Let X,, , X, be a sequence of independent and identically distributed random variables with an unknown underlying continuous cumulative distribution function F. Relative to this unknown distribution function suppose one would like to test a null hypothesis concerning the goodness of fit of F to some distribution function using symmetric functions of sample spacings. In some applications the nul...

MESERVEY, R., 1971. The coastline fit of Africa and South America. Palaeogeography, Palaeoclimatol., Palaeoecol., 9: 233-243. It has become axiomatic that the pre-drift reconstruction of Africa and South America is to be made by fitting together the continental shelves. Although this procedure is very plausible, actually the detailed fit of the coastlines is better than that of the shelves and ...

A new approach to representing a time-limited, and essentially bandlimited signal x(t), by a set of discrete frequency/time values is proposed. The set of discrete frequencies is the set of frequency locations at which (real and imaginary parts of) the Fourier transform of x(t) cross certain levels and the set of discrete time values corresponds to the traditional level crossings of x(t). The p...

Abstract—This paper studies the fault tolerant control (FTC) problem for a class of nonlinear discrete-time systems with guaranteed H∞ performance objective in the presence of actuator faults. The mode of faults under consideration is typical aberration of actuator effectiveness. The novelty of this paper is that the effect of the nonlinear terms is described as an index in order to transform t...

The hybrid dynamics of the genetic regulatory networks (GRNs) have attracted much research attention in recent years. This paper is concerned with the stability analysis of piecewise GRNs. Depending on whether the state partitions and mode transitions are known or unknown as a priori, the proposed networks are divided into two categories, i.e., switched GRNs and hybrid GRNs. It is shown that, b...

We propose an algorithm that computes the ε-correlated equilibria with global-optimal (i.e., maximum) expected social welfare for single stage polynomial games. We first derive an infinite-dimensional formulation of ε-correlated equilibria using Kantorovich polynomials and re-express it as a polynomial positivity constraint. In addition, we exploit polynomial sparsity to achieve a leaner proble...

Sum of squares (SOS) decompositions for nonnegative polynomials are usually computed numerically, using convex optimization solvers. Although the underlying floating point methods in principle allow for numerical approximations of arbitrary precision, the computed solutions will never be exact. In many applications such as geometric theorem proving, it is of interest to obtain solutions that ca...

This paper is concerned with the high-performance robust control of discrete-time linear time-invariant (LTI) systems with semi-algebraic uncertainty regions. It is assumed that a robustly stabilizing static controller is given whose gain depends polynomially on the uncertain variables. The problem of tuning this parameter-dependent gain with respect to a prescribed quadratic cost function is f...

We extend a template-based approach for synthesizing switching controllers for semi-algebraic hybrid systems, in which all expressions are polynomials. This is achieved by combining a QE (quantifier elimination)-based method for generating continuous invariants with a qualitative approach for predefining templates. Our synthesis method is relatively complete with regard to a given family of pre...

In this paper, we propose an approach to automatically compute invariant clusters for semialgebraic hybrid systems. An invariant cluster for an ordinary differential equation (ODE) is a multivariate polynomial invariant g(~u, ~x) = 0, parametric in ~u, which can yield an infinite number of concrete invariants by assigning different values to ~u so that every trajectory of the system can be over...