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:

**2012 (Volume 22)**

Number 2

Exponential stability of nonlinear neutral type systems

Michael Gil'(Ben Gurion University of the Negev, Beer-Sheva, Israel) |

Nonlinear neutral type systems with distributed and discrete delays are considered. Explicit exponential stability conditions are established. The main tool is a combined usage of the recent norm estimates for the matrix resolvents, the Urysohn theorem and estimates for fundamental solutions of the linear parts.

**keywords:** neutral type systems, nonlinear systems, stability

Computation of initial conditions and inputs for given outputs of fractional and positive discrete-time linear systems

Tadeusz Kaczorek(Bialystok University of Technology, Poland) |

The problem of computation of initial conditions and inputs for given outputs of fractional standard and positive discrete-time linear systems is formulated and solved. Necessary and sufficient conditions for existence of solution to the problem are established. It is shown that there exist the unique solutions to the problem only if the pair (A,C) of the system is observable.

**keywords:** computation, initial condition, observability, positive, discrete-time, linear, system

An active electromagnetic stabilization of the Leipholz column

Tomasz Szmidt, Piotr Przybyłowicz(Warsaw University of Technology, Poland) |

We study the application of electromagnetic actuators for the active stabilization of the Leipholz column. The cases of the compressive and tensional load of the column placed in air and in water are considered. The partial differential equation of the column is discretized by Galerkin’s procedure, and the stability of the obtained control system is evaluated by the eigenvalues of its linearization. Four different methods of active stabilization are investigated. They incorporate control systems based on feedback proportional to the transverse displacement of the column, its velocity and the current in the electromagnets. Conditions in which these strategies are effective in securing safe operation of the column are discussed in detail.

**keywords:** follower load, flutter, closed-loop control, active stabilization, electromagnetic actuators

Regular design equations for the discrete reduced-order Kalman filter

Peter Hippe(Universitat Erlangen-Nurnberg, Germany) |

In the presence of white Gaussian noises at the input and the output of a system Kalman filters provide a minimum-variance state estimate. When part of the measurements can be regarded as noise-free, the order of the filter is reduced. The filter design can be carried out both in the time domain and in the frequency domain. In the case of full-order filters all measurements are corrupted by noise and therefore the design equations are regular. In the presence of noise-free measurements, however, they are not regular so that standard software cannot readily be applied in a time-domain design. In the frequency domain the spectral factorization of the non-regular polynomial matrix equation causes no problems. However, the known proof of optimality of the factorization result requires a regular measurement covariance matrix. This paper presents regular (reduced-order) design equations for the reduced-order discrete-time Kalman filter in the time and in the frequency domains so that standard software is applicable. They also allow to formulate the conditions for the stability of the filter and to prove the optimality of the existing solutions.

**keywords:** optimal estimation, polynomials, multivariable systems, discrete-time systems

Comparison of two controllers for directional control of a hybrid electric vehicle

Basanta Kumar Dash(Biju Patnaik University of Technology, Rourkela, India) | Bidyadhar Subudhi(National Institute of Technology, Rourkela, India) |

Directional response of a vehicle implies changing its direction when sustaining lateral acceleration while moving on the road. From this response, the vehicle’s explicit capabilities as well as its contribution to the system performance of the driver/vehicle combination are obtained. In vehicle control literature, handling is often used interchangeably with cornering, turning, or directional response. This paper focuses one aspect of the handling i.e. directional response. Two different controllers, namely a PID controller and a Fuzzy Logic Controller (FLC) for a hybrid electric vehicle (HEV) are designed in this paper to control the vehicle’s steering in a smooth lane change maneuver. The performances of the aforesaid two controllers have been studied extensively in this paper. For achieving an improved path tracking and directional response, parameters of both the PID and FLC have been tuned and their performances have been compared. Further, the effect of changing the scale factors in the fuzzy logic approach to obtaining directional response is presented. To validate the above two control performances, a nonlinear simulation model of a HEV is developed and is used in simulation studies. Both the controllers track the desired directional signal efficiently. Both PID and Fuzzy controllers provide competitive performances. Although with the assumption of all parameters of the vehicle available PID controller exhibits slightly better dynamic performance but in the real-world scenario the fuzzy controller is preferred due to its robustness i.e. it does not depend on the parameters of the vehicle.

**keywords:** directional control, active steering, fuzzy logic control, PID control, hybrid vehicle, four-wheel drive

LMI based control design for linear systems with distributed time delays

Anna Filasova, Daniel Gontkovic, Dusan Krokavec( Technical University of Kosice, Czech Rep.) |

The paper concerns the problem of stabilization of continuous-time linear systems with distributed time delays. Using extended form of the Lyapunov-Krasovskii functional candidate, the controller design conditions are derived and formulated with respect to the incidence of structured matrix variables in the linear matrix inequality formulation. The result give sufficient condition for stabilization of the system with distributed time delays. It is illustrated with a numerical example to note reduced conservatism in the system structure.

**keywords:** linear matrix inequality, systems with distributed time delays, Lyapunov-Krasovskii functional, state control, asymptotic stability

Neuro-fuzzy control design of processes in chemical technologies

Lenka Blahova, Jan Dworan, Jana Kmetova ( Slovak University of Technology, Bratislava, Slovak Rep.) |

The paper presents design of neuro-fuzzy control and its application in chemical technologies. Our approach to neuro-fuzzy control is a combination of the neural predictive controller and the neuro-fuzzy controller (Adaptive Network-based Fuzzy Inference System - ANFIS). These controllers work in parallel. The output of ANFIS adjusts the output of the neural predictive controller to enhance the control performance. Such design of an intelligent control system is applied to control of the continuous stirred tank reactor and laboratory mixing process.

**keywords:** neuro-fuzzy control, chemical reactor, neural predictive controller, ANFIS, laboratory process

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