2018 (vol. 28) - Number 4

*T. Kaczorek:*

A new method for computation of positive realizations of fractional linear continuous-time systems

*A. Biswas, A. Sarkar:*

Development of dual hesitant fuzzy prioritized operators based on Einstein operations with their application to multi-criteria group decision making

*L. Li, R. Zhang, J. Wang, X. Shang:*

Some q-orthopair linguistic Heronian mean operators with their application to multi-attribute group decision making

*J. Duda:*

Lyapunov matrices approach to the parametric optimization of a system with two delays and a PD controller

*M. Lhous, M. Rachik, El M. Magri:*

Ideal observability for bilinear discrete-time systems with and without delays in observation

*P.T. Anh, A. Babiarz, A. Czornik, M. Niezabitowski:*

Variation of constant formulas for fractional difference equations

*K. Bingi, R. Ibrahim, M. Noh Karsiti, S. Miya Hassan, V. Rajah Harindran:*

A comparative study of 2DOF PID and 2DOF fractional order PID controllers on a class of unstable systems

ACS Abstract:

**2015 (Volume 25)**

Number 2

On reconstructing unknown characteristics of a nonlinear system of differential equations

A. Kuklin, N. Nikulina(Institute of Economics of UD RAS, Ekaterinburg, Russia) | V. Maksimov(Institute of Mathematics and Mechanics of UD RAS, Ekaterinburg, Russia) |

Problems of dynamical reconstruction of unknown characteristics for nonlinear equations described the process of diffusion of innovations through results of observations of phase states are considered. Solving algorithms, which are stable with respect to informational noises and computational errors, are designed. The algorithms are based on the principle of auxiliary models with adaptive controls.

**keywords:** nonlinear differential equations, dynamical reconstruction

Robust stability of a class of uncertain fractional order linear systems with pure delay

M. Buslowicz(Bialystok University of Technology, Poland) |

The paper considers the robust stability problem of uncertain continuous-time fractional order linear systems with pure delay in the following two cases: a) the state matrix is a linear convex combination of two known constant matrices, b) the state matrix is an interval matrix. It is shown that the system is robustly stable if and only if all the eigenvalues of the state matrix multiplied by delay in power equal to fractional order are located in the open stability region in the complex plane. Parametric description of boundary of this region is derived. In the case a) the necessary and sufficient computational condition for robust stability is established. This condition is given in terms of eigenvalue-loci of the state matrix, fractional order and time delay. In the case b) the method for determining the rectangle with sides parallel to the axes of the complex plane in which all the eigenvalues of interval matrix are located is given and the sufficient condition for robust stability is proposed. This condition is satisfied if the rectangle multiplied by delay in power equal to fractional order lie in the stability region. The considerations are illustrated by numerical examples.

**keywords:** linear system, fractional, continuous-time, pure delay, robust stability, interval matrix

Permutation, no-wait, no-idle flow shop problems

M. Makuchowski(Wroclaw University of Technology, Poland) |

The paper compares the schedules of different variants of the flow shop problem, i.e. permutation, no waiting and no idle flow shop problems. It is assessed the impact of the constraints on the extension of the schedules and correlations of the length of the schedules for these variants. It is also examined the effectiveness of a set of insert type algorithms. The efficiency of the algorithms is tested on well-known literature benchmarks.

**keywords:** flow shop problem, permutation constraint, no-wait constraint, no-idle constraint, permutation-graph models

Model of time-varying linear systems and Kolmogorov equations

A.V. Krumov(Higher School of Transport, Sofia, Bulgaria) |

In the paper an approximate model of time-varying linear systems using a sequence of time-invariant systems is suggested. The conditions for validity of the approximation are proven with a theorem. Examples comparing the numerical solution of the original system and the analytical solution of the model are given. For the system under the consideration a new criterion giving sufficient conditions for robust Lagrange stability is suggested. The criterion is proven with a theorem. Examples are given showing stable and non stable solutions of a time-varying system and the results are compared with the numerical Runge-Kutta solution of the system. In the paper an important application of the described method of solution of linear systems with time-varying coefficients, namely analytical solution of the Kolmogorov equations is shown.

Parametric programming of industrial robots

P. Szulczynski, K. Kozlowski(Poznan University of Technology, Poland) |

This article proposes the use of parametric design software, commonly used by architects, in order to obtain complex trajectory and program code for industrial robots. The paper describes the drawbacks of existing solutions and proposes a new script to obtain a correct program. The result of the algorithm was verified experimentally.

**keywords:** robotics, robot programming, CAAD/CAM, parametric design

Descriptor standard and positive discrete-time nonlinear systems

T. Kaczorek(Bialystok University of Technology, Poland) |

A method of analysis of descriptor nonlinear discrete-time systems with regular pencils of linear part is proposed. The method is based on the Weierstrass-Kronecker decomposition of the pencils. Necessary and sufficient conditions for the positivity of the nonlinear systems are established. A procedure for computing the solution to the equations describing the nonlinear systems are proposed and demonstrated on numerical examples.

**keywords:** descriptor, Weierstrass-Kronecker decomposition, non-linear system, positivity

Multimodal processes scheduling in mesh-like network environment

G. Bocewicz(Koszalin University of Technology, Poland) | Z. Banaszak(Warsaw University of Technology, Poland) |

Multimodal processes planning and scheduling play a pivotal role in many different domains including city networks, multimodal transportation systems, computer and telecommunication networks and so on. Multimodal process can be seen as a process partially processed by locally executed cyclic processes. In that context the concept of a Mesh-like Multimodal Transportation Network (MMTN) in which several isomorphic subnetworks interact each other via distinguished subsets of common shared intermodal transport interchange facilities (such as a railway station, bus station or bus/tram stop) as to provide a variety of demand-responsive passenger transportation services is examined. Consider a mesh-like layout of a passengers transport network equipped with different lines including buses, trams, metro, trains etc. where passenger flows are treated as multimodal processes. The goal is to provide a declarative model enabling to state a constraint satisfaction problem aimed at multimodal transportation processes scheduling encompassing passenger flow itineraries. Then, the main objective is to provide conditions guaranteeing solvability of particular transport lines scheduling, i.e. guaranteeing the right match-up of local cyclic acting bus, tram, metro and train schedules to a given passengers flow itineraries.

**keywords:** passengers flow scheduling, multimodal processes, cyclic scheduling, mesh-like structure

Synthesis and evaluation of the smart electric powered wheelchair route stabilization concept - a simulation study

K. Skrzypczyk, A. Galuszka, W. Ilewicz, T. Antas(Silesian University of Technology, Poland) |

The paper addresses the problem of algorithm synthesis for controlling the motion of an electric powered wheelchair. The aim of the algorithm is to stabilize the wheelchair following a linear path and avoiding obstacles if occurred on its way. The main restriction imposed on the project is the application of simple low-cost sensors. That implies the system to cope with a number of inaccuracies and uncertainties related to the measurements. The goal of this work is to evaluate the possibility of the wheelchair project with a navigation system which aids a disable person to move in a complex and dynamic areas. Exemplary simulations are presented in order to discuss the results obtained.

**keywords:** autonomous robots, robot navigation, sensory system, electric powered wheelchair, motion control

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