In this paper, we study the maximum principle for stochastic optimal control problems of forward-backward stochastic difference systems (FBSΔSs). Two types of FBSΔSs are investigated. The first one ...is described by a partially coupled forward-backward stochastic difference equation (FBSΔE) and the second one is described by a fully coupled FBSΔE. By adopting an appropriate representation of the product rule and an appropriate formulation of the adjoint process, we deduce the adjoint difference equation. Finally, the maximum principle for this optimal control problem with the control domain being convex is established.
Full text
Available for:
BFBNIB, GIS, IJS, KISLJ, NUK, PNG, UL, UM, UPUK
This paper aims to investigate the oscillatory characteristics of a neutral third order nonlinear difference equation. Utilizing the comparison principle, we get some new standards that guarantee ...that any solution to the neutral difference equation oscillates or approaches zero. Applications are then examined to show that the key theorems are valid.
In Section 3 of our paper, the confusion with indices resulted in the incorrect statement of Theorems 3.3, 3.4, 3.3
and 3.4
(pp. 864-867), as well as influenced Example 4.3 (pp. 872-873). We ...sincerely apologize and present the corrected version below.
Full text
Available for:
BFBNIB, GIS, IJS, KISLJ, NUK, PNG, UL, UM, UPUK
This paper discusses the behaviors and solutions of some rational recursive relations of twenty-fourth order using the
iteration technique and the modulus operator. The stability of the equilibrium ...points are comprehensively analyzed. We also present
other properties such as periodicity, oscillation and bounded solutions. Some numerical examples are obviously given to ensure the
validity of the theoretical work. These examples are plotted using MATLAB. The proposed techniques can be utilized to be applied on
other nonlinear equations.
This paper discusses the behaviors and solutions of some rational recursive relations of twenty-fourth order using the
iteration technique and the modulus operator. The stability of the equilibrium points are comprehensively analyzed. We also present
other properties such as periodicity, oscillation and bounded solutions. Some numerical examples are obviously given to ensure the
validity of the theoretical work. These examples are plotted using MATLAB. The proposed techniques can be utilized to be applied on
other nonlinear equations.
This article considers the decentralized control for networked control systems (NCSs) with asymmetric information. In this NCSs model, the controller 2 (C2) shares its observations and part of its ...historical control inputs with the controller 1 (C1), whereas C2 cannot obtain the information of C1 due to network constraints. Under the linear control strategies assumption, we present the optimal estimators for C1 and C2 respectively based on asymmetric observations. Since the information for C1 and C2 are asymmetric, the estimation error covariance (EEC) is coupled with the controller which means that the classical separation principle fails. By applying the Pontryagin's maximum principle, we obtain a solution to the forward and backward stochastic difference equations. Based on this solution, we derive the optimal controllers to minimize a quadratic cost function. Combining the linear optimal controllers with the EEC, the controller C1 is decoupled from the EEC. It should be emphasized that the control gain is dependent on the estimation gain. What is more, the estimation gain satisfies the forward Riccati equation and the control gain satisfies the backward Riccati equation which makes the problem more challenging. We propose iterative solutions to the Riccati equations and give a suboptimal solution to the optimal decentralized control problem.
This paper aims to highlight certain limitations in the study of fuzzy fractional discrete equations (FFDEs) based on the generalized Hukuhara difference (gH-difference) in the previous papers. In ...general, the equivalence between FFDEs and the associated fuzzy discrete fractional sum equations (FDFSEs) is not achieved, requiring the introduction of an appropriate hypothesis to establish this equivalence. Furthermore, this paper introduces the fundamental theory of fuzzy fractional discrete calculus through granular arithmetic operations between fuzzy intervals to address restrictions in the formerly mentioned approaches involving the generalized Hukuhara difference. These operations are constructed based on the concept of the horizontal membership function (HMF) utilized in multidimensional fuzzy arithmetic (MFA). Additionally, the paper proposes the application of fractional discrete calculus to two types of time-discretization diffusion equations with non-zero right-hand sides. Finally, several numerical examples are provided to validate the main results.
Full text
Available for:
GEOZS, IJS, IMTLJ, KILJ, KISLJ, NLZOH, NUK, OILJ, PNG, SAZU, SBCE, SBJE, UILJ, UL, UM, UPUK, ZAGLJ, ZRSKP
Abstract
In this paper, we are connected with oscillation of third-order linear neutral delay difference equation of the form
Δ
(
c
2
(
σ
)
Δ
(
c
1
(
σ
)
Δ
h
(
σ
)
)
)
+
p
(
σ
)
x
(
σ
−
ς
)
=
0
,
σ
≥
...σ
0
>
0
,
where
h
(
σ
)
=
x
(
σ
)
+
q
(
σ
)
x
(
σ
−
η
)
. Here
c
1
(
σ
) and
c
2
(
σ
) are the sequence of positive integers,
p
(
σ
) and
q
(
σ
) are positive and real sequences such that
q
(
σ
) ≥
q
0
> 1 and
p
(
σ
) ≠ 0,
ς
,
η
are positive integers, such that
ς
>
η
.
Abstract
The paper is concerned with asymptotic and stability behaviors of fixed solutions of the second order nonlinear delay difference equation of the form ?
2
(x
n
+p
n
x
n-k
-q
n
x
n-l
)+ f(x
n
...) = 0, n = 0,1,2, · ··,. Examples are provided to illustrate the results.
PDF
