On the composability of consistency conditions

This paper presents a formal framework, which is based on the notion of a serialization set, that enables to compose a set of consistency conditions into a more restrictive one. To exemplify the utility of this framework, a list of very basic consistency conditions is identified, and it is shown that various compositions of the basic conditions yield some of the most commonly used consistency conditions, such as sequential consistency, causal memory, and Pipelined RAM. The paper also lists several applications that can benefit from even weaker semantics than Pipelined RAM that can be expressed as a composition of a small subset of the basic conditions.     

On the necessity of the invariance conditions for reach control on polytopes

We study the Reach Control Problem (RCP) to make the solutions of an affine system defined on a polytopic state space reach and exit a prescribed facet of the polytope in finite time without first leaving the polytope. So-called invariance conditions are used to prevent solutions from leaving the polytope through facets which are not designated as the exit facet. These conditions are known to be necessary for solvability of the RCP on polytopes by continuous state feedback. We study whether the invariance conditions are also necessary for solvability of the RCP on polytopes by open-loop controls. We show by way of a counterexample that surprisingly the answer is negative. We identify a suitable class of polytopes for which the invariance conditions remain necessary conditions.     

Optimality conditions of sliding modes and the maximum principle for control problems with the scalar argument

Various types of optimality criteria and conditions, which define the set of admissible solution, are brought to the canonical form. For the problem set in this form, the optimality conditions of sliding modes are stated. It is shown that the optimality conditions emerge from these conditions in the form of the maximum principle for problems with a scalar argument and an arbitrary combination of the optimality criterion and constraints.     

On the convergence condition of generalized root iterations for the inclusion of polynomial zeros

Using a fixed point relation based on the logarithmic derivative of the k-th order of an algebraic polynomial and the definition of the k-th root of a disk, a family of interval methods for the simultaneous inclusion of complex zeros in circular complex arithmetic was established by Petković [M.S. Petković, On a generalization of the root iterations for polynomial complex zeros in circular interval arithmetic, Computing 27 (1981) 37–55]. In this paper we give computationally verifiable initial conditions that guarantee the convergence of this parallel family of inclusion methods. These conditions are significantly relaxed compared to the previously stated initial conditions presented in literature.     

On the equivalence relations of detectability and PE conditions

This note investigates equivalent relations of detectability and persistency excitation (PE) for general nonlinear time-varying systems. Three new definitions relating to the detectability are proposed and discussed. As a preliminary result, we show that these detectability conditions are all equivalent under a mild assumption. Furthermore, two PE conditions that are a nonlinear-version extension of the PE proposed in present literature are defined. Very interestingly, it can be shown that these nonlinear-version PE conditions are both equivalent to the proposed detectability conditions under the same assumption. To the best of our knowledge, this is a first result about the connection between detectability and PE in the area of nonlinear time-varying systems. Moreover, by combining a newly developed stability criterion with the proposed results, an interesting example is given to illustrate how the classic PE conditions for linear systems can be extended and used in nonlinear systems. From this example, it can also be seen that the uniformly asymptotic stability can be guaranteed either using the detectability conditions or by the PE conditions based on our approach.     

Application of the Polynomial Chaos Expansion to the simulation of chemical reactors with uncertainties

In this paper we consider the simulation of probabilistic chemical reactions in isothermal and adiabatic conditions. Models for reactions under isothermal conditions result in advection equations, adiabatic conditions yield the reactive Euler equations. In order to treat with scattering data, the equations are projected onto the polynomial chaos space. Scattering data can largely affect the estimation of quantities in the system, including variable optimization. This is demonstrated on a selective non-catalytic reduction of nitric oxide.     

Frequency domain conditions for the stability of perturbed polynomials

New necessary and sufficient conditions for the stability of perturbed polynomials of continuous systems are given in the frequency domain. The conditions are equivalent and in some respects more powerful than the well-known Kharitonov conditions. The new conditions allow considerable freedom in distributing the available uncertainty margin among the different coefficients of a polynomial and provide an indication as to whether the maximum allowable margin of uncertainty for a given polynomial has been reached.     

On the necessity of looped-functionals arising in the analysis of pseudo-periodic,sampled-data and hybrid systems

Looped-functionals have been shown to be relevant for the analysis of a wide variety of systems. However, the conditions obtained in previous papers on the analysis of sampled-data, impulsive and switched systems have only been shown to be sufficient for the characterisation of their associated discrete-time stability conditions. We prove here that these conditions are also necessary. This result is derived for a wider class of linear systems, referred to as impulsive pseudo-periodic systems, that encompass periodic, impulsive, sampled-data and switched systems as special cases.     

Experiments with automata when the upper bound of the number of their states is unknown

The properties of a class of initial finite automata are investigated; the class is possibly infinite, and each input-output signal of a fixed set of automata from this class is produced by no more than one state. The exact finiteness conditions of this class and its important subclasses and exact existence conditions of check experiments related to these classes are found. The existence conditions of experiments on recognition of such automata are also described. Translated from Kibernetika i Sistemnyi Analiz, No. 4, pp. 59–71, July–August, 1999.     

On the use of spline functions of even degree for the numerical solution of the delay differential equations

One considers and investigates the notion of natural spline functions of even degree, satisfying given derivative-interpolating conditions on simple knots. By using such spline functions we shall develop some theory and algorithms for the numerical solution of a class of delay differential equations. It will be shown that such kind of spline functions are very suitable for the numerical treatment of delay differential equations with initial conditions.