Takao Fujii ◽  
Masaru Narazaki
Keyword(s):  
Optimal Control ◽  
Inverse Problem ◽  
Optimality Condition

Optimal control of the viscous Camassa–Holm equation

2009 ◽  
Vol 10 (1) ◽  
pp. 519-530 ◽  
Author(s):  
Lixin Tian ◽  
Chunyu Shen ◽  
Danping Ding
Keyword(s):  
Optimal Control ◽  
Holm Equation
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