2022 (vol. 32) - Number 1

*J. Cvejn:*

The magnitude optimum design of the PI controller for plants with complex roots and dead time

*S.F. Al-Azzawi, M.A. Hayali:*

Coexisting of self-excited and hidden attractors in a new 4D hyperchaotic Sprott-S system with a single equilibrium point

*M.A. Hammami, N. El Houda Rettab, F. Delmotte:*

On the state estimation for nonlinear continuous-time fuzzy systems

*M. Ilyas, M.A. Khan, A. Khan, Wei Xie, Y. Khan:*

Observer design estimating the propofol concentration in PKPD model with feedback control of anesthesia administration

*L. Moysis, M. Tripathi, M. Marwan:*

Adaptive observer design for systems with incremental quadratic constraints and nonlinear outputs – application to chaos synchronization

*S. Vaidyanathan, K. Benkouider, A. Sambas:*

A new multistable jerk chaotic system, its bifurcation analysis, backstepping control-based synchronization design and circuit simulation

*T.T. Tuan, H. Zabiri, M.I.A. Mutalib, Dai-Viet N. Vo:*

Disturbance-Kalman state for linear offset free MPC

*Yuan Xu, Jun Wang:*

A novel multiple attribute decision-making method based on Schweizer-Sklar *t*-norm and *t*-conorm with *q*-rung dual hesitant fuzzy information

*T. Kaczorek:*

Observers of fractional linear continuous-time systems

ACS Abstract:

**2021 (Volume 31)**

Number 2

Sliding mode observers for fault identification in linear systems not satisfying matching and minimum phase conditions

A. Zhirabok, A. Shumsky(Far Eastern Federal University, Vladivostok, Russia) | A. Zuev(Institute of Marine Technology Problems, Vladivostok, Russia) | V. Filaretov(Institute of Automation and Processes of Control, Vladivostok, Russia) |

The paper studies the fault identification problem for linear control systems under the unmatched disturbances. A novel approach to the construction of a sliding mode observer is proposed for systems that do not satisfy common conditions required for fault estimation,in particular matching condition, minimum phase condition, and detectability condition. The suggested approach is based on the reduced order model of the original system. This allows to reduce complexity of sliding mode observer and relax the limitations imposed on the original system.

**keywords:** linear systems, faults, identification, disturbances, sliding mode observers

Output tracking control of an aircraft subject to additive state dependent disturbance: an optimal control approach

I. Tanyer(AdresGezgini Inc., Izmir, Turkey) | E. Tatlicioglu(Ege University, Izmir, Turkey) | E. Zergeroglu(Gebze Technical University, Kocaeli, Turkey) |

In this paper, model reference output feedback tracking control of an aircraft subject to additive, uncertain, nonlinear disturbances is considered. In order to present the design steps in a clear fashion: first, the aircraft dynamics is temporarily assumed as known with all the states of the system available. Then a feedback linearizing controller minimizing a performance index while only requiring the output measurements of the system is proposed. As the aircraft dynamics is uncertain and only the output is available, the proposed controller makes use of a novel uncertainty estimator. The stability of the closed loop system and global asymptotic tracking of the proposed method are ensured via Lyapunov based arguments, asymptotic convergence of the controller to an optimal controller is also established. Numerical simulations are presented in order to demonstrate the feasibility and performance of the proposed control strategy.

**keywords:** optimal control, aerospace applications, nonlinear systems, mechanical/mechatronics applications, robust control

Fractional discrete-continuous model of heat transfer process

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

The paper proposes a new, state space, finite dimensional, fractional order model of a heat transfer in one dimensional body. The time derivative is described by Caputo operator. The second order central difference describes the derivative along the length. The analytical formulae of the model responses are proved. The stability, convergence, and positivity of the model are also discussed. Theoretical results are verified by experiments.

