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:

**2019 (Volume 29)**

Number 3

The LQG homing problem for a Wiener process with random infinitesimal parameters

M. Lefebvre, A. Moutassim(Polytechnique Montréal, Canada) |

The problem of optimally controlling a Wiener process until it leaves an interval (a, b) for the first time is considered in the case when the infinitesimal parameters of the process are random. When a = -∞, the exact optimal control is derived by solving the appropriate system of differential equations, whereas a very precise approximate solution in the form of a polynomial is obtained in the two-barrier case.

**keywords:** stochastic optimal control, first-passage time, dynamic programming, Brownian motion

Small time local controllability of driftless nonholonomic systems in a task-space

I. Duleba, A. Mielczarek(Wroclaw University of Science and Technology, Poland) |

In this paper a small time local controllability, naturally defined in a configuration space, is transferred into a task-space. It was given its analytical characterization and practical implications. A special attention was put on singular configurations. Theoretical considerations were illustrated with two calculation examples. An extensive comparison of the proposed construction with the controllability defined in an endogenous configuration space approach was presented pointing out to their advantages and disadvantages.

**keywords:** nonholonomic system, small time local controllability, configuration space, task-space

A robust model free controller for a class of SISO nonaffine nonlinear systems: Application to an electropneumatic actuator

A. Boubakir, S. Labiod(University of Jijel, Algeria) | F. Boudjema(National Polytechnic School, Algeria) |

This paper presents a robust model free controller (RMFC) for a class of uncertain continuous-time single-input single-output (SISO) minimum-phase nonaffine-in-control systems. Firstly, the existence of an unknown dynamic inversion controller that can achieve control objectives is demonstrated. Afterwards, a fast approximator is designed to estimate as best as possible this dynamic inversion controller. The proposed robust model free controller is an equivalent realization of the designed fast approximator. The perturbation theory and Tikhonov’s theorem are used to analyze the stability of the overall closed-loop system. The performance of the developed controller are verified experimentally in the position control of a pneumatic actuator system.

**keywords:** dynamic inversion control, model free controller, nonaffine nonlinear systems, singular perturbation theory

A comprehensive approach to double inverted pendulum modelling

K. Andrzejewski, M. Czyżniewski, M. Zielonka, R. Łangowski, T. Zubowicz(Gdańsk University of Technology, Poland) |

The problem of mathematical modelling and indication of properties of a DIP has been investigated in this paper. The aim of this work is to aggregate the knowledge on a DIP modelling using the Euler-Lagrange formalism in the presence of external forces and friction. To indicate the main properties important for simulation, model parameters identification and control system synthesis, analytical and numerical tools have been used. The investigated properties include stability of equilibrium points, a chaos of dynamics and non-minimum phase behaviour around an upper position. The presented results refer to the model of a physical (constructed) DIP system.

**keywords:** double inverted pendulum, modelling, non-linear dynamics, Lagrangian mechanics

A new 4-D dynamical system exhibiting chaos with a line of rest points, its synchronization and circuit model

S. Vaidyanathan(Vel Tech University, India) | A. Sambas(Universitas Muhammadiyah Tasikmalaya, Indonesia) | S. Zhang(XiangtanUniversity, China) |

A new 4-D dynamical system exhibiting chaos is introduced in this work. The proposed nonlinear plant with chaos has an unstable rest point and a line of rest points. Thus, the new nonlinear plant exhibits hidden attractors. A detailed dynamic analysis of the new nonlinear plant using bifurcation diagrams is described. Synchronization result of the new nonlinear plant with itself is achieved using Integral Sliding Mode Control (ISMC). Finally, a circuit model using MultiSim of the new 4-D nonlinear plant with chaos is carried out for practical use.

**keywords:** chaos, chaotic systems, circuit design, synchronization

Buffer management in solving a real sequencing problem in the automotive industry – Paint Shop 4.0 concept

S. Bysko, J. Krystek(Silesian University of Technology, Poland) | Sz. Bysko(ProPoint Sp. z o.o. Sp. k., Poland) | R. Lenort(SKODA AUTO University, Czech Republic) |

The paper presents a Car Sequencing Problem, widely considered in the literature. The issue considered by the researchers is only a reduced problem in comparison with the problem in real automotive production. Consequently, a newconcept, called Paint Shop 4.0., is considered from the viewpoint of a sequencing problem. The paper is a part of the previously conducted research, identified as Car Sequencing Problem with Buffers (CSPwB), which extended the original problem to a problem in a production line equipped with buffers. The new innovative approach is based on the ideas of Industry 4.0 and the buffer management system. In the paper, sequencing algorithms that have been developed so far are discussed. The original Follow-up Sequencing Algorithm is presented, which is still developed by the authors. The main goal of the research is to find the most effective algorithm in terms of minimization of painting gun changeovers and synchronization necessary color changes with periodic gun cleanings. Carried out research shows that the most advanced algorithm proposed by the authors outperforms other tested methods, so it is promising to be used in the automotive industry.

**keywords:** sequencing, car production, paint shop, buffer management, changeovers

Explicit commutativity conditions for second-order linear time-varying systems with non-zero initial conditions

M.E. Koksal(Ondokuz Mayis University, Turkey) |

Although the explicit commutativitiy conditions for second-order linear time-varying systems have been appeared in some literature, these are all for initially relaxed systems. This paper presents explicit necessary and sufficient commutativity conditions for commutativity of second-order linear time-varying systems with non-zero initial conditions. It has appeared interesting that the second requirement for the commutativity of non-relaxed systems plays an important role on the commutativity conditions when non-zero initial conditions exist. Another highlight is that the commutativity of switched systems is considered and spoiling of commutativity at the switching instants is illustrated for the first time. The simulation results support the theory developed in the paper.

**keywords:** commutativity, linear systems, analogue control, robust control, differential equations, non-zero initial conditions

Stability of discrete-time fractional linear systems with delays

A. Ruszewski(Bialystok University of Technology, Poland) |

The stability analysis for discrete-time fractional linear systems with delays is presented. The state-space model with a time shift in the difference is considered. Necessary and sufficient conditions for practical stability and for asymptotic stability have been established. The systems with only one matrix occurring in the state equation at a delayed moment have been also considered. In this case analytical conditions for asymptotic stability have been given. Moreover parametric descriptions of the boundary of practical stability and asymptotic stability regions have been presented.

**keywords:** fractional, discrete-time, stability, time-delay

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