2019 (vol. 29) - Number 4

*J. Klamka, As.Zh. Khurshudyan:*

Averaged controllability of heat equation in unbounded domains with random geometry and location of controls: The Green's function approach

*Xin-Tao Wang, Hai-Hua Yu:*

Generalized PI observer design for descriptor linear system

*E. Jezierski, P. Łuczak, P. Smyczyński, D. Zarychta:*

Human--robot cooperation in sorting of randomly distributed objects

*Suresh Rasappan:*

Synchronization of neuronal bursting using backstepping control with recursive feedback

*Z. Yaghoubi, H.A. Talebi:*

Cluster consensus of general fractional-order nonlinear multi agent systems via adaptive sliding~mode controller

*J. Duda:*

The parametric optimization of a system with two delays and a PI controller

*Q. Liu, R. Ding, C. Chen:*

State estimation of networked control systems over limited capacity and dropout channels

*R. Hrebik, J. Kukal:*

Anomalous and traditional diffusion modelling in SOM learning

ACS Abstract:

**2019 (Volume 29)**

Number 4

Averaged controllability of heat equation in unbounded domains with random geometry and location of controls: The Green's function approach

J. Klamka(Silesian University of Technology, Poland) | As.Zh. Khurshudyan(Shanghai Jiao Tong University, Shanghai, China and National Academy of Sciences of Armenia) |

The constrained averaged controllability of linear one-dimensional heat equation defined on R and R+ is studied. The control is carried out by means of the time-dependent intensity of a heat source located at an uncertain interval of the corresponding domain, the end-points of which are considered as uniformly distributed random variables. Employing the Green's function approach, it is shown that the heat equation is not constrained averaged controllable neither in R nor in R+. Sufficient conditions on initial and terminal data for the averaged exact and approximate controllabilities are obtained. However, constrained averaged controllability of the heat equation is established in the case of point heat source, the location of which is considered as a uniformly distributed random variable. Moreover, it is obtained that the lack of averaged controllability occurs for random variables with arbitrary symmetric density function.

**keywords:** lack of controllability, constrained controllability, heuristic method, averaged dynamics, uniformly distributed random variable

Generalized PI observer design for descriptor linear system

Xin-Tao Wang, Hai-Hua Yu(Heilongjiang University, China) |

A kind of generalized proportional-integral(GPI) observer for descriptor linear systems is introduced. We first propose two complete parametric solutions to generalized Sylvester matrix equation corresponding to the left eigenvector matrices in the case of Jordan form. Then a parametric design approach for the observer is presented. The proposed method provides all parametric expression of the gain matrices and the corresponding finite left eigenvector matrix and guarantees the regularity and impulse-freeness of the expanded error system. Two numerical examples are given to explain the design procedure and illustrate the effectiveness of the proposed method.

**keywords:** generalized proportional-integral observer, Sylvester matrix equation, regularity, impulse-freeness

Human--robot cooperation in sorting of randomly distributed objects

E. Jezierski, P. Łuczak, P. Smyczyński, D. Zarychta(Lodz University of Technology, Poland) |

The paper presents the possibilities of teaching a robot controller to perform operations of autonomous segregation of objects differing in features that can be identified using a vision system. Objects can be arranged freely on the robot scene also covered with others. In the learning phase, a robot operator presents the segregation method by moving subsequent objects held in a human hand, e.g. a red object to container A, a green object to container B, etc. The robot system, after recognizing the idea of segregation that is being done using the vision system, continues this work in an autonomous way, until all identified objects will be removed from robotic scene. There are no restrictions on the dimensions, shapes and placement of containers collecting segregated objects. The developed algorithms were verified on a test bench equipped with two modern robots KUKA LBR iiwa 14 R820.

