scholarly journals Existence Results for Optimal Control Problems with Some Special Nonlinear Dependence on State and Control

2009 ◽  
Vol 48 (2) ◽  
pp. 415-437 ◽  
Author(s):  
Pablo Pedregal ◽  
Jorge Tiago
Keyword(s):  
Optimal Control ◽  
Optimal Control Problems ◽  
Existence Results ◽  
Nonlinear Dependence ◽  
Control Problems ◽  
And Control

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 A New Approach for Solving Optimal Nonlinear Control Problems Using Decriminalization and Rationalized Haar Functions

2011 ◽  
Vol 1 ◽  
pp. 387-394 ◽  
Author(s):  
Zhen Yu Han ◽  
Shu Rong Li
Keyword(s):  
Optimal Control ◽  
Optimal Control Problems ◽  
Nonlinear Optimal Control ◽  
Control Problems ◽  
State Variables ◽  
Linear Quadratic ◽  
Control Variables ◽  
Linear Quadratic Optimal Control ◽  
Haar Functions ◽  
And Control

This paper presents a numerical method based on quasilinearization and rationalized Haar functions for solving nonlinear optimal control problems including terminal state constraints, state and control inequality constraints. The optimal control problem is converted into a sequence of quadratic programming problems. The rationalized Haar functions with unknown coefficients are used to approximate the control variables and the derivative of the state variables. By adding artificial controls, the number of state and control variables is equal. Then the quasilinearization method is used to change the nonlinear optimal control problems with a sequence of constrained linear-quadratic optimal control problems. To show the effectiveness of the proposed method, the simulation results of two constrained nonlinear optimal control problems are presented.

scholarly journals OPTIMAL CONTROL REALIZATIONS OF LAGRANGIAN SYSTEMS WITH SYMMETRY

2011 ◽  
Vol 08 (07) ◽  
pp. 1627-1651 ◽  
Author(s):  
M. DELGADO-TÉLLEZ ◽  
A. IBORT ◽  
T. RODRÍGUEZ DE LA PEÑA
Keyword(s):  
Optimal Control ◽  
Control Systems ◽  
Optimal Control Problems ◽  
Lagrangian System ◽  
Control Problems ◽  
Lagrangian Systems ◽  
Explicit Realization ◽  
Control Equation ◽  
And Control

A new relation among a class of optimal control systems and Lagrangian systems with symmetry is discussed. It will be shown that a family of solutions of optimal control systems whose control equation are obtained by means of a group action are in correspondence with the solutions of a mechanical Lagrangian system with symmetry. This result also explains the equivalence of the class of Lagrangian systems with symmetry and optimal control problems discussed in [1, 2]. The explicit realization of this correspondence is obtained by a judicious use of Clebsch variables and Lin constraints, a technique originally developed to provide simple realizations of Lagrangian systems with symmetry. It is noteworthy to point out that this correspondence exchanges the role of state and control variables for control systems with the configuration and Clebsch variables for the corresponding Lagrangian system. These results are illustrated with various simple applications.

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