Optimal Control of a Chaotic Map: Fixed Point Stabilization and Attractor Confinement

1997 ◽  
Vol 07 (02) ◽  
pp. 437-446 ◽  
Author(s):  
C. Piccardi ◽  
L. L. Ghezzi
Keyword(s):  
Optimal Control ◽  
Fixed Point ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Chaotic Attractor ◽  
Chaotic Map ◽  
Optimal Controller ◽  
Control Of Chaos ◽  
One Dimensional ◽  
Suppression Of Chaos

Optimal control is applied to a chaotic system. Reference is made to a well-known one-dimensional map. Firstly, attention is devoted to the stabilization of a fixed point. An optimal controller is obtained and compared with other controllers which are popular in the control of chaos. Secondly, allowance is made for uncertainty and emphasis is placed on the reduction rather than the suppression of chaos. The aim becomes that of confining a chaotic attractor within a prescribed region of the state space. A controller fulfilling this task is obtained as the solution of a min-max optimal control problem.

scholarly journals THE OPTIMAL CONTROL PROBLEM FOR ONE-DIMENSIONAL NONLINEAR SHRODINGER EQUATIONS WITH A SPECIAL GRADIENT TERM

2019 ◽  
pp. 49-66
Author(s):  
G. Yagub ◽  
N. S. Ibrahimov ◽  
M. Zengin
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Quality Criterion ◽  
Necessary Condition ◽  
Gradient Term ◽  
Complex Coefficient ◽  
Existence And Uniqueness Theorem ◽  
One Dimensional ◽  
Nonlinear Part

In this paper we consider the optimal control problem for a one-dimensional nonlinear Schrodinger equation with a special gradient term and with a complex coefficient in the nonlinear part, when the quality criterion is a final functional and the controls are quadratically summable functions. In this case, the questions of the correctness of the formulation and the necessary condition for solving the optimal control problem under consideration are investigated. The existence and uniqueness theorem for the solution is proved and a necessary condition is established in the form of a variational inequality. Along with these, a formula is found for the gradient of the considered quality criterion.

scholarly journals An uncertain optimal control model with n jumps and application

2012 ◽  
Vol 9 (4) ◽  
pp. 1453-1468 ◽  
Author(s):  
Liubao Deng ◽  
Yuanguo Zhu
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Theory ◽  
Control Problem ◽  
Credibility Theory ◽  
Linear Quadratic ◽  
Subsidy Policy ◽  
One Dimensional ◽  
The One ◽  
Important Branch

Optimal control theory is an important branch of modern control theory which has been widely applied in various sciences. Uncertain optimal control is a theory dealing with optimal control problems which are based a new uncertainty theory and differs from the stochastic optimal control based on probability theory and fuzzy optimal control based on fuzzy set theory or credibility theory. As the further work of the uncertain optimal control with jump in the one-dimensional case and multidimensional linear-quadratic (LQ) uncertain optimal control problem with jump which has a quadratic objective function for a linear uncertain control system with jump, a general uncertain optimal control problem with n jumps in the multi-dimensional cases is considered in this paper. The principle of optimality is presented and the equation of optimality is obtained about multidimensional uncertain optimal control with n jumps. Finally, as an application, an optimal control problem in R&D (Research and Development) fiscal subsidy policy is discussed and the optimal control decisions are obtained.

scholarly journals Time Needed to Control an Epidemic with Restricted Resources in SIR Model with Short-Term Controlled Population: A Fixed Point Method for a Free Isoperimetric Optimal Control Problem

2018 ◽  
Vol 23 (4) ◽  
pp. 64 ◽  
Author(s):  
Imane Abouelkheir ◽  
Fadwa El Kihal ◽  
Mostafa Rachik ◽  
Ilias Elmouki
Keyword(s):  
Optimal Control ◽  
Fixed Point ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Health Resources ◽  
Control Policy ◽  
Fixed Point Method ◽  
Point Method ◽  
Control Functions ◽  
Optimal Duration

In this paper, we attempt to determine the optimal duration of an anti-epidemic control strategy which targets susceptible people, under the isoperimetric condition that we could not control all individuals of this category due to restricted health resources. We state and prove the local and global stability conditions of free and endemic equilibria of a simple epidemic compartmental model devised in the form of four ordinary differential equations which describe the dynamics of susceptible-controlled-infected-removed populations and where it is taken into account that the controlled people cannot acquire long-lived immunity to move towards the removed compartment due to the temporary effect of the control parameter. Thereafter, we characterize the sought optimal control and we show the effectiveness of this limited control policy along with the research of the optimal duration that is needed to reduce the size of the infected population. The isoperimetric constraint is defined over a fixed horizon, while the objective function is defined over a free horizon present under a quadratic form in the payoff term. The complexity of this optimal control problem requires the execution of three numerical methods all combined together at the same time, namely, the forward–backward sweep method to generate the optimal state and control functions, the secant method adapted to the isoperimetric restriction, and, finally, the fixed point method to obtain the optimal final time.

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