Study of a One-Dimensional Optimal Control Problem with a Purely State-Dependent Cost

2016 ◽  
Vol 28 (1) ◽  
pp. 133-151 ◽  
Author(s):  
A. V. Dmitruk ◽  
A. K. Vdovina
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
One Dimensional ◽  
State Dependent

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.

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.

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