Using Gröbner Basis Theory to Compute Constraint Networks in Globally Solved Form

Using Gröbner Basis Theory to Compute Constraint Networks in Globally Solved Form

Approximate Dynamic Programming for Networks: Fluid Models and Constraint Reduction

This paper demonstrates the feasibility of using approximate linear programming (ALP) to compute nearly optimal average cost for multiclass queueing network control problems. ALP works directly with the LP form of the optimality equations, but approximates the di¤erential cost by a linear form. We use quadratics, piece-wise quadratic value functions from ‡uid models, and other approximating fun...

Multidimensional FIR Filter Bank Design Using Gröbner Bases

A multivariate polynomial matrix-factorization algorithm is introduced and discussed. This algorithm and another algorithm for computing a globally minimal generating matrix of the syzygy of solutions associated with a polynomial matrix are both associated with a zero-coprimeness constraint that characterizes perfect-reconstruction filter banks. Generalizations, as well as limitations of recent...

Optimal Coding Subgraph Selection under Survivability Constraint

Nowadays communication networks have become an essential and inevitable part of human life. Hence, there is an ever-increasing need for expanding bandwidth, decreasing delay and data transfer costs. These needs necessitate the efficient use of network facilities. Network coding is a new paradigm that allows the intermediate nodes in a network to create new packets by combining the packets recei...

Time Optimal Control Using Gröbner Bases

Abstract: The paper presents the solution of the time optimal control with the help of Gröbner Bases theory. First the set of polynomial equations for the triple integrator system with unknowns corresponding to the switching times is constructed and later it is solved in the computer algebra system Maple using the Groebner library. In dependence of resulting switching times the control action i...