2,109 research outputs found
Mathematical control of complex systems
Copyright © 2013 ZidongWang et al.This is an open access article distributed under the Creative Commons Attribution License,
which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited
A General Backwards Calculus of Variations via Duality
We prove Euler-Lagrange and natural boundary necessary optimality conditions
for problems of the calculus of variations which are given by a composition of
nabla integrals on an arbitrary time scale. As an application, we get
optimality conditions for the product and the quotient of nabla variational
functionals.Comment: Submitted to Optimization Letters 03-June-2010; revised 01-July-2010;
accepted for publication 08-July-201
Backward variational approach on time scales with an action depending on the free endpoints
We establish necessary optimality conditions for variational problems with an
action depending on the free endpoints. New transversality conditions are also
obtained. The results are formulated and proved using the recent and general
theory of time scales via the backward nabla differential operator.Comment: Submitted 17-Oct-2010; revised 18-Dec-2010; accepted 4-Jan-2011; for
publication in Zeitschrift fuer Naturforschung
Robust measurement-based buffer overflow probability estimators for QoS provisioning and traffic anomaly prediction applicationm
Suitable estimators for a class of Large Deviation approximations of rare
event probabilities based on sample realizations of random processes have been
proposed in our earlier work. These estimators are expressed as non-linear
multi-dimensional optimization problems of a special structure. In this paper,
we develop an algorithm to solve these optimization problems very efficiently
based on their characteristic structure. After discussing the nature of the
objective function and constraint set and their peculiarities, we provide a
formal proof that the developed algorithm is guaranteed to always converge. The
existence of efficient and provably convergent algorithms for solving these
problems is a prerequisite for using the proposed estimators in real time
problems such as call admission control, adaptive modulation and coding with
QoS constraints, and traffic anomaly detection in high data rate communication
networks
Robust measurement-based buffer overflow probability estimators for QoS provisioning and traffic anomaly prediction applications
Suitable estimators for a class of Large Deviation approximations of rare event probabilities based on sample realizations of random processes have been proposed in our earlier work. These estimators are expressed as non-linear multi-dimensional optimization problems of a special structure. In this paper, we develop an algorithm to solve these optimization problems very efficiently based on their characteristic structure. After discussing the nature of the objective function and constraint set and their peculiarities, we provide a formal proof that the developed algorithm is guaranteed to always converge. The existence of efficient and provably convergent algorithms for solving these problems is a prerequisite for using the proposed estimators in real time problems such as call admission control, adaptive modulation and coding with QoS constraints, and traffic anomaly detection in high data rate communication networks
An optimal control approach to inventory-production systems with weibull distributed deterioration
Problem statement: We studied the inventory-production system with two-parameter Weibull distributed deterioration items.Approach: The inventory model was developed as linear optimal control problem and by the Pontryagin maximum principle, the optimal control problem was solved analytically to obtain the optimal solution of the problem.Results: It was then illustrated with the help of an example.By the principle of optimality we also established the Riccati based solution of the Hamilton-Jacobi-Bellman (HJB) equation associated with this control problem. Conclusion: As an application to quadratic control theory we showed an optimal control policy to exist from the optimality conditions in the HJB equation
Stochastic Optimal Control with Neural Networks and Application to a Retailer Inventory Problem
Overwhelming computational requirements of classical dynamic programming algorithms render them inapplicable to most practical stochastic problems. To overcome this problem a neural network based Dynamic Programming (DP) approach is described in this study. The cost function which is critical in a dynamic programming formulation is approximated by a neural network according to some designed weight-update rule based on Temporal Difference(TD)learning. A Lyapunov based theory is developed to guarantee an upper error bound between the output of the cost neural network and the true cost. We illustrate this approach through a retailer inventory problem
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