scholarly journals On Determining Initial Conditions of Equations Flexural-Torsional Vibrations of a Bar

2019 ◽  
Vol 12 (1) ◽  
pp. 25-38
Author(s):  
Aysel Ramazanova
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Boundary Value Problem ◽  
Optimal Control Theory ◽  
Initial Conditions ◽  
Torsional Vibrations ◽  
Sufficient Optimality Condition ◽  
Straight Line ◽  
Gradient Of The Functional ◽  
Necessary And Sufficient

The problem of finding the initial conditions in the boundary-value problem for the system of flexural-torsional vibrations of a bar with additional conditions on the straight line is reduced to an optimal control problem and studied by the methods of optimal control theory. The gradient of the functional is calculated and using the gradient expression a necessary and sufficient optimality condition are proved.

An optimal control problem for a system of linear hyperbolic differential equations with constant coefficients

2015 ◽  
Vol 22 (2) ◽  
Author(s):  
Hamlet F. Guliyev ◽  
Vera B. Nazarova
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Fourth Order ◽  
Hyperbolic Equations ◽  
Sufficient Conditions ◽  
Constant Coefficients ◽  
Gradient Of The Functional ◽  
Necessary And Sufficient ◽  
Hyperbolic Differential Equations

AbstractIn this paper, an optimal control problem is considered for a system of fourth order hyperbolic equations with constant coefficients. The gradient of the functional is calculated and the necessary and sufficient conditions of optimality in the form of an integral inequality are derived.

Some Sufficiency Conditions for Pareto-Optimal Control

1973 ◽  
Vol 95 (4) ◽  
pp. 356-361 ◽  
Author(s):  
G. Leitmann ◽  
W. Schmitendorf
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Pareto Optimality ◽  
Optimal Control Theory ◽  
Cooperative Games ◽  
Sufficient Conditions ◽  
Pareto Optimal ◽  
Vector Valued ◽  
Sufficiency Conditions

We consider the optimal control problem with vector-valued criterion (including cooperative games) and seek Pareto-optimal (noninferior) solutions. Scalarization results, together with modified sufficiency theorems from optimal control theory, are used to deduce sufficient conditions for Pareto-optimality. The utilization of these conditions is illustrated by various examples.

scholarly journals Distributed-Order Non-Local Optimal Control

Axioms ◽  
2020 ◽  
Vol 9 (4) ◽  
pp. 124
Author(s):  
Faïçal Ndaïrou ◽  
Delfim F. M. Torres
Keyword(s):  
Optimal Control ◽  
Maximum Principle ◽  
Control Theory ◽  
Optimality Condition ◽  
Optimal Control Theory ◽  
Sufficient Optimality Condition ◽  
Weak Version ◽  
Fractional Optimal Control ◽  
Non Local ◽  
Distributed Order

Distributed-order fractional non-local operators were introduced and studied by Caputo at the end of the 20th century. They generalize fractional order derivatives/integrals in the sense that such operators are defined by a weighted integral of different orders of differentiation over a certain range. The subject of distributed-order non-local derivatives is currently under strong development due to its applications in modeling some complex real world phenomena. Fractional optimal control theory deals with the optimization of a performance index functional, subject to a fractional control system. One of the most important results in classical and fractional optimal control is the Pontryagin Maximum Principle, which gives a necessary optimality condition that every solution to the optimization problem must verify. In our work, we extend the fractional optimal control theory by considering dynamical system constraints depending on distributed-order fractional derivatives. Precisely, we prove a weak version of Pontryagin’s maximum principle and a sufficient optimality condition under appropriate convexity assumptions.

scholarly journals CONSTRAINT ALGORITHM FOR EXTREMALS IN OPTIMAL CONTROL PROBLEMS

2009 ◽  
Vol 06 (07) ◽  
pp. 1221-1233 ◽  
Author(s):  
MARÍA BARBERO-LIÑÁN ◽  
MIGUEL C. MUÑOZ-LECANDA
Keyword(s):  
Optimal Control ◽  
Maximum Principle ◽  
Optimal Control Problem ◽  
Control Theory ◽  
Control Problem ◽  
Optimal Control Theory ◽  
Optimal Control Problems ◽  
Necessary Conditions ◽  
Control Problems ◽  
Affine System

A geometric method is described to characterize the different kinds of extremals in optimal control theory. This comes from the use of a presymplectic constraint algorithm starting from the necessary conditions given by Pontryagin's Maximum Principle. The algorithm must be run twice so as to obtain suitable sets that once projected must be compared. Apart from the design of this general algorithm useful for any optimal control problem, it is shown how to classify the set of extremals and, in particular, how to characterize the strict abnormality. An example of strict abnormal extremal for a particular control-affine system is also given.

scholarly journals Optimal control theory with general constraints

1981 ◽  
Vol 23 (2) ◽  
pp. 115-126 ◽  
Author(s):  
John M. Blatt
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Optimal Control Theory ◽  
Time Dependent ◽  
Necessary Condition ◽  
Sufficient Condition ◽  
General Constraints ◽  
Elementary Methods ◽  
And Control

AbstractWe consider an optimal control problem with, possibly time-dependent, constraints on state and control variables, jointly. Using only elementary methods, we derive a sufficient condition for optimality. Although phrased in terms reminiscent of the necessary condition of Pontryagin, the sufficient condition is logically independent, as can be shown by a simple example.

scholarly journals On an optimal control problem involving second order hyperbolic systems with boundary controls

1983 ◽  
Vol 27 (1) ◽  
pp. 139-148 ◽  
Author(s):  
K.G. Choo ◽  
K.L. Teo ◽  
Z.S. Wu
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Hyperbolic Systems ◽  
Sufficient Conditions ◽  
Second Order ◽  
Optimal Controls ◽  
Convergence Properties ◽  
Boundary Controls ◽  
Necessary And Sufficient

In this paper, we consider an optimal control problem involving second-order hyperbolic systems with boundary controls. Necessary and sufficient conditions are derived and a result on the existence of optimal controls is obtained. Also, a computational algorithm which generated minimizing sequences of controls is devised and the convergence properties of the algorithm are investigated.

Blade Design of Axial-Flow Compressors by the Method of Optimal Control Theory—Physical Model and Mathematical Expression

1987 ◽  
Vol 109 (1) ◽  
pp. 99-102 ◽  
Author(s):  
Chuan-gang Gu ◽  
Yong-miao Miao
Keyword(s):  
Optimal Control ◽  
Control Theory ◽  
Physical Model ◽  
Optimal Control Theory ◽  
Initial Conditions ◽  
Axial Flow ◽  
Mathematical Expression ◽  
Type Problem ◽  
Or Efficiency ◽  
Flow Type

In the design of compressor blades we put forward an optimization flow-type problem which enables the designers to consider the optimization of specified performance index of the flow-type characteristics, such as that of work or efficiency of a compressor stage. The method of the diffusion factor flow-type design (DFFTD), presented by the authors [1], is taken here as a physical model. On the basis of optimal control theory a mathematical model of the optimal flow-type problem has been established and further recast into a typical form of optimal control problem with free initial conditions, terminal constraints, and state variable inequality constraints.

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