2020 (vol. 30) - Number 3

*M.A. Hammami, N.H. Rettab:*

On the region of attraction of dynamical systems: Application to Lorenz equations

*J. Rudy, J. Pempera, C. Smutnicki:*

Improving the TSAB algorithm through parallel computing

*Chiranjibe Jana, Madhumangal Pal , Guiwu Wei:*

Multiple Attribute Decision Making method based on intuitionistic Dombi operators and its application in~mutual fund evaluation

*S. Ogonowski, D. Bismor, Z. Ogonowski:*

Control of complex dynamic nonlinear loading process for electromagnetic mill

*N.A. Baleghi, M.H. Shafiei:*

An observer-based controller design for nonlinear discrete-time switched systems with~time-delay and affine parametric uncertainty

*Amine El Bhih, Youssef Benfatah, Mostafa Rachik:*

Exact determinantions of maximal output admissible set for a class of~semilinear discrete systems

*Archana Tiwari, Debanjana Bhattacharyya, K.C. Pati:*

Controllabilty and stability analysis on a group associated with Black-Scholes equation

*A. Sambas, I.M. Moroz, S. Vaidyanathan:*

A new 4-D hyperchaotic system with no equilibrium, its multistability, offset boosting and circuit simulation

*A.S.S. Abadi, P.A. Hosseinabadi, S. Mekhilef, A. Ordys:*

A new strongly predefined time sliding mode controller for a class of cascade high-order nonlinear systems

ACS Abstract:

**2020 (Volume 30)**

Number 1

Switching controller synthesis for discrete-time switched linear systems with average dwell time

Wei He, Wei Xie, Weilin Wu, Langwen Zhang(South China University of Technology, China) |

This paper addresses weighted L2 gain performance switching controller design of discrete-time switched linear systems with average dwell time (ADT) scheme. Two kinds of methods, so called linearizing change-of-variables based method and controller variable elimination method, are considered for the output-feedback control with a supervisor enforcing a reset rule at each switching instant are considered respectively. Furthermore, some comparison between these two methods are also given.

**keywords:** discrete-time switched linear systems, L2 performance, average dwell time, controller state reset, linear matrix inequalities

A new multi-stable chaotic hyperjerk system, its special features, circuit realization, control and synchronization

Viet-Thanh Pham(Ton Duc Thang University, Vietnam; Lodz University of Technology, Poland) | Sundarapandian Vaidyanathan(Vel Tech University, India) | Christos Volos(Aristotle University of Thessaloniki, Greece) | Sajad Jafari(Amirkabir University of Technology, Iran) | Tomasz Kapitaniak(Lodz University of Technology, Poland) |

Researchers have paid significant attention on hyperjerk systems, especial hyperjerk ones with chaos. A new hyperjerk system with seven terms and two parameters is analyzed. Chaotic attractors as well as coexisting attractors are displayed by the hyperjerk system. Thus it is a new multi-stable chaotic hyperjerk system. Further properties of the proposed hyperjerk system such as circuit design and backstepping-based control and synchronization are reported.

**keywords:** chaos, hyperjerk system, multi-stable, control, synchronization, circuit design

The combined effect of fractional filter and Smith Predictor for enhanced closed-loop performance of integer order time-delay systems: some investigations

Shaival Hemant Nagarsheth, Shambhu Nath Sharma(Sardar Vallabhbhai National Institute of Technology, India) |

This paper proposes a generalized fractional controller for integer order systems with time delay. The fractional controller structure is so adopted to have a combined effect of fractional filter and Smith predictor. Interestingly, the resulting novel controller can be decomposed into fractional filter cascaded with an integer order PID controller. The method is applied to two practical examples i.e. liquid level system and Shell control fractionator system. The closed-loop responses resulting from the proposed method are compared with that of the available methods in the literature. For quantitative evaluations of the proposed method, Integral Absolute Error (IAE) and Integral Square Control Input (ISCI) performance criteria are employed. The proposed method effectively enhances the closed-loop response by improving the IAE values, reducing the control effort inputs to achieve the desired output. The disturbance rejection and robustness tests are also carried out. The robustness test reveals a significant improvement in the maximum absolute sensitivity measure. That is displayed in numerical simulations of the paper.

