Optimality conditions for extremal controls in bilinear and quadratic problems

Срочко, В. А.; Antonik, V. G.

doi:10.3103/s1066369x1605008x

Cited by 2 publications

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“…This problem is not a linear optimal control problem because the cost-functional and first differential equation contain terms of y 2 v type. In the authors' opinion, special methods for bilinear problems will be efficient for similar problems [13,14].…”

Section: Illustrative Examplementioning

confidence: 99%

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An Optimal Control Problem by a Hybrid System of Hyperbolic and Ordinary Differential Equations

Arguchintsev

Поплевко

2021

Games

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This paper deals with an optimal control problem for a linear system of first-order hyperbolic equations with a function on the right-hand side determined from controlled bilinear ordinary differential equations. These ordinary differential equations are linear with respect to state functions with controlled coefficients. Such problems arise in the simulation of some processes of chemical technology and population dynamics. Normally, general optimal control methods are used for these problems because of bilinear ordinary differential equations. In this paper, the problem is reduced to an optimal control problem for a system of ordinary differential equations. The reduction is based on non-classic exact increment formulas for the cost-functional. This treatment allows to use a number of efficient optimal control methods for the problem. An example illustrates the approach.

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Section: Illustrative Examplementioning

confidence: 99%

“…Note that the auxiliary problems (12) and (13) are currently well-known and can be solved by applying many efficient methods developed for solving optimal control problems for systems of ordinary differential equations [3,[10][11][12][13][14].…”

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An Optimal Control Problem by a Hybrid System of Hyperbolic and Ordinary Differential Equations

Arguchintsev

Поплевко

2021

Games

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Determination of functional parameters in boundary conditions of linear hyperbolic systems by optimal control methods

Arguchintsev

Kedrina

2021

J. Phys.: Conf. Ser.

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An inverse problem of a functional parameter determination is considered for a hybrid system of population dynamics. Dynamics of several interacting populations is described by a system of first-order linear hyperbolic equations. The boundary conditions for this system are determined from the initial problem for ordinary differential equations. The problem is interpreted as an optimal control problem. A non-classic optimality condition of variational maximum principle type is proved. The original problem in distributed parameter systems is reduced to the optimal control problem for ordinary differential equations.

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Optimality conditions for extremal controls in bilinear and quadratic problems

Cited by 2 publications

References 1 publication

An Optimal Control Problem by a Hybrid System of Hyperbolic and Ordinary Differential Equations

An Optimal Control Problem by a Hybrid System of Hyperbolic and Ordinary Differential Equations

Determination of functional parameters in boundary conditions of linear hyperbolic systems by optimal control methods

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