This paper presents two types of recurrent neural networks, continuous-time and discrete-time ones, for solving linear inequality and equality systems. In addition to the basic continuous-time and discrete-time neural-network models, two improved discrete-time neural networks with faster convergence rate are proposed by use of scaling techniques. The proposed neural networks can solve a linear ...

This paper deals with state estimation problem for linear systems with state equality constraints. Using noisy measurements which are available from the observable system, we construct the optimal estimate which also satisfies linear equality constraints. For this purpose, after reviewing modeling problems in linear stochastic systems with state equality constraints, we formulate a projected sy...

The 0/1 knapsack equality polytope is, by deenition, the convex hull of 0/1 solutions of a single linear equation. A special form of this polytope | where the deening linear equation has nonnegative integer coeecients and the number of variables having co-eecient one exceeds the right-hand-side | is considered. Equality constraints of this form arose in a real-world application of integer progr...

A surjective space transformation technique is used to convert an original dual linear programming problem with equality and inequality constraints into a problem involving only equality constraints. Continuous and discrete versions of the stable gradient projection method are applied to the reduced problem. The numerical methods involve performing inverse transformations. The convergence rate ...

Based on an invariance-type property of the Lee-compositions of a linear Lee code, additional equality constraints can be introduced to the linear programming problem of linear Lee codes. In this paper, we formulate this property in terms of an action of the multiplicative group of the field [Formula: see text] on the set of Lee-compositions. We show some useful properties of certain sums of Le...

This paper presents a new observer design methodology for a time varying actuator fault estimation. A new linear matrix inequality (LMI) design algorithm is developed to tackle the limitations (e.g. equality constraint and robustness problems) of the well known so called fast adaptive fault estimation observer (FAFE). The FAFE is capable of estimating a wide range of time-varying actuator fault...