Solution to Singular Optimal Control by Backward Differential Flow

This paper presents a backward differential flow for solving singular optimal control problems. By using Krotov equivalent transformation, the cost functional is converted to a class of global optimization problems. Some properties of the flow are given to reveal the significant relationship between the dynamic of the flow and the geometry of the feasible set. The proposed method is also used in solving a class of variational problems. Some examples are illustrated.

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Upper and Lower bounds for a certain class of constrained variational problems

Journal of the Australian Mathematical Society ◽

10.1017/s1446788700039069 ◽

1963 ◽

Vol 3 (4) ◽

pp. 449-453

Author(s):

M. A. Hanson

Keyword(s):

Optimal Control ◽

Optimal Control Problems ◽

Existence Of Solutions ◽

Necessary Conditions ◽

Optimization Problems ◽

Inequality Constraints ◽

Variational Problems ◽

Upper And Lower Bounds ◽

Control Problems ◽

Constrained Variational Problems

Certain optimization problems involving inequality constraints, known as optimal control problems have been extensively studied during recent years especially in relation to the calculation of optimal rocket thrusts and trajectories. A summary of these works is given by Berkovitz [1] who also establishes necessary conditions for the existence of solutions for a wide class of such problems.

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A Method for the Numerical Solution of Singular Optimal Control Problems Using an Adaptive Radau Collocation Method

AIAA Scitech 2021 Forum ◽

10.2514/6.2021-1456 ◽

2021 ◽

Author(s):

Elisha R. Pager ◽

Anil V. Rao

Keyword(s):

Optimal Control ◽

Numerical Solution ◽

Collocation Method ◽

Optimal Control Problems ◽

Control Problems ◽

Singular Optimal Control

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High-order relaxation approaches for adjoint-based optimal control problems governed by nonlinear hyperbolic systems of conservation laws

Journal of Numerical Mathematics ◽

10.1515/jnma-2013-1002 ◽

2016 ◽

Vol 24 (1) ◽

Cited By ~ 2

Author(s):

Elimboto M. Yohana ◽

Mapundi K. Banda

Keyword(s):

Optimal Control ◽

Conservation Laws ◽

Optimal Control Problems ◽

Initial Conditions ◽

Hyperbolic Systems ◽

Control Problems ◽

Computational Investigation ◽

Backward Problem ◽

Systems Of Conservation Laws ◽

The Cost

AbstractA computational investigation of optimal control problems which are constrained by hyperbolic systems of conservation laws is presented. The general framework is to employ the adjoint-based optimization to minimize the cost functional of matching-type between the optimal and the target solution. Extension of the numerical schemes to second-order accuracy for systems for the forward and backward problem are applied. In addition a comparative study of two relaxation approaches as solvers for hyperbolic systems is undertaken. In particular optimal control of the 1-D Riemann problem of Euler equations of gas dynamics is studied. The initial values are used as control parameters. The numerical flow obtained by optimal initial conditions matches accurately with observations.

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Shifted Chebyshev schemes for solving fractional optimal control problems

Journal of Vibration and Control ◽

10.1177/1077546319852218 ◽

2019 ◽

Vol 25 (15) ◽

pp. 2143-2150 ◽

Cited By ~ 1

Author(s):

M Abdelhakem ◽

H Moussa ◽

D Baleanu ◽

M El-Kady

Keyword(s):

Optimal Control ◽

Fractional Order ◽

Chebyshev Polynomials ◽

Optimal Control Problems ◽

Optimization Problems ◽

Control Problems ◽

Numerical Examples ◽

Fractional Optimal Control ◽

Functional Approximation ◽

Fractional Optimal Control Problems

Two schemes to find approximated solutions of optimal control problems of fractional order (FOCPs) are investigated. Integration and differentiation matrices were used in these schemes. These schemes used Chebyshev polynomials in the shifted case as a functional approximation. The target of the presented schemes is to convert such problems to optimization problems (OPs). Numerical examples are included, showing the strength of the schemes.

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