An extension of the Legendre transform to non-convex functions with vanishing Hessian as a mix of envelope and general solutions of the Clairaut equation is proposed. Applying this to constraint systems, the procedure of finding a Hamiltonian for a singular Lagrangian is just that of solving a corresponding Clairaut equation with a subsequent application of the proposed Legendre-Clairaut transf...

The Problem: The goal of this project is to systematically enumerate feasible conformations (three-dimensional configurations) of a flexible molecule, subject to a given set of constraints on the distances between atoms and on the torsional angles of rotatable bonds. Without any constraints, the conformation space of a flexible molecule is astronomical (exponential in the number of degrees of f...

In order to tackle realistic engineering applications where constrained problems such as the NavierStokes equations are encountered, the trend is to employ Uzawa’s algorithm, which consists of computing the momentum equation separately from the constraints. Examples of constraints include the divergence-free constraint and the zero-normal velocity constraint to a boundary (slip boundary conditi...

We present in this paper an algorithm based upon the Constraint Satisfaction Problem model, used at the \ Ecole des Mines de Nantes" to generate examination timetables. A strong constraint is that the computing time must be less than 1 minute. This led us to develop an incomplete algorithm, using local repair techniques, instead of an exhaustive search method. The program has been validated on ...

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...

General extensions of general relativity (GR) based on bona fide degrees freedom predict a fifth force which operates within massive objects, opening up an exciting opportunity to perform precision tests gravity at stellar scales. Here, focussing scalar-tensor theories for dark energy, we utilise the Sun as our laboratory and search imprints fifth-force effect solar equilibrium structure. With ...

We study the Hamiltonian formalism for second order and fourth nonlinear Schr\"{o}dinger equations. In case of equation, we consider cubic logarithmic nonlinearities. Since Lagrangians generating these equations are degenerate, follow Dirac-Bergmann to construct their corresponding Hamiltonians. obtain consistent motion, imposes some set constraints which contribute total along with Lagrange mu...

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...

Constraint-based problems are hard combinatorial problems and are usually solved by heuristic search methods. In this paper, we consider applying a machine learning approach to improve the performance of these search-based solvers. We apply reinforcement learning in the context of Constraint Satisfaction Problems (CSP) to learn a value function, which results in a novel solving strategy. The mo...