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 4

Hyperchaos, adaptive control and synchronization of a novel 5-D hyperchaotic system with three positive Lyapunov exponents and its SPICE implementation

Sundarapandian Vaidyanathan(Vel Tech. University, Tamilnadu, India) | Christos Volos(Aristotle University of Thessaloniki, Greece) | Viet-Thanh Pham(Hanoi University of Science and Technology, Vietnam) |

In this research work, a twelve-term novel 5-D hyperchaotic Lorenz system with three quadratic nonlinearities has been derived by adding a feedback control to a ten-term 4-D hyperchaotic Lorenz system (Jia, 2007) with three quadratic nonlinearities. The 4-D hyperchaotic Lorenz system (Jia, 2007) has the Lyapunov exponents L1 = 0.3684, L2 = 0.2174, L3 = 0 and L4 = -12.9513, and the Kaplan-Yorke dimension of this 4-D system is found as D_KY = 3.0452. The 5-D novel hyperchaotic Lorenz system proposed in this work has the Lyapunov exponents L1 = 0.4195, L2 = 0.2430, L3 = 0.0145, L4 = 0 and L5 = -13.0405, and the Kaplan-Yorke dimension of this 5-D system is found as D_KY = 4.0159. Thus, the novel 5-D hyperchaotic Lorenz system has a maximal Lyapunov exponent (MLE), which is greater than the maximal Lyapunov exponent (MLE) of the 4-D hyperchaotic Lorenz system. The 5-D novel hyperchaotic Lorenz system has a unique equilibrium point at the origin, which is a saddle-point and hence unstable. Next, an adaptive controller is designed to stabilize the novel 5-D hyperchaotic Lorenz system with unknown system parameters. Moreover, an adaptive controller is designed to achieve global hyperchaos synchronization of the identical novel 5-D hyperchaotic Lorenz systems with unknown system parameters. Finally, an electronic circuit realization of the novel 5-D hyperchaotic Lorenz system using SPICE is described in detail to confirm the feasibility of the theoretical model.

**keywords:** chaos, hyperchaos, control, synchronization, circuit realization

Approximation method for a fractional order transfer function with zero and pole

K. Oprzedkiewicz(AGH University of Science and Technology, Krakow, Poland) |

The paper presents an approximation method for elementary fractional order transfer function containing both pole and zero. This class of transfer functions can be applied for example to build model - based special control algorithms.

The proposed method bases on Charef approximation. The problem of cancelation pole by zero with useful conditions was considered, the accuracy discussion with the use of interval approach was done also. Results were depicted by examples.

**keywords:** fractional order systems, fractional order transfer function, Charef approximation

Adaptive output-feedback following control for time-delay systems

M. Tarnik, J. Murgas, E. Miklovicova(Slovak University of Technology in Bratislava, Slovak Republic) |

Adaptive control of the time-delay systems is presented in the paper. Despite the use of MRAC based design, only the model following (not perfect model following) is considered. The methods of a classical MRAC design are preserved to the maximum extent which allows further extensions of the algorithm such as the robust adaptive control modifications. The adaptive algorithm effectiveness is presented by means of illustrative examples.

**keywords:** adaptive control, model following, input time-delay

Intelligent control algorithm for ship dynamic positioning

W. Meng, L.H. Sheng, M. Qing, B.G. Rong(Wuhan University of Technology, China) |

Ship motion in the sea is a complex nonlinear kinematics. The hydrodynamic coefficients of ship model are very difficult to accurately determine. Establishing accurate mathematical model of ship motion is difficult because of changing random factors in the marine environment. Aiming at seeking a method of control to realize ship positioning, intelligent control algorithms are adopt utilizing operator's experience. Fuzzy controller and the neural network controller are respectively designed. Through simulations and experiments, intelligent control algorithm can deal with the complex nonlinear motion, and has good robustness. The ship dynamic positioning system with neural network control has high positioning accuracy and performance.

**keywords:** dynamic positioning, fuzzy control, neural network control, BP algorithm

Off-line robustification of Generalized Predictive Control for uncertain systems

K.K. Otmane, L. Nezli(Ecole Nationale Polytechnique, ENP, Algers, Algeria) | N. Bali(University of Sciences and Technology Houari Boumediene, Algers, Algeria) |

An off-line methodology was proposed for enhancing the robustness of an initial Generalized Predictive Control (GPC) by convex optimization of the Youla parameter. However, this procedure of robustification is restricted with the case of the systems affected only by unstructured uncertainties. This paper proposes an extension of this method to the systems subjected to both unstructured and structured polytopic uncertainties. The main idea consists in adding supplementary constraints to the optimization problem which validates the Lipatov stability condition at each vertex of the polytope. These polytopic uncertainties impose a set of non convex quadratic constraints. The globally optimal solution is found by means of the GloptiPoly3 software. Therefore, this robustification provides stability robustness towards unstructured uncertainties for the nominal system, while guaranteeing stability properties over a specified polytopic domain of uncertainties. Finally, an illustrative example is given.

**keywords:** Generalized Predictive Control, polytopic uncertainties, relaxation, robust control, Youla parametrization

Adaptive sliding mode formation control of multiple underwater robots

B. Das, B.B. Pati(VSS University of Technology, Odisha, India) | B. Subudhi(National Institute of Technology, Rourkela, India) |

This paper proposes a new adaptive sliding mode control scheme for achieving coordinated motion control of a group of autonomous underwater vehicles with variable added mass. The control law considers the communication constraints in the acoustic medium. A common reference frame for velocity is assigned to a virtual leader dynamically. The performances of the proposed adaptive SMC were compared with that of a passivity based controller. To save the time and traveling distance for reaching the FRP by the follower AUVs, a sliding mode controller is proposed in this paper that drives the state trajectory of the AUV into a switching surface in the state space. It is observed from the obtained results that the proposed SMC provides improved performance in terms of accurately tracking the desired trajectory within less time compared to the passivity based controller. A communication consensus is designed ensuring the transfer of information among the AUVs so that they move collectively as a group. The stability of the overall closed-loop systems are analysed using Lyapunov theory and simulation results confirmed the robustness and efficiency of proposed controller.

**keywords:** AUV, SMC, passivity, cooperative control

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