Nonlinear control allocation is an important part of modern nonlinear dynamic inversion based flight systems which require a highly accurate model aircraft aerodynamics. Generally, accurately implemented onboard determines how well the system nonlinearities can be canceled. Thus, more results in better cancellation, leading to higher performance controller. In this paper, presented that combine...

We study a class of orthonormal exponential bases for the space L2[0, 1] and introduce the concept of spectral sequences. We characterize piecewise linear spectral sequences with the knot at 1/2 and investigate the non-continuity of the piecewise linear spectral sequences. From a special construction of a piecewise constant spectral sequence, the classical Walsh system is recovered.

Diffusion processes are often regarded as among the more abstruse stochastic processes, but diffusion processes are actually relatively elementary, and thus are natural first candidates to consider in queueing applications. To help demonstrate the advantages of diffusion processes, we show that there is a large class of one-dimensional diffusion processes for which it is possible to give conven...

The concept of permutograph is introduced and properties of integral functions on permutographs are established. The central result characterizes the class of integral functions that are representable as lattice polynomials. This result is used to establish lattice polynomial representations of piecewise linear functions on R and continuous selectors on linear orders.

Height coordinate ocean models commonly represent topography as a ‘‘staircase’’ of discontinuous steps that are fitted to the model grid. Here the ramifications of an alternative approach are studied in which ‘‘shaved cells’’ are used to represent irregular topography. The problem is formulated using the finite-volume method and care is taken to ensure that the discrete forms have appropriate c...

We study succinct representations of a convex univariate function φ over a finite domain. We show how to construct a succinct representation, namely a piecewise-linear function φ̄ approximating φ when given a black box access to an L-approximation oracle φ̃ of φ (the oracle value is always within a multiplicative factor L from the true value). The piecewise linear function φ̄ has few breakpoints (...

This paper describes a new technique called piecewise linear reasoning (PLR) for analyzing dynamic systems describable by finite sets of ordinary differential equs tions. Current qualitative reasoning programs derive the abstract behavior of a system by simulating handcrafted “qualitative” versions of the differential equations that characterize it and summarizing the results. PLR infers more d...

We consider the problem of fitting a convex piecewise-linear function, with some specified form, to given multi-dimensional data. Except for a few special cases, this problem is hard to solve exactly, so we focus on heuristic methods that find locally optimal fits. The method we describe, which is a variation on the K-means algorithm for clustering, seems to work well in practice, at least on d...

Classical Morse Theory [8] considers the topological changes of the level sets Mh = {x ∈ M | f(x) = h } of a smooth function f defined on a manifold M as the height h varies. At critical points, where the gradient of f vanishes, the topology changes. These changes can be classified locally, and they can be related to global topological properties of M . Between critical values, the level sets v...

In this paper, we present a mixed-integer linear programming (MILP) formulation of piecewise, polyhedral relaxation (PPR) multilinear term using its convex-hull representation. Based on the PPR’s solution, also MILP whose solutions are feasible for nonconvex, equations. We then computational results showing effectiveness proposed formulations standard benchmark nonlinear programs (NLPs) with te...