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:

**2017 (Volume 27)**

Number 1

Rational taxation in an open access fishery model

D.B. Rokhlin, A. Usov(Southern Federal University, Russia) |

We consider a model of fishery management, where *n* agents exploit a single population with strictly concave continuously differentiable growth function of Verhulst type. If the agent actions are coordinated and directed towards the maximization of the discounted cooperative revenue, then the biomass stabilizes at the level, defined by the well known ‘golden rule’. We show that for independent myopic harvesting agents such optimal (or ε-optimal) cooperative behavior can be stimulated by the proportional tax, depending on the resource stock, and equal to the marginal value function of the cooperative problem. To implement this taxation scheme we prove that the mentioned value function is strictly concave and continuously differentiable, although the instantaneous individual revenues may be neither concave nor differentiable.

**keywords:** marginal value function, stimulating taxes, myopic agents, optimal control

State estimation in a decentralized discrete time LQG control for a multisensor system

Z. Duda(Silesian University of Technology, Poland) |

In the paper a state filtration in a decentralized discrete time Linear Quadratic Gaussian problem formulated for a multisensor system is considered. Local optimal control laws depend on global state estimates and are calculated by each node. In a classical centralized information pattern the global state estimators use measurements data from all nodes. In a decentralized system the global state estimates are computed at each node using local state estimates based on local measurements and values of previous controls, from other nodes.

In the paper, contrary to this, the controls are not transmitted between nodes. It leads to nonconventional filtration because the controls from other nodes are treated as random variables for each node. The cost for the additional reduced transmission is an increased filter computation at each node.

**keywords:** multisensor system, LQG problem, Kalman filter

Robust *H*_{∞} output feedback control of bidirectional inductive power transfer systems

A. Swain, M.J. Neath(The University of Auckland, New Zealand) | D. Almakhles(Prince Sultan University, Saudi Arabia) |

Bidirectional Inductive power transfer (IPT) systems behave as high order resonant networks and hence are highly sensitive to changes in system parameters. Traditional PID controllers often fail to maintain satisfactory power regulation in the presence of parametric uncertainties. To overcome these problems, this paper proposes a robust controller which is designed using linear matrix inequality (LMI) techniques. The output sensitivity to parametric uncertainty is explored and a linear fractional transformation of the nominal model and its uncertainty is discussed to generate a standard configuration for µ-synthesis and LMI analysis. An *H*_{∞} controller is designed based on the structured singular value and LMI feasibility analysis with regard to uncertainties in the primary tuning capacitance, the primary and pickup inductors and the mutual inductance. Robust stability and robust performance of the system is studied through µ-synthesis and LMI feasibility analysis. Simulations and experiments are conducted to verify the power regulation performance of the proposed controller.

**keywords:** inductive power transfer, wireless power transfer, robust control, Linear Matrix Inequalities, sensitivity analysis

An adaptive control scheme for hyperbolic partial differential equation system (drilling system) with unknown coefficient

H.S. Farahani, H.A. Talebi, M. BagherMenhaj(Amirkabir University of Technology, Iran) |

The adaptive boundary stabilization is investigated for a class of systems described by second-order hyperbolic PDEs with unknown coefficient. The proposed control scheme utilizes only measurement on top boundary and assumes anti-damping dynamics on the opposite boundary which is the main feature of our work. To cope with the lack of full state measurements, we introduce Riemann variables which allow us reformulate the second-order in time hyperbolic PDE as a system with linear input-delay dynamics. Then, the infinite-dimensional time-delay tools are employed to design the controller. Simulation results which applied on mathematical model of drilling system are given to demonstrate the effectiveness of the proposed control approach.

Pointwise observation of the state given by complex time lag parabolic system

A. Kowalewski(AGH University of Science and Technology, Poland) |

Various optimization problems for linear parabolic systems with multiple constant time lags are considered. In this paper, we consider an optimal distributed control problem for a linear complex parabolic system in which different multiple constant time lags appear both in the state equation and in the Neumann boundary condition. Sufficient conditions for the existence of a unique solution of the parabolic time lag equation with the Neumann boundary condition are proved. The time horizon *T* is fixed. Making use of the Lions scheme, necessary and sufficient conditions of optimality for the Neumann problem with the quadratic performance functional with pointwise observation of the state and constrained control are derived. The example of application is also provided.

**keywords:** distributed control, parabolic system, time lags, pointwise observation

New perspectives of analog and digital simulations of fractional order systems

A. Charef(Université des Frères Mentouri - Constantine, Algeria) |

In the recent decades, fractional order systems have been found to be useful in many areas of physics and engineering. Hence, their efficient and accurate analog and digital simulations and numerical calculations have become very important especially in the fields of fractional control, fractional signal processing and fractional system identification. In this article, new analog and digital simulations and numerical calculations perspectives of fractional systems are considered. The main feature of this work is the introduction of an adjustable fractional order structure of the fractional integrator to facilitate and improve the simulations of the fractional order systems as well as the numerical resolution of the linear fractional order differential equations. First, the basic ideas of the proposed adjustable fractional order structure of the fractional integrator are presented. Then, the analog and digital simulations techniques of the fractional order systems and the numerical resolution of the linear fractional order differential equation are exposed. Illustrative examples of each step of this work are presented to show the effectiveness and the efficiency of the proposed fractional order systems analog and digital simulations and implementations techniques.

**keywords:** adjustable fractional operators, Charef approximation, fractional differential equation, fractional integrator, fractional systems

Eigenvalue assignment in fractional descriptor discrete-time linear systems

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

The problem of eigenvalue assignment in fractional descriptor discrete-time linear systems is considered. Necessary and sufficient conditions for the existence of a solution to the problem are established. A procedure for computation of the gain matrices is given and illustrated by a numerical example.

**keywords:** eigenvalue assignment, fractional, descriptor, discrete-time linear system, gain matrix

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