**keywords:** human--robot cooperation, vision system, collaborative robots

Synchronization of neuronal bursting using backstepping control with recursive feedback

Suresh Rasappan(Vel Tech University, India) |

J.L. Hindmarsh, R.M. Rose introduced the concept of neuronal burst. In this paper, synchronization is investigated for the construction of a model of neuronal burst using backstepping control with recursive feedback. Synchronization for a model of neuronal bursting system is established using Lyapunov stability theory. The backstepping scheme is a recursive procedure that links the choice of a Lyapunov function with the design of a controller. The backstepping control method is effective and convenient to synchronize identical systems. Numerical simulations are furnished to illustrate and validate the synchronization result derived in this paper.

**keywords:** Hindmarsh-Rose neuronal bursting system, chaos, synchronization, backstepping control, Lyapunov, stability

Cluster consensus of general fractional-order nonlinear multi agent systems via adaptive sliding~mode controller

Z. Yaghoubi, H.A. Talebi(Amirkabir University of Technology, Iran) |

In this paper cluster consensus is investigated for general fractional-order multi agent systems with nonlinear dynamics via adaptive sliding mode controller. First, cluster consensus for fractional-order nonlinear multi agent systems with general form is investigated. Then, cluster consensus for the fractional-order nonlinear multi agent systems with first-order and general form dynamics is investigated by using adaptive sliding mode controller. Sufficient conditions for achieving cluster consensus for general fractional-order nonlinear multi agent systems are proved based on algebraic graph theory, Lyapunov stability theorem and Mittag-Leffler function. Finally, simulation examples are presented for first-order and general form multi agent systems, i.e. a single-link flexible joint manipulator which demonstrates the efficiency of the proposed adaptive controller.

**keywords:** nonlinear multi agent systems, cluster consensus, fractional-order systems, adaptive sliding mode controller

The parametric optimization of a system with two delays and a PI controller

J. Duda(AGH University of Science and Technology, Poland) |

In the paper a Lyapunov matrices approach to the parametric optimization problem of a time-delay system with two commensurate delays and a PI-controller is presented. The value of integral quadratic performance index is equal to the value of the Lyapunov functional for the initial function of the time-delay system. The Lyapunov functional is determined by means of the Lyapunov matrix. In the paper is presented the example of a scalar system with two delays and a PI controller.

**keywords:** time-delay system, Lyapunov matrix, Lyapunov functional

State estimation of networked control systems over limited capacity and dropout channels

Q. Liu, R. Ding(Shenyang Ligong University, China) | C. Chen(Chinese Academy of Science, China) |

This paper investigates state estimation of linear time-invariant systems where the sensors and controllers are geographically separated and connected over limited capacity, additive white Gaussian noise (AWGN) communication channels. Such channels are viewed as dropout (erasure) channels. In particular, we consider the case with limited data rates, present a necessary and sufficient condition on the data rate for mean square observability over an AWGN channel. The system is mean square observable if the data rate of the channel is larger than the lower bound given. It is shown in our results that there exist the inherent tradeoffs among the limited data rate, dropout probability, and observability. An illustrative example is given to demonstrate the effectiveness of the proposed scheme.

**keywords:** linear time-invariant systems, limited capacity, observability, state estimation, networked control, data rate

Anomalous and traditional diffusion modelling in SOM learning

R. Hrebik, J. Kukal(CTU in Prague, Czech Republic) |

The traditional self organizing map (SOM) is learned by Kohonen learning. The main disadvantage of this approach is in epoch based learning when the radius and rate of learning are decreasing functions of epoch index. The aim of study is to demonstrate advantages of diffusive learning in single epoch learning and other cases for both traditional and anomalous diffusion models. We also discuss the differences between traditional and anomalous learning in models and in quality of obtained SOM. The anomalous diffusion model leads to less accurate SOM which is in accordance to biological assumptions of normal diffusive processes in living nervous system. But the traditional Kohonen learning has been overperformed by novel diffusive learning approaches.

**keywords:** self organization, Kohonen map, diffusion learning, anomalous diffusion, SOM

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