2018 (vol. 28) - Number 4

*T. Kaczorek:*

A new method for computation of positive realizations of fractional linear continuous-time systems

*A. Biswas, A. Sarkar:*

Development of dual hesitant fuzzy prioritized operators based on Einstein operations with their application to multi-criteria group decision making

*L. Li, R. Zhang, J. Wang, X. Shang:*

Some q-orthopair linguistic Heronian mean operators with their application to multi-attribute group decision making

*J. Duda:*

Lyapunov matrices approach to the parametric optimization of a system with two delays and a PD controller

*M. Lhous, M. Rachik, El M. Magri:*

Ideal observability for bilinear discrete-time systems with and without delays in observation

*P.T. Anh, A. Babiarz, A. Czornik, M. Niezabitowski:*

Variation of constant formulas for fractional difference equations

*K. Bingi, R. Ibrahim, M. Noh Karsiti, S. Miya Hassan, V. Rajah Harindran:*

A comparative study of 2DOF PID and 2DOF fractional order PID controllers on a class of unstable systems

ACS Abstract:

**2015 (Volume 25)**

Number 3

Lyapunov matrices approach to the parametric optimization of time-delay systems

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

In the paper a Lyapunov matrices approach to the parametric optimization problem of time-delay systems with a P-controller is presented. The value of integral quadratic performance index of quality is equal to the value of Lyapunov functional for the initial function of the time-delay system. The Lyapunov functional is determined by means of the Lyapunov matrix.

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

Topology optimization for elastic base under rectangular plate subjected to moving load

S.H. Jilavyan, As.Zh. Khurshudyan(Yerevan State University, Armenia) |

Distribution optimization of elastic material under elastic isotropic rectangular thin plate subjected to concentrated moving load is investigated in the present paper. The aim of optimization is to damp its vibrations in finite (fixed) time. Accepting Kirchhoff hypothesis with respect to the plate and Winkler hypothesis with respect to the base, the mathematical model of the problem is constructed as two--dimensional bilinear equation, i.e. linear in state and control function. The maximal quantity of the base material is taken as optimality criterion to be minimized. The Fourier distributional transform and the Bubnov--Galerkin procedures are used to reduce the problem to integral equality type constraints. The explicit solution in terms of two--dimensional Heaviside`s function is obtained, describing piecewise--continuous distribution of the material. The determination of the switching points is reduced to a problem of nonlinear programming. Data from numerical analysis are presented.

**keywords:** distributed system, moving load, Kirchhoff plate, Winkler base, topology optimization, problem of moments, L-inftynity-optimal control, distributions, Bubnov--Galerkin procedure

Fusion Kalman filtration with k-step delay sharing pattern

Z. Duda(Silesian Technical University, Gliwice, Poland) |

A fusion hierarchical state filtration with k-step delay sharing pattern for a multisensor system is considered. A global state estimate depends on local state estimates determined by local nodes using local information. Local available information consists of local measurements and k-step delay global information - global estimate sent from a central node. Local estimates are transmitted to the central node to be fused. The synthesis of local and global filters is presented. It is shown that a fusion filtration with k-step delay sharing pattern is equivalent to the optimal centralized classical Kalman filtration when local measurements are transmitted to the center node and used to determine a global state estimate. It is proved that the k-step delay sharing pattern can reduce covariances of local state errors.

**keywords:** fusion Kalman filtration, multisensor system, k-step delay sharing pattern

Minimum energy control of positive 2D continuous-discrete linear systems with bounded inputs

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

A new formulation of the minimum energy control problem for the positive 2D continuous-discrete linear systems with bounded inputs is proposed. Necessary and sufficient conditions for the reachability of the systems are established. Conditions for the existence of the solution to the minimum energy control problem and a procedure for computation of an input minimizing the given performance index are given. Effectiveness of the procedure is demonstrated on numerical example.

**keywords:** 2D continuous-discrete, linear, positive, reachability, minimum energy control

Analysis and adaptive control of a novel 3-D conservative no-equilibrium chaotic system

S. Vaidyanathan(Vel Tech University, Tamilnadu, India) | Ch. Volos(Aristotle University of Thessaloniki, Greece) |

First, this paper announces a seven-term novel 3-D conservative chaotic system with four quadratic nonlinearities. The conservative chaotic systems are characterized by the important property that they are volume conserving. The phase portraits of the novel conservative chaotic system are displayed and the mathematical properties are discussed. An important property of the proposed novel chaotic system is that it has no equilibrium point. Hence, it displays hidden chaotic attractors. The Lyapunov exponents of the novel conservative chaotic system are obtained as L_1 = 0.0395, L_2 = 0 and L_3 = -0.0395. The Kaplan-Yorke dimension of the novel conservative chaotic system is D_{KY} = 3. Next, an adaptive controller is designed to globally stabilize the novel conservative chaotic system with unknown parameters. Moreover, an adaptive controller is also designed to achieve global chaos synchronization of the identical conservative chaotic systems with unknown parameters. MATLAB simulations have been depicted to illustrate the phase portraits of the novel conservative chaotic system and also the adaptive control results.

**keywords:** chaos, chaotic system, conservative chaotic system, adaptive control, synchronization

A Two-stage approach for an optimum solution of the car assembly scheduling problem. Part 1. Problem statement, solution outline and tutorial example

M. Mazur(General Motors Manufacturing Poland) | A. Niederlinski(University of Economics in Katowice, Poland) |

A new approach to solving realistic car assembly scheduling problems for mixed model assembly line is presented. It is proposed to decompose the problem into two subproblems: 1) a sequencing problem that generates admissible car sequences fulfilling capacity constraints for all car models in the production plan, 2) a scheduling problem that determines an admissible car sequence with shortest makespan. The details of this approach are illustrated by a simple numerical example.

**keywords:** car sequencing, car assembly scheduling, workstation capacity constraints

A Two-stage approach for an optimum solution of the car assembly scheduling problem. Part 2. CLP solution and real-world example

M. Mazur(General Motors Manufacturing Poland) | A. Niederlinski(University of Economics in Katowice, Poland) |

A Constraint Logic Programming (CLP) tool for solving the problem discussed in Part 1 of the paper has been designed. It is outlined and discussed in the paper. The program has been used for solving a real-world car assembly scheduling problem.

**keywords:** car sequencing, car assembly scheduling, workstation capacity constraints, constraint logic programming

Modeling and control of an unstable system using probabilistic fuzzy inference system

N. Sozhamadevi(Anna University, Tiruchirappalli, India) | N. Sozhamadevi, S. Sathiyamoorthy(J.J. College of Engineering and Technology, Tiruchirappalli, India) |

A new type Fuzzy Inference System is proposed, a Probabilistic Fuzzy Inference system which model and minimizes the effects of statistical uncertainties. The blend of two different concepts, degree of truth and probability of truth in a unique framework leads to this new concept. This combination is carried out both in Fuzzy sets and Fuzzy rules, which gives rise to Probabilistic Fuzzy Sets and Probabilistic Fuzzy Rules. Introducing these probabilistic elements, a distinctive probabilistic fuzzy inference system is developed and this involves fuzzification, inference and output processing. This integrated approach accounts for all of the uncertainty like rule uncertainties and measurement uncertainties present in the systems and has led to the design which performs optimally after training. In this paper a Probabilistic Fuzzy Inference System is applied for modeling and control of a highly nonlinear, unstable system and also proved its effectiveness.

**keywords:** inverted pendulum and cart system, probabilistic fuzzy set, probabilistic fuzzy relation, probabilistic fuzzy inference system, probabilistic fuzzy logic controller

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