Authors:
Edwin Engin Yaz,
Yvonne Ilke Yaz,
Volume: 1, Page 2873 Paper number 1015
Abstract:
A general formulation is presented for finite horizon suboptimal control
of a class of discrete-time, nonautonomous, uncertain, nonlinear stochastic
systems. Full state information is assumed to be available in controller
derivation and optimization is carried out for a variety of performance
criteria within a common framework. These performance criteria include
H-2, H-infinity, and various dissipative control objectives for such
stochastic systems. It is shown that the results obtained in this paper
include the previous ones in the literature as special cases.
Authors:
Vladislav Tadić,
Volume: 1, Page 2875 Paper number 1785
Abstract:
Motivated by the problem of the asymptotic behavior of temporal-difference
learning algorithms with non-linear function approximation, the local
almost sure asymptotic properties of stochastic approximation algorithms
are analyzed for violated Kushner-Clark conditions. First, the algorithms
with additive noise are analyzed for the case where the noise is state-dependent.
The obtained results are then applied to the analysis of the algorithms
with non-additive noise. Using these general results, the analysis
of temporal-difference learning algorithms is carried out for the case
of a general non-linear function approximation and under the assumptions
allowing the underlying Markov chain to be positive Harris. The general
results are also illustrated by an example where the noise is non-additive,
correlated and satisfies strong mixing conditions.
Authors:
Alexander S. Poznyak,
Volume: 1, Page 2881 Paper number 1009
Abstract:
The new form of the strong law of large numbers for dependent vector
sequences using the ''double averaged'' correlation function is presented.
The suggested theorem generalizes well-known Cramer-Lidbetter's theorem
and give more general conditions for fulfilling the strong law of large
numbers within the class of vector random processes generated by a
non stationary stable forming filters with an absolutely integrable
impulse function.
Authors:
Patrick A. Florchinger,
Volume: 1, Page 2883 Paper number 9018
Abstract:
The purpose of this paper is to extend to affine in the control stochastic
differential systems the well--known result of Jurdjevic- Quinn. This
result incorporates a previous result in the stochastic context proved
by Florchinger.
Authors:
Leslaw Socha,
Volume: 1, Page 2885 Paper number 1590
Abstract:
The sufficient conditions of exponential string stability for a few
class of nonlinear composite stochastic systems are established. The
excitations are assumed to be parametric white noises. In this case
the objective is to anaalyze composite systems in their lower order
subsystems and in term of their interconnecting structure. The cases
of exponential string stability for weak coupling systems, vehicle-following
systems and l_2 string stability for weak coupling systems are considered.
Authors:
Andrew E.B. Lim,
Xun Yu Zhou,
Volume: 1, Page 2890 Paper number 1812
Abstract:
This paper is concerned with optimal control of linear backward stochastic
differential equations (BSDEs) with a quadratic cost criteria, or backward
linear--quadratic (BLQ) control. The solution of this problem is obtained
completely and explicitly by using an approach which is based primarily
on the completion-of-squares technique. Two alternative, though equivalent,
expressions for the optimal control are obtained. The first of these
involves a pair of Riccati type equations, an uncontrolled BSDE and
an uncontrolled forward stochastic differential equation (SDE), while
the second is in terms of a Hamiltonian system. A key step in our
derivation is a proof of global solvability of the aforementioned Riccati
equations. Although of independent interest, this issue has particular
relevance to the BLQ problem since these Riccati equations play a central
role in our solution. Last but not least, it is demonstrated that the
optimal control obtained coincides with the solution of a certain forward
linear--quadratic (LQ) problem. This, in turn, reveals the origin of
the Riccati equations introduced.
Authors:
Peng-Fei Yao,
Volume: 1, Page 2896 Paper number 20
Abstract:
We consider some observability inequalities from boundary for a general
shallow shell with a middle surface, any shape. At first, an estimate
is established by the geometric multiplier method in the case that
no boundary conditions are imposed under some checkable geometric conditions.
Then our results yield continuous observability estimates for two kinds
of boundary conditions which have physical meaning with an explicit
observability time; hence, by duality, exact controllability results.
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