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 1

On optimal boundary and distributed control of partial integro--differential equations

A.Z. Khurshudyan(Yerevan State University, Yerevan, Armenia) |

A method of optimal control problems investigation for linear partial integro--differential equations of convolution type is proposed, when control process is carried out by boundary functions and right hand side of equation. Using Fourier real generalized integral transform control problem solution is reduced to minimization procedure of chosen optimality criterion under constraints of equality type on desired control function. Optimality of control impacts is obtained for two criteria, evaluating their linear momentum and total energy. Necessary and sufficient conditions of control problem solvability are obtained for both criteria. Numerical calculations are done and control functions are plotted for both cases of control process realization.

**keywords:** optimal control, integro-differential equation, equation of convolution type, Fourier generalized transform, impulsive control

Fractional descriptor observers for fractional descriptor continuous-time linear system

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

Fractional descriptor full-order observers for fractional descriptor continuous-time linear systems are proposed. Necessary and sufficient conditions for the existence of the observers are established. The design procedure of the observers is demonstrated on two numerical examples.

**keywords:** fractional descriptor linear systems, design, full-order, fractional, observer

LMI based fuzzy observer design for Takagi-Sugeno models containing vestigial nonlinear terms

D. Krokavec, A. Filasova(Technical University of Kosice, Slovakia) |

The paper deals with the problem of full order fuzzy observer design for the class of continuous-time nonlinear systems, represented by Takagi-Sugeno models containing vestigial nonlinear terms. On the basis of the Lyapunov stability criterion and the incremental quadratic inequalities, two design conditions for this kind of system model are outlined in the terms of linear matrix inequalities. A numerical example is given to illustrate the procedure and to validate the performances of the proposed approach.

**keywords:** Takagi-Sugeno models, fuzzy observer, linear matrix inequality, incremental quadratic inequality

Fusion Kalman filtration for distributed multisensor systems

Z. Duda(Silesian University of Technology, Gliwice, Poland) |

In the paper, fusion state hierarchical filtration for a multisensor system is considered. An optimal global Kalman filter is realized by a central node in the information form. The state estimate depends on local information that should be sent by local nodes. Two information structures are considered in the paper.

In the first case local estimates are based on the local measurement information. It leads to distributed Kalman filter fusion that is well known in a literature. In the second case local node has additionally global information of the system with one step delay. A synthesis of local filters is presented. An advantage of this structure is discussed.

**keywords:** fusion Kalman filtration, multisensor system, one step delay information

Application of adaptive multivariable Generalized Predictive Control to a HVAC system in real time

M. Gulan, M. Salaj, B. Rohal'-Ilkiv(Slovak University of Technology in Bratislava, Slovakia) |

This paper presents the application of a Multivariable Generalized Predictive Controller (MGPC) for simultaneous temperature and humidity control in a Heating, Ventilating and Air-Conditioning (HVAC) system. The multivariable controlled process dynamics is modeled using a set of MISO models on-line identified from measured input-output process data. The controller synthesis is based on direct optimization of selected quadratic cost function with respect to amplitude and rate input constraints. Efficacy of the proposed adaptive MGPC algorithm is experimentally demonstrated on a laboratory-scale model of HVAC system. To control the air-conditioning part of system the designed multivariable predictive controller is considered in a cascade dual-rate control scheme with PID auxiliary controllers.

**keywords:** predictive control, multivariable systems, constrained optimization, HVAC system, cascade control

A modified PWM three intervals control for a matrix converter in real time

M.M. Rezaoui, L. Nezli, M.O. Mahmoudi(Ecole Nationale Polytechnique, Algiers, Algeria) | A. Kouzou(University of Djelfa, Algeria) | H. Abu Rub(Texas A&M University, Doha, Qatar) |

In this paper, the application of the proposed control strategy PWM three intervals with 3x5 matrix converter is presented and analyzed. This control strategy is developed for the control of the multi-phases matrix converter, where the main aim is to ensure the waveform quality of the output voltages and the input currents based on the THD evaluation. Simulation results and real time implementation on dSpace 1103 of 3x5 matrix converter under R-L load are presented for the validation of the proposed control strategy and to clarify the main related advantages.

**keywords:** matrix converter [3x5], THD, PWM three intervals, real time

Reduced order hybrid function projective combination synchronization of three Josephson junctions

K.S. Ojo, A.N. Njah(University of Lagos, Lagos, Nigeria) | O.I. Olusola( University of Agriculture, Abeokuta, Nigeria) | S.T. Ogunjo(Federal University of Technology, Akure, Ondo State, Nigeria) |

In this paper, we examine reduced order hybrid function projective combination synchronization of three chaotic systems consisting of: (i) two third chaotic Josephson junctions as drives and one second order chaotic Josephson junction as response system; (ii) one third order chaotic Josephson junction as the drive and two second order chaotic Josephson junctions as the slaves using active backstepping technique. The analytic results confirm the realization of reduced order hybrid function projective combination synchronization using active backstepping technique. Numerical simulations are performed to validate the analytical results.

**keywords:** function projective synchronization, Josephson junction, backstepping control, chaos, reduced order synchronization, combination synchronization

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