Sándor Molnár

Observability and observers in a food web

The problem of the possibility of recovering the time-dependent state of a whole population system from the observation of certain components has been studied in earlier publications, in terms of the observability concept of mathematical systems theory. In the present note a method is proposed for effectively calculating the state process. For an illustration an observer system for a simple food web is numerically constructed.

Monitoring environmental change in an ecosystem

The monitoring and analysis of the processes taking place in an ecosystem is a key issue for a sustainable human activity. A system of populations, as the biotic component of a complex ecosystem is usually affected by the variation of its abiotic environment. Even in nearly natural ecosystems an abiotic effect like climatic implications of global warming may cause important changes in the dynamics of the population system. In ecosystems involving field cultivation or any industrial activity; the abiotic parameter in question may be the concentration of a substance, changing, e.g. as a result of pollution, application of a pesticide, or a fertilizer, etc. In many cases the observation of the densities of each population may be technically complicated or expensive, therefore the question arises whether from the observation of the densities of certain (indicator) populations, the whole state process of the population system can be uniquely recovered. The paper is aimed at a methodological development of the state monitoring, under the conditions of a changing environment. It is shown, how the technique of mathematical systems theory can be applied not only for the approximate calculation of the state process on the basis of the observed data, even under the effect of an exogene abiotic change with known dynamics; but in certain cases, also for the estimation of the unknown biological effect of the change of an abiotic parameter. The proposed methodology is applied to simple illustrative examples concerning a three-species predator-prey system.

On “verticum”-type linear systems with time-dependent linkage

Abstract “Verticum”-type linear systems with time-dependent coupling are particular time-dependent systems consisting of subsystems such that the temporal output of the i -th subsystem is one of the inputs of the consecutive subsystem. Kalmans type rank conditions are proved for the controllability and the observability of these systems under a very simply expressed differential-algebraic condition for the time-dependent coefficients.

Introduction to matrix theory : with applications to business and economics

Vectors and Matrices Vector Spaces and Inner-Product Spaces Systems of Linear Equations and Inverses of Matrices Determinants Linear Mappings and Matrices Eigenvalues, Invariant Subspaces, Canonical Forms Special Matrices Elements of Matrix Analysis.

An N-person Stackelberg leader-leader model

This paper introduces a general N-firm Stackelberg-type leader-leader model under the assumption that at each time period t, each firm estimates the marginal costs of all other firms on the basis of their outputs in the preceding time period t-1. First the mathematical model is formulated, and then local and global stability conditions are presented.

Some notes on the time-variant Lyapunov theory

Abstract The well-known Lyapunov theory is extended to time variant discrete systems when the state space is bounded. We show that in addition to the usual Lyapunov stability assumptions very light conditions on the state transition functions are sufficient for stability and asymptotical stability.

Equilibrium control of nonlinear verticum-type systems, applied to integrated pest control.

Linear verticum-type control and observation systems have been introduced for modelling certain industrial systems, consisting of subsystems, vertically connected by certain state variables. Recently the concept of verticum-type observation systems and the corresponding observability condition have been extended by the authors to the nonlinear case. In the present paper the general concept of a nonlinear verticum-type control system is introduced, and a sufficient condition for local controllability to equilibrium is obtained. In addition to a usual linearization, the basic idea is a decomposition of the control of the whole system into the control of the subsystems. Starting from the integrated pest control model of Rafikov and Limeira (2012) and Rafikov et al. (2012), a nonlinear verticum-type model has been set up an equilibrium control is obtained. Furthermore, a corresponding bioeconomical problem is solved minimizing the total cost of integrated pest control (combining chemical control with a biological one).

Future trends in road transport systems in Hungary and in the EU

Efficient transport is a key ingredient in the competitiveness of an economy. Intra-EU passenger transport has grown more than the population – which means a greater mobility (more kilometres travelled) per person – but less than GDP. The road transport systems affect practically all the environmental elements, and they have a role in every harmful effect the environmental protection is dealing with. At the same time, the degree of the environment pollution and the role of the road transport within total pollution are significantly different. The impacts on nature conservation caused by road transport infrastructure and operation are of greater importance. Beyond direct land use, the separation of the habitats, the separation effect of the highly trafficked lines greatly influence the biodiversity, the survival of the valuable groups of the flora and fauna. From landscaping aspect the increased construction, the implementation of industrial sites experienced along the expressways and also expected along the planned sections may result to unfavourable effect indirectly, especially in the agglomeration.

Controllability and Reachability of Dynamic Discrete-Time Linear Systems

For discrete-time linear systems, controllability and reachability are not equivalent. Instead of the well-known Kalmans rank condition, which characterizes reachability, controllability to origin of the time invariant, discrete-time linear system is equivalent to the Fuhrmanns rank condition. In the first part of this paper we prove that controllability to origin of time varying discrete-time linear systems, under a difference-algebraic condition, is equivalent to a generalized Fuhrmanns rank condition. In the second part we prove that reachability and observability for time varying discrete-time linear systems are equivalent to a structured Kalmans rank condition, under the difference algebraic independence of the structure matrices.

Approximation of LPV-Systems with Constant-Parametric Switching Systems

A common problem in systems and control theory is to provide an approximation to non-linear systems. We provide a novel approach as a general solution to this problem originally conceived by Gamkrelidze. We consider and solve a general approximation problem which provides the fundamentals for various switching-type systems thus encompassing a wide range of systems theory problems.