CONSTRUCTION OF SUBOPTIMAL FEEDBACK CONTROL FOR CHAOTIC SYSTEMS USING B-SPLINES WITH OPTIMALLY CHOSEN KNOT POINTS

2001 ◽  
Vol 11 (09) ◽  
pp. 2375-2387 ◽  
Author(s):  
H. W. J. LEE ◽  
K. L. TEO ◽  
W. R. LEE ◽  
S. WANG
Keyword(s):  
Optimal Control ◽  
Feedback Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Numerical Approach ◽  
Optimal Feedback Control ◽  
B Splines ◽  
Decision Variables ◽  
Spline Basis ◽  
The Lorenz System

In this paper we consider a class of optimal control problem involving a chaotic system, where all admissible controls are required to satisfy small boundedness constraints. A numerical approach is developed to seek for an optimal feedback control for the optimal control problem. In this approach, the state space is partitioned into subregions, and the controller is approximated by a linear combination of a modified third order B-spline basis functions. The partition points are also taken as decision variables in this formulation. An algorithm based on this approach is proposed. To show the effectiveness of the proposed method, a control problem involving the Lorenz system is solved by the proposed approach. The numerical results demonstrate that the method is efficient in the construction of a robust, near-optimal control.

Optimal feedback control of stochastic McShane differential systems

1974 ◽  
Vol 11 (2) ◽  
pp. 302-309 ◽  
Author(s):  
N. U. Ahmed ◽  
K. L. Teo
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Necessary Conditions ◽  
Parabolic Type ◽  
Optimal Feedback Control ◽  
Distributed Parameter ◽  
Optimal Controls ◽  
Necessary Conditions For Optimality ◽  
Reduced Problem

In this paper, the optimal control problem of system described by stochastic McShane differential equations is considered. It is shown that this problem can be reduced to an equivalent optimal control problem of distributed parameter systems of parabolic type with controls appearing in the coefficients of the differential operator. Further, to this reduced problem, necessary conditions for optimality and an existence theorem for optimal controls are given.

Optimal feedback control of stochastic McShane differential systems

1974 ◽  
Vol 11 (02) ◽  
pp. 302-309
Author(s):  
N. U. Ahmed ◽  
K. L. Teo
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Necessary Conditions ◽  
Parabolic Type ◽  
Optimal Feedback Control ◽  
Distributed Parameter ◽  
Optimal Controls ◽  
Necessary Conditions For Optimality ◽  
Reduced Problem

In this paper, the optimal control problem of system described by stochastic McShane differential equations is considered. It is shown that this problem can be reduced to an equivalent optimal control problem of distributed parameter systems of parabolic type with controls appearing in the coefficients of the differential operator. Further, to this reduced problem, necessary conditions for optimality and an existence theorem for optimal controls are given.

scholarly journals Optimal Performance of Variable Stiffness Devices for Structural Control

2006 ◽  
Vol 129 (2) ◽  
pp. 171-177 ◽  
Author(s):  
John Leavitt ◽  
Faryar Jabbari ◽  
James E. Bobrow
Keyword(s):  
Optimal Control ◽  
Feedback Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Structural Control ◽  
Vibration Suppression ◽  
Variable Stiffness ◽  
Experimental Results ◽  
Control Law ◽  
Structural Vibrations

This paper addresses control of structural vibrations using semi-active actuators that are capable of manipulating stiffness and∕or producing variable stiffness. Usually vibration suppression is achieved using damping devices rather than stiffness ones. However, stiffness devices can produce large forces and have significant advantages for shock isolation purposes. In this work we use a passivity approach to establish the requirements for the control law for a structure equipped with semi-active stiffness devices. We also solve an optimal control problem that demonstrates that our passive, resetting feedback control law approximates the optimal control. Simulation and experimental results are presented in support of the proposed approach.

scholarly journals Finite Element Approximation of Optimal Control Problem with Weighted Extended B-Splines

Mathematics ◽  
2019 ◽  
Vol 7 (5) ◽  
pp. 452 ◽  
Author(s):  
Madiha Sana ◽  
Muhammad Mustahsan
Keyword(s):  
Optimal Control ◽  
Finite Element ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Finite Element Approximation ◽  
Element Approximation ◽  
State Variables ◽  
B Splines ◽  
Regularity Of Solution ◽  
Distinct Aspect

In this research article, an optimal control problem (OCP) with boundary observations is approximated using finite element method (FEM) with weighted extended B-splines (WEB-splines) as basis functions. This type of OCP has a distinct aspect that the boundary observations are outward normal derivatives of state variables, which decrease the regularity of solution. A meshless FEM is proposed using WEB-splines, defined on the usual grid over the domain, R 2 . The weighted extended B-spline method (WEB method) absorbs the regularity problem as the degree of the B-splines is increased. Convergence analysis is also performed by some numerical examples.

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