**keywords:** generalized fractional controller, Smith predictor, time delay system, general-ized inverse, Bode?s ideal transfer function

Global path planning for multiple AUVs using GWO

Madhusmita Panda, Bikramaditya Das, Bibhuti Bhusan Pati(Veer Surendra Sai University of Technology, India) |

In global path planning (GPP), an autonomous underwater vehicle (AUV) tracks a predefined path. The main objective of GPP is to generate a collision free sub-optimal path with minimum path cost. The path is defined as a set of segments, passing through selected nodes known as waypoints. For smooth planar motion, the path cost is a function of the path length, the threat cost and the cost of diving. Path length is the total distance travelled from start to end point, threat cost is the penalty of collision with the obstacle and cost of diving is the energy expanse for diving deeper in ocean. This paper addresses the GPP problem for multiple AUVs in formation. Here, Grey Wolf Optimization (GWO) algorithm is used to find the suboptimal path for multiple AUVs in formation. The results obtained are compared to the results of applying Genetic Algorithm (GA) to the same problem. GA concept is simple to understand, easy to implement and supports multi-objective optimization. It is robust to local minima and have wide applications in various fields of science, engineering and commerce. Hence, GA is used for this comparative study. The performance analysis is based on computational time, length of the path generated and the total path cost. The resultant path obtained using GWO is found to be better than GA in terms of path cost and processing time. Thus, GWO is used as the GPP algorithm for three AUVs in formation. The formation follows leader-follower topography. A sliding mode controller (SMC) is developed to minimize the tracking error based on local information while maintaining formation, as mild communication exists. The stability of the sliding surface is verified by Lyapunov stability analysis. With proper path planning, the path cost can be minimized as AUVs can reach their target in less time with less energy expanses. Thus, lower path cost leads to less expensive underwater missions.

**keywords:** Autonomous Underwater Vehicle (AUV), Genetic Algorithm(GA), Global Path Planning (GPP), GreyWolf Optimization(GWO), Sliding Mode Control (SMC), waypoints

Tracking of dynamic gesture fingertips position in video sequence

Tomasz Grzejszczak(Silesian Uni- versity of Technology, Poland) | Reinhard Molle, Robert Roth(University of Wuppertal, Germany) |

The field of research of this paper combines Human Computer Interface, gesture recognition and fingertips tracking. Most gesture recognition algorithms processing color images are unable to locate folded fingers hidden inside hand contour. With use of hand landmarks detection and localization algorithm, processing directional images, the fingertips are tracked whether they are risen or folded inside the hand contour. The capabilities of the method, repeatibility and accuracy, are tested with use of 3 gestures that are recorded on the USB camera. Fingertips are tracked in gestures presenting a linear movement of an open hand, finger folding into fist and clenched fist movement. In conclusion, a discussion of accuracy in application to HCI is presented.

**keywords:** hand landmarks, tracking, fingertip detection, hand gesture, gesture recognition, HMI, HCI

Motion control algorithm and tuning rules for mechanical devices with low sampling-rate electronics

Jorge Juan Gil, Inaki Diaz(TECNUN, University of Navarra, and CEIT, San Sebastián, Spain) |

Controlling mechanical systems with position and velocity cascade loops is one of the most effective methods to operate this type of systems. However, when using low-rate sampling electronics, the implementation is not trivial and the resulting performance can be poor. This paper proposes effective tuning rules that only require establishing the bandwidth of the inner velocity loop and an estimation of the inertia of the mechanism. Since discrete-time mechatronic systems can also exhibit unstable behavior, several stability conditions are also derived. By using the proposed methodology, a P-PI control algorithm is developed for a desktop haptic device, obtaining good experimental performance with low sampling-rate electronics.

**keywords:** motion control, cascade control loops, discrete-time systems, stability, mechatronic systems

An output sensitivity problem for a class of linear distributed systems with uncertain initial state

Abdelilah Larrache, Mustapha Lhous, Soukaina Ben Rhila, Mostafa Rachik(Hassan II University of Casablanca, Marocco) | Abdessamad Tridane(United Arab Emirates University, United Arab Emirates) |

In this paper, we consider an infinite dimensional linear systems. It is assumed that the initial state of system is not known throughout all the domain , the initial state is supposed known on one part of the domainand uncertain on the rest. That means with * *where and * * for* *, i.e., where the values are supposed known and unknown and is the indicator function. The uncertain part of the initial state is said to be -admissible if the sensitivity of corresponding output signal relatively to uncertainties is less to the threshold .The main goal of this paper is to determine the set of all possible gain operators that makes the system insensitive to all uncertainties. The characterization of this set is investigated and an algorithmic determination of each gain operators is presented. Some examples are given.

**keywords:** linear system, distributed system, uncertain initial state, gain operators, observability, stability, linear programming

Constrained Output Iterative Learning Control

Kaloyan Yovchev, Kamen Delchev, Evgeniy Krastev(Sofia University, Bulgaria) |

Iterative Learning Control (ILC) is a well-known method for control of systems performing repetitive jobs with high precision. This paper presents Constrained Output ILC (COILC) for non-linear state space constrained systems. In the existing literature there is no general solution for applying ILC to such systems. This novel method is based on the Bounded Error Algorithm (BEA) and resolves the transient growth error problem, which is a major obstacle in applying ILC to non-linear systems. Another advantage of COILