2020 (vol. 30) - Number 4

*A.B. Malinowska, R. Kamocki, R. Almeida, T. Odzijewicz:*

On the existence of optimal consensus control for the fractional Cucker--Smale model

*R. Grymin, W. Bożejko, J. Pempera, M. Wodecki, Z. Chaczko:*

Algorithm for solving the Discrete-Continuous Inspection Problem

*T. Kaczorek, A. Ruszewski:*

Global stability of discrete-time nonlinear systems with descriptor standard and fractional positive linear parts and scalar feedbacks

*R. Arora, K. Gupta:*

Fuzzy goal programming technique for multi-objective indefinite quadratic bilevel programming problem

*P. Nowak, J. Czeczot, P. Grelewicz:*

Tuning rules for industrial use of the second-order Reduced Active Disturbance Rejection Controller

*M.I. Gomoyunov:*

Optimal control problems with a fixed terminal time in linear fractional-order systems

*Muhafzan, A. Nazra, L. Yulianti, Zulakmal, R. Revina:*

On LQ optimization problem subject to fractional order irregular singular systems

*M. Blizorukova, V. Maksimov:*

On one algorithm for reconstruction of an disturbance in a linear system of ordinary differential equations

ACS Abstract:

**2014 (Volume 24)**

Number 2

Optimal reorientation of spacecraft orbit

I.A. Pankratov(Saratov State University, Saratov, Russia) | Yu.N. Chelnokov, Ya.G. Sapunkov(Saratov State University and Institute of Precision Mechanics and Control Russian Academy of Sciences, Saratov, Russia) |

The problem of optimal reorientation of the spacecraft orbit is considered. For solving the problem we used quaternion equations of motion written in rotating coordinate system. The use of quaternion variables makes this consideration more efficient. The problem of optimal control is solved on the basis of the maximum principle. An example of numerical solution of the problem is given.

**keywords:** spacecraft, optimal control, quaternion

Numerical solution of fractional neutron point kinetics model in nuclear reactor

T. Nowak, K. Duzinkiewicz, R Piotrowski(Gdansk University of Technology, Gdansk, Poland) |

This paper presents results concerning solutions of the fractional neutron point kinetics model for a nuclear reactor. Proposed model consists of a bilinear system of fractional and ordinary differential equations. Three methods to solve the model are presented and compared. The first one entails application of discrete Grunwald-Letnikov definition of the fractional derivative in the model. Second involves building an analog scheme in the FOMCON Toolbox in MATLAB environment. Third is the method proposed by Edwards. The impact of selected parameters on the model's response was examined. The results for typical input were discussed and compared.

**keywords:** fractional differential equation, fractional derivatives and integrals, system of equations, nuclear reactor, neutron point kinetics

Optimization of thermo-electric coolers using hybrid genetic algorithm and simulated annealing

D.V.K. Khanh, P. Vasant, I. Elamvazuthi, V.N. Dieu(Universiti Teknologi PETRONAS, Malaysia) |

Thermo-electric Coolers (TECs) nowadays are applied in a wide range of thermal energy systems. This is due to their superior features where no refrigerant and dynamic parts are needed. TECs generate no electrical or acoustical noise and are environmentally friendly. Over the past decades, many researches were employed to improve the efficiency of TECs by enhancing the material parameters and design parameters. The material parameters are restricted by currently available materials and module fabricating technologies. Therefore, the main objective of TECs design is to determine a set of design parameters such as leg area, leg length and the number of legs. Two elements that play an important role when considering the suitability of TECs in applications are rated of refrigeration (ROR) and coefficient of performance (COP). In this paper, the review of some previous researches will be conducted to see the diversity of optimization in the design of TECs in enhancing the performance and efficiency. After that, single-objective optimization problems (SOP) will be tested first by using Genetic Algorithm (GA) and Simulated Annealing (SA) to optimize geometry properties so that TECs will operate at near optimal conditions. Equality constraint and inequality constraint were taken into consideration.

