Numerical solution of minimax problems of optimal control, part 1

Miele, A.; Mohanty, B.P.; Venkataraman, P.; Kuo, Y. M.

doi:10.1007/bf00934325

Cited by 29 publications

(2 citation statements)

References 12 publications

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“…CY>O) (10) which is a convex subset in U. Note that the image of fl by r, Imfl, is also convex, since H is convex and T is a bounded linear operator.…”

Section: ;T)b(t)w(t)dt (9)mentioning

confidence: 96%

Computational method for minimax optimization in the time domain

Ohtsuka¹,

Fujii²

1994

Journal of Guidance, Control, and Dynamics

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A computational method is proposed in this paper for a minimax problem in the time domain. A minimax problem for a linear system is formulated and analyzed by vector space methods. The uniqueness of the optimal solution is analyzed readily in the present approach, and its geometric interpretation is presented. The further analysis based on duality shows that the infimum or a lower bound of the value of the performance index is calculated through supplementary optimization problems, and the minimax problem is solved as an optimization problem with an inequality constraint. The proposed approach provides a simple computational method for the minimax problem. Two numerical examples demonstrate simple implementation of the proposed method. NomenclatureImfl SON T* t f = image of a set H = sign function of a vector, SGN(jc) = [sgiife)] = adjoint operator of a linear operator T = terminal time, > t Q

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“…CY>O) (10) which is a convex subset in U. Note that the image of fl by r, Imfl, is also convex, since H is convex and T is a bounded linear operator.…”

Section: ;T)b(t)w(t)dt (9)mentioning

confidence: 96%

Computational method for minimax optimization in the time domain

Ohtsuka¹,

Fujii²

1994

Journal of Guidance, Control, and Dynamics

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“…Under the assumption that jc*(/) arid u*(t) exist andF(jc(/)) is of order one, o>/(jt*(r)) is not empty because w=w*(r), r €(//,?/) satisfies Eqs. (7) and (8). In the case where the control u is scalar, or F only contains one component of vector control u, CO/(JC*(T)) is solved directly from Eq.…”

Section: Remarkmentioning

confidence: 99%

Optimal control problems with maximum functional

Vinh

1991

Journal of Guidance, Control, and Dynamics

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This paper considers the optimal control problem with a performance index that includes a maximum functional. Necessary conditions are derived that are more general than those of previous work, some of which is shown to be reducible and, therefore, included in the results found here. An illustrative example demonstrates that necessary conditions are satisfied by a unique solution of the problem. The problem of threat avoidance for aircraft is formulated as the optimal control problem considered here. Numerical results for a subsonic glider are presented.

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