scholarly journals Optimal program control in the class of quadratic splines for linear systems

2020 ◽  
Vol 16 (4) ◽  
pp. 462-470
Author(s):  
Alexander S. Popkov ◽  
Keyword(s):  
Control Problem ◽  
Control Function ◽  
Optimization Methods ◽  
Mixed Integer ◽  
Quadratic Functional ◽  
Control Functions ◽  
Quadratic Splines ◽  
Special Software ◽  
Constrained Programming ◽  
Quadratically Constrained

This article describes an algorithm for solving the optimal control problem in the case when the considered process is described by a linear system of ordinary differential equations. The initial and final states of the system are fixed and straight two-sided constraints for the control functions are defined. The purpose of optimization is to minimize the quadratic functional of control variables. The control is selected in the class of quadratic splines. There is some evolution of the method when control is selected in the class of piecewise constant functions. Conveniently, due to the addition/removal of constraints in knots, the control function can be piecewise continuous, continuous, or continuously differentiable. The solution algorithm consists in reducing the control problem to a convex mixed-integer quadratically-constrained programming problem, which could be solved by using well-known optimization methods that utilize special software.

scholarly journals A nonlinear plate control without linearization

2017 ◽  
Vol 15 (1) ◽  
pp. 179-186
Author(s):  
Kenan Yildirim ◽  
Ismail Kucuk
Keyword(s):  
Optimal Control ◽  
Nonlinear Systems ◽  
Control Problem ◽  
Performance Index ◽  
Control Function ◽  
Initial Boundary ◽  
Quadratic Functional ◽  
Penalty Term ◽  
Nonlinear Plate ◽  
Optimal Control Function

Abstract In this paper, an optimal vibration control problem for a nonlinear plate is considered. In order to obtain the optimal control function, wellposedness and controllability of the nonlinear system is investigated. The performance index functional of the system, to be minimized by minimum level of control, is chosen as the sum of the quadratic 10 functional of the displacement. The velocity of the plate and quadratic functional of the control function is added to the performance index functional as a penalty term. By using a maximum principle, the nonlinear control problem is transformed to solving a system of partial differential equations including state and adjoint variables linked by initial-boundary-terminal conditions. Hence, it is shown that optimal control of the nonlinear systems can be obtained without linearization of the nonlinear term and optimal control function can be obtained analytically for nonlinear systems without linearization.

scholarly journals On The Dense Controllability for The Parabolic Problem with Time-Distributed Functional

2018 ◽  
Vol 71 (1) ◽  
pp. 9-25
Author(s):  
Irina V. Astashova ◽  
Alexey V. Filinovskiy
Keyword(s):  
Heat Equation ◽  
Control Problem ◽  
Existence And Uniqueness ◽  
Parabolic Problem ◽  
Control Function ◽  
One Dimensional ◽  
Cost Functional ◽  
Control Functions ◽  
Quadratic Cost

Abstract We consider a control problem for one-dimensional heat equation with quadratic cost functional. We prove the existence and uniqueness of a control function from a prescribed set, and study the structure of the set of accessible temperature functions. We also prove the dense controllability of the problem for some set of control functions.

scholarly journals On optimal boundary and distributed control of partial integro–differential equations

2014 ◽  
Vol 24 (1) ◽  
pp. 5-25 ◽  
Author(s):  
Asatur Zh. Khurshudyan
Keyword(s):  
Differential Equations ◽  
Control Problem ◽  
Integral Transform ◽  
Control Function ◽  
Sufficient Conditions ◽  
Control Process ◽  
Problem Solution ◽  
Control Functions ◽  
Minimization Procedure ◽  
And Control

Abstract A method of optimal control problems investigation for linear partial integro-differential equations of convolution type is proposed, when control process is carried out by boundary functions and right hand side of equation. Using Fourier real generalized integral transform control problem solution is reduced to minimization procedure of chosen optimality criterion under constraints of equality type on desired control function. Optimality of control impacts is obtained for two criteria, evaluating their linear momentum and total energy. Necessary and sufficient conditions of control problem solvability are obtained for both criteria. Numerical calculations are done and control functions are plotted for both cases of control process realization.

Data Storage in the Cerebellar Model Articulation Controller (CMAC)

1975 ◽  
Vol 97 (3) ◽  
pp. 228-233 ◽  
Author(s):  
J. S. Albus
Keyword(s):  
Control Problem ◽  
Data Storage ◽  
Iterative Process ◽  
Control Function ◽  
Cerebellar Model Articulation Controller ◽  
Control Functions ◽  
Level Data ◽  
Manipulator Control

The storage of manipulator control functions in the CM AC memory is accomplished by an iterative process which, if the control function is sufficiently smooth, will converge. There are several different techniques for loading the CM AC memory depending on the amount of data which has already been stored and the degree of accuracy which is desired. The CM AC system lends itself to a “natural” partitioning of the control problem into manageable subproblems. At each level the CM AC controller translates commands from the next higher level into sequences of instructions to the next lower level. Data storage, or training, is accomplished first at the lowest level and must be completed, or nearly so, at each level before it can be initiated at the next higher level.

Dynamics Response Control of a Mindlin-Type Beam

2017 ◽  
Vol 17 (03) ◽  
pp. 1750039 ◽  
Author(s):  
Kenan Yildirim ◽  
Seda G. Korpeoglu ◽  
Ismail Kucuk
Keyword(s):  
Optimal Control ◽  
Partial Differential Equations ◽  
Maximum Principle ◽  
Control Problem ◽  
Control Function ◽  
Initial Boundary ◽  
Response Control ◽  
Adjoint Variables ◽  
Dynamics Response ◽  
Optimal Control Function

Optimal boundary control for damping the vibrations in a Mindlin-type beam is considered. Wellposedness and controllability of the system are investigated. A maximum principle is introduced and optimal control function is obtained by means of maximum principle. Also, by using maximum principle, control problem is reduced to solving a system of partial differential equations including state, adjoint variables, which are subject to initial, boundary and terminal conditions. The solution of the system is obtained by using MATLAB. Numerical results are presented in table and graphical forms.

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