**keywords:** thermo-electric coolers, genetic algorithm, simulated annealing, coefficient of performance, rate of refrigeration, fitness function

Could k-NN classifier be useful in tree leaves recognition?

K. Horaisova, J. Kukal(Czech Technical University in Prague, Czech Republic) |

The problem of optimal reorientation of the spacecraft orbit is considered. For solving the problem we used quaternion equations of motion written in rotating coordinate system. The use of quaternion variables makes this consideration more efficient. The problem of optimal control is solved on the basis of the maximum principle. An example of numerical solution of the problem is given.This paper presents a method for affine invariant recognition of two-dimensional binary objects based on 2D Fourier power spectrum. Such function is translation invariant and their moments of second order enable construction of affine invariant spectrum except of the rotation effect. Harmonic analysis of samples on circular paths generates Fourier coefficients whose absolute values are affine invariant descriptors. Affine invariancy is approximately saved also for large digital binary images as demonstrated in the experimental part. The proposed method is tested on artificial data set first and consequently on a large set of 2D binary digital images of tree leaves. High dimensionality of feature vectors is reduced via

the kernel PCA technique with Gaussian kernel and the k-NN classifier is used for image classification. The results are summarized as k-NN classifier sensitivity after dimensionality reduction. The resulting descriptors after dimensionality reduction are able to distinguish real contours

of tree leaves with acceptable classification error. The general methodology is directly applicable to any set of large binary images. All calculations were performed in the MATLAB environment.

**keywords:** binary image, Fourier transform, affine invariance, harmonic analysis, pattern recognition, k-NN classifier

Positivity and asymptotic stability of descriptor linear systems with regular pencils

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

The positivity and asymptotic stability of the descriptor linear continuous-time and discrete-time systems with regular pencils are addressed. Necessary and sufficient conditions for the positivity and asymptotic stability of the systems are established using the Drazin inverse matrix approach. Effectiveness of the conditions are demonstrated on numerical examples.

**keywords:** descriptor, Drazin inverse, linear, system, positivity, asymptotic stability

Dynamic systems with a finite degrees of freedom number

R. Ladzinski(Warsaw University of Technology, Warsaw, Poland) |

Taking as a starting point the law of conservation of the total energy of the system, and introducing two basic state functions - the Lagrangian and the Rayleigh function, the general form of the equation of motion for any dynamic system with a finite number of degrees of freedom is derived. The theory is illustrated by considering the rotating - type electromechanical energy converter with six degrees of freedom being the model of all essentially important types of DC and AC machines, including rotating power amplifiers, induction - and synchronous type motors - all of them discussed from both, the steady-state and the transient point of view. In the next part of the paper there is described a simple electric circuit with its model characterized by the holonomic constraints of the velocity-type. Finally, there is presented the kinematics and dynamics of the interesting mechanical system - the gyroscope placed on the rotating Earth.

**keywords:** analytical dynamics, electromechanical systems, circuit theory

Design of multivariable fractional order PID controller using covariance matrix adaptation evolution strategy

S. Sivananaitha Perumal, S. Baskar(Dr Sivanthi Aditanar College of Engineering, Thiruchendur, India) |

This paper presents an automatic tuning of multivariable Fractional-Order Proportional, Integral and Derivative controller (FO-PID) parameters using Covariance Matrix Adaptation Evolution Strategy (CMAES) algorithm. Decoupled multivariable FO-PI and FO-PID controller structures are considered. Oustaloup integer order approximation is used for the fractional integrals and derivatives. For validation, two Multi-Input Multi- Output (MIMO) distillation columns described by Wood and Berry and Ogunnaike and Ray are considered for the design of multivariable FO-PID controller. Optimal FO-PID controller is designed by minimizing Integral Absolute Error (IAE) as objective function. The results of previously reported PI/PID controller are considered for comparison purposes. Simulation results reveal that the performance of FO-PI and FO-PID controller is better than integer order PI/PID controller in terms of IAE. Also, CMAES algorithm is suitable for the design of FO-PI / FO-PID controller.

**keywords:** fractional order controller, PID control, CMAES algorithm, distillation column

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