**keywords:** non integer order systems, heat transfer equation, finite difference, Caputo operator, positive systems

The unique solvability of stationary and non-stationary incompressible melt models in the case of their linearization

S.Sh. Kazhikenova(Karaganda Technical University, Kazakhstan) |

The article presents "-approximation of hydrodynamics equations’ stationary model along with the proof of a theorem about existence of a hydrodynamics equations’ strongly generalized solution. It was proved by a theorem on the existence of uniqueness of the hydrodynamics equations’ temperature model’s solution, taking into account energy dissipation. There was implemented the Galerkin method to study the Navier–Stokes equations, which provides the study of the boundary value problems correctness for an incompressible viscous flow both numerically and analytically. Approximations of stationary and non-stationary models of the hydrodynamics equations were constructed by a system of Cauchy–Kovalevsky equations with a small parameter ". There was developed an algorithm for numerical modelling of the Navier–Stokes equations by the finite difference method.

**keywords:** Navier-Stokes equations, hydrodynamic, approximations, mathematical models, incompressible melt

Synchronization of FitzHugh-Nagumo reaction-diffusion systems via one-dimensional linear control law

A. Ouannas(University of Larbi Ben M?hidi, Algeria) | F. Mesdoui(The University of Jordan, Amman, Jordan) | S. Momani, I. Batiha(Ajman University, Ajman, UAE) | G. Grassi(Universita del Salento, Lecce, Italy) |

The Fitzhugh-Nagumo model (FN model), which is successfully employed in modeling the function of the so-called membrane potential, exhibits various formations in neuronal networks and rich complex dynamics. This work deals with the problem of control and synchronization of the FN reaction-diffusion model. The proposed control law in this study is designed to be uni-dimensional and linear law for the purpose of reducing the cost of implementation. In order to analytically prove this assertion, Lyapunov’s second method is utilized and illustrated numerically in one- and/or two-spatial dimensions.

**keywords:** FitzHugh-Nagumo; synchronization; uni-dimensional control; linear control; reaction-diffusion system; neuronal networks; Lyapunov?s second method

An improvement of Gamma approximation for reduction of continuous interval systems

J.K. Bokam(Gandhi Institute of Technology and Management, Andhra Pradesh, India) | V.P. Singh(Malaviya National Institute of Technology Jaipur, India) | R. Devarapalli(BIT Sindri, Dhanbad, Jharkhand) | F.P. García Márquez(University of Castilla-La Mancha, Spain) |

In recent, modeling practical systems as interval systems is gaining more attention of control researchers due to various advantages of interval systems. This research work presents a new approach for reducing the high-order continuous interval system (HOCIS) utilizing improved Gamma approximation. The denominator polynomial of reduced-order continuous interval model (ROCIM) is obtained using modified Routh table, while the numerator polynomial is derived using Gamma parameters. The distinctive features of this approach are: (i) It always generates a stable model for stable HOCIS in contrast to other recent existing techniques; (ii) It always produces interval models for interval systems in contrast to other relevant methods, and, (iii) The proposed technique can be applied to any system in opposite to some existing techniques which are applicable to second-order and third-order systems only. The accuracy and effectiveness of the proposed method are demonstrated by considering test cases of single-input single-output (SISO) and multi-input-multi-output (MIMO) continuous interval systems. The robust stability analysis for ROCIM is also presented to support the effectiveness of proposed technique.

**keywords:** continuous interval systems, Kharitonov polynomials, Routh approximation, modelling, SISO systems, MIMO systems

On transformation of conditional, conformant and parallel planning to linear programming

A. Galuszka, E. Probierz(Silesian University of Technology, Poland) |

Classical planning in Artificial Intelligence is a computationally expensive problem of finding a sequence of actions that transforms a given initial state of the problem to a desired goal situation. Lack of information about the initial state leads to conditional and conformant planning that is more difficult than classical one. A parallel plan is the plan in which some actions can be executed in parallel, usually leading to decrease of the plan execution time but increase of the difficulty of finding the plan. This paper is focused on three planning problems which are computationally difficult: conditional, conformant and parallel conformant. To avoid these difficulties a set of transformations to Linear Programming Problem (LPP), illustrated by examples, is proposed. The results show that solving LPP corresponding to the planning problem can be computationally easier than solving the planning problem by exploring the problem state space. The cost is that not always the LPP solution can be interpreted directly as a plan.

