We derive optimality conditions for the paths of a Dubins vehicle when the state space is partitioned into two patches with different vehicle’s forward velocity. We recast this problem as a hybrid optimal control problem and solve it using optimality principles for hybrid systems. Among the optimality conditions, we derive a “refraction” law at the boundary of the patches which generalizes the ...

In a recent paper by the first author, a simple proof was given of a result by Tutte on the validity of barycentric mappings, recast in terms of the injectivity of piecewise linear mappings over triangulations. In this note, we make a short extension to the proof to deal with arbitrary tilings. We also give a simple counterexample to show that convex combination mappings over tetrahedral meshes...

We recast into histories-based form a quantum field theory defined earlier in operator language for a free scalar field on a background causal set. The resulting decoherence functional resembles that of the continuum theory but the counterpart of the d’Alembertian operator is nonlocal and a generalized inverse of the discrete retarded Green function. We comment on the significance of this and w...

Linear programming (LP) formulations are often employed to solve stationary, infinitehorizon Markov decision process (MDP) models. We present an LP approach to solving nonstationary, finite-horizon MDP models that can potentially overcome the computational challenges of standard MDP solution procedures. Specifically, we establish the existence of an LP formulation for risk-neutral MDP models wh...

This article addresses the problem of urbanization of information systems. The development of an information system company is certainly a complex task. Hence the choice for organizations to opt for an urbanization approach of their information. In our work we are interested in a comprehensive approach to recast Information System (IS). This approach is oriented service (Service Oriented Archit...

This article is a continuation of an article on defining functions on trees (see [6]). In this article we develop terminology specialized for binary trees, first defining binary trees and binary grammars. We recast the induction principle for the set of parse trees of binary grammars and the scheme of defining functions inductively with the set as domain. We conclude with defining the scheme of...

The Multivariable Continuous-time Generalised Predictive Controller (CGPC) is recast in a state-space form and shown to include Gen-eralised Minimum Variance (GMV) and an new algorithm, Predictive GMV (PGMV) as special cases. Comparisons are drawn with the exact linearisation methods of nonlinear control and it is noted that the state-space approach extends readily to the nonlinear case. The re...

H2 preview control in the discrete-time domain is approached in a strict geometric perspective. The original formulation in the frequency domain is recast in the time domain. Then, it is shown how the problem in the time-domain can be reduced to the combination of elementary subproblems. This approach requires a structural analysis of the properties of the singular Hamiltonian system associated...

This article is a first step in the direction of extending possibilistic planning to account for incomplete and imprecise knowledge of the world state. Fundamental definitions are given and the possibilistic planning problem is recast in this new setting. Finally, it is shown that, under certain conditions, possibilistic planning with imprecise and incomplete state descriptions is no harder tha...