A SECOND-ORDER MAXIMUM PRINCIPLE IN OPTIMAL CONTROL UNDER STATE CONSTRAINTS

Tonon, Daniela; Hoehene, Daniel; Frankowska, Halina

Tonon, Daniela; Hoehene, Daniel; Frankowska, Halina (2013), A SECOND-ORDER MAXIMUM PRINCIPLE IN OPTIMAL CONTROL UNDER STATE CONSTRAINTS, Serdica Mathematical Journal, 39, 3-4, p. 233–270

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Type

Article accepté pour publication ou publié

External document link

http://www.math.bas.bg/serdica/

Date

2013

Journal name

Serdica Mathematical Journal

Volume

Number

3-4

Publisher

Bulgarian Academy of Sciences, Institute of Mathematics

Pages

233–270

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Author(s)

Tonon, Daniela
Hoehene, Daniel
Frankowska, Halina

Abstract (EN)

A second-order variational inclusion for control systems under state constraints is derived and applied to investigate necessary optimality conditions for the Mayer optimal control problem. A new pointwise condition verified by the adjoint state of the maximum principle is obtained as well as a second-order necessary optimality condition in the integral form. Finally, a new sufficient condition for normality of the maximum principle is proposed. Some extensions to the Mayer optimization problem involving a differential inclusion under state constraints are also provided.

Subjects / Keywords

second-order tangents; second-order necessary optimality conditions; optimal control