**keywords:** planning, conformant planning, conditional planning, parallel planning, uncertainty, linear programming, computational complexity

Mittag-Leffler stability analysis of a class of homogeneous fractional systems

Tarek Fajraoui, Boulbaba Ghanmi, Fehmi Mabrouk, Faouzi Omri(University of Gafsa, Tunisia) |

In this paper,we start by the research of the existence of Lyapunov homogeneous function for a class of homogeneous fractional Systems, then we shall prove that local and global behaviors are the same. The uniform Mittag-Leffler stability of homogeneous fractional time-varying systems is studied. A numerical example is given to illustrate the efficiency of the obtained results.

**keywords:** homogeneous fractional systems, Lyapunov homogeneous function, Mittag-Leffler stability

Heating control of a finite rod with a mobile source

S.H.Jilavyan, E.R. Grigoryan(Yerevan State University, Yerevan, Armenia) | A.Zh. Khurshudyan(National Academy of Sciences of Armenia, Yerevan, Armenia) |

The Green’s function approach is applied for studying the exact and approximate nullcontrollability of a finite rod in finite time by means of a source moving along the rod with controllable trajectory. The intensity of the source remains constant. Applying the recently developed Green’s function approach, the analysis of the exact null-controllability is reduced to an infinite system of nonlinear constraints with respect to the control function. A sufficient condition for the approximate null-controllability of the rod is obtained. Since the exact solution of the system of constraints is a long-standing open problem, some heuristic solutions are used instead. The efficiency of these solutions is shown on particular cases of approximate controllability.

**keywords:** null-controllability, mobile control, nonlinear constraints, triangular wave, rectangular wave, Green?s function approach, heuristic control, lack of exact controllability

Power-aware scheduling of data-flow hardware circuits with symbolic control

M. Özbaltan(Erzurum Technical University, Erzurum, Turkey) | N. Berthier(University of Liverpool, UK) |

We devise a tool-supported framework for achieving power-efficiency of data-flowhardware circuits. Our approach relies on formal control techniques, where the goal is to compute a strategy that can be used to drive a given model so that it satisfies a set of control objectives. More specifically, we give an algorithm that derives abstract behavioral models directly in a symbolic form from original designs described at Register-transfer Level using a Hardware Description Language, and for formulating suitable scheduling constraints and power-efficiency objectives. We show how a resulting strategy can be translated into a piece of synchronous circuit that, when paired with the original design, ensures the aforementioned objectives. We illustrate and validate our approach experimentally using various hardware designs and objectives.

**keywords:** symbolic discrete controller synthesis, digital synchronous circuits, power-efficiency

Unified design method of time delayed PI controller for first order plus dead-time process models with different dead-time to time constant

A.R. Pathiran(Ethiopian Technical University, Addis Ababa, Ethiopia) | R. Muniraj(P.S.R. Engineering College, Sivakasi, Virudhunagar District, Tamilnadu, India) | M.W. Iruthayarajan(National Engineering College, Kovilpatti, India) | S.R.B. Prabhu(Surya Engineering College, Mettukadai, India) | T. Jarin(Jyothi Engineering College, Thrissur, India) |

The time delay element present in the PI controller brings dead-time compensation capability and shows improved performance for dead-time processes. However, design of robust time delayed PI controller needs much responsiveness for uncertainty in dead-time processes. Hence in this paper, robustness of time delayed PI controller has been analyzed for First Order plus Dead-Time (FOPDT) process model. The process having dead-time greater than three times of time constant is very sensitive to dead-time variation. A first order filter is introduced to ensure robustness. Furthermore, integral time constant of time delayed PI controller is modified to attain better regulatory performance for the lag-dominant processes. The FOPDT process models are classified into dead-time/lag dominated on the basis of dead-time to time constant ratio. A unified tuning method is developed for processes with a number of dead-time to time constant ratio. Several simulation examples and experimental evaluation are exhibited to show the efficiency of the proposed unified tuning technique. The applicability to the process models other than FOPDT such as high-order, integrating, right half plane zero systems are also demonstrated via simulation examples.

**keywords:** PI controller, time delayed PI controller, dead-time compensation

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