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J(u( )) Ji (u( )).

i N

,
uNE NE \U	DG	u U	DG	: J(u) J(uNE ) ,	(5)
	DG		DG
	(4)				.

uNE NE \U	DG	u U					DG		: J(u) J(uNE ) ,																(6)
																									.
i N uNE NE \U					DG			u U			DG		: J			(u) J					i	(uNE ),			(7)
					DG						DG				i						i				,		-
																									,		-
i N uNE NE \U				DG			u U			DG		: J		i	(u) J					(uNE ),					(8)
				DG						DG				i					i						.		-
, (7) → (5), (6) → (8).																									.		-
, (7) → (5), (6) → (8).
UDG NE U* ,																									(1)-(4)		-
UDG ,									.
UDG ,												(6)										(8),			,		-
													.														-
													.
,													.									,
																						,
																						(			)
(3)		.																							(1)-
(3)
J(u()) max																									(9)
(2)-(3).
						Arg max J(u( )) .																UOC U *		,			-
			U			Arg max J(u( )) .																UOC U *	U	,			-
									u( ) U																		.
																											.
,								UOC
																		U		\UOC u UOC : J(u) J(						), . .
																	u	U		\UOC u UOC : J(u) J(					u	), . .
UOC																,									.		-
(4).																,											-
(4).																											-
																											-
																(1)-(4).						,					,
																						(4).					-
(9), (2)-(4).																											-
(9), (2)-(4).
													.														-
																									,		-
																						( - ,			.)		-
Д12Ж.																											-
Д12Ж.

	,									,	,
	,									,	-
											(	)
			(							).		-

J0 (p( ),q( ),u( )) e t g0 (x(t), p(t),q(t),u(t),t)dt max												(10)
		0
p(t) P,q(t) Q;												(11)

Ji (p( ),q( ),u( )) e t gi (x(t), pi (t),u(t),t)dt max												(12)
		0
ui (t) Ui (qi (t)),		i N;										(13)
	(3)	(4).							g0, J0 -
	;	p(t) (p1(t),..., pn (t)) -										;
q(t) (q1(t),...,qn (t))-										.	,	,
												,
								(4)		.		,
										NE(p,q) ,		-
	.											,
(1)-(3).
Umax	Arg max	max J			0		(p,q,u) -
	p P,q Q u U(q)				0
	p P,q Q u U(q)
	;
Umax	Arg max	max					J	0	(p,q,u) -
NE	p P,q Q u NE( p,q)							0
	p P,q Q u NE( p,q)									;
										;
U*	Arg max	max	J	0		(p,q,u)				-
max	p P,q Q u U*			0
	p P,q Q u U*
,	;

UNE* (p,q) NE(p,q) U * -

;

UHDG(p,q) UNEmax Umax* U

	,
(p,q) -	-

(p,q) P Q:UHDG ,			(10)-(13),
(3)-(4)		.
М		.	-
		Д11Ж.	-
-	-	Д11Ж.
(	)	,	-
		.	-
Д5Ж		ε-	-
,		,
		7

Д14Ж. Д11Ж.

. Д15Ж

v(t) (t, x(t)); v(t) (t,u(t)).

), -

v(t) q(t)

SCI J0max J0NE ,

Jmax	max max J	0	(p,q,u),
0	p P,q Q u U(q)	0
	p P,q Q u U(q)

.	,	-
	,	-
		-
		-
		-
	.	Д16Ж
(	)	-
		-

:v(t) (t)

v(t) (t)

2t 2x v(t) p(t);

J0NE max min

p P,q Q u NE( p,q)

1t	1x (		-
(		) Д17,18Ж;
		(5),	(7)
		(14)
J0 (p,q,u).

			.	SCI 0 .	SCI 0
	.		.			-
	.					-
.						-
.		Д19Ж.
	Д20-21Ж	Д19Ж.				-
	Д20-21Ж				-	-
		.	Д22Ж		,	-
.						-
.	Д23Ж					-
	Д23Ж		.	Д24Ж	-	-
			.	Д24Ж		-
						-
	(	).	Д25Ж			-
-						-
.	Д26Ж	.		-
	Д27Ж	.				-
	Д27Ж					-
	.	Д28Ж				-
	.	Д29-30Ж		-	,	-
	.	Д29-30Ж			,
					(	-
)	.	Д31Ж			-	-
	.	Д32-33]
		8

.
.
,		,
,	,	-
	.	-
	(
)	(	,
).
	,	-
	,	-
.		-
.		,
.

	1.	. .					. -	.:	, 1977. -
255 .
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-				, 2007. - 584 .
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	13.	, 2012. - 432 .				/		. .,
	13.					/		. .,
.	.,	.	.,	. . -	.:	, 1983. - 393 .
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	, 2014 (6), 86-102.					//				-
	, 2014 (6), 86-102.
	15.		. .,	.	.,	. .
		, 2016, 8(4), 14-29.				//
		, 2016, 8(4), 14-29.

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17.Olsder G. J. Phenomena in inverse Stackelberg games, part 2: Dynamic problems // Journal of Optimization Theory and Applications, 2009, 143 (3), 601–618.

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Automation and Remote Control, 2015, 76(2), 264-277.
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	. 2018. №1. URL: ivdon.ru/ru/magazine/archive/n1y2018/4670.
20.	. .,	. .,	. .			//
			, 2014, 6(4), 535-542.			//
			, 2014, 6(4), 535-542.
21.	. .,	. .,	. .			-
			, 2015, 7(2), 281-288.			//
			, 2015, 7(2), 281-288.
22.	. .,	. .,	. .		-	-
.	. 55. - ., 2015.	.326-342.			//
.	. 55. - ., 2015.	.326-342.
23.	. .,	. .,	. .,		. .,	. .,
. .,	. .	-				-
	//		.		. 55. - ., 2015. .343-361.
24.	. .,	. .,		. .	.
	, 2016, 28(7), 96-106.				//
	, 2016, 28(7), 96-106.
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	, 2017, 6, 122-137.
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		(	. 2016. №4.		) //	.
-	.		. 2016. №4.		.25-29.

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				//	,
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			:		(	-
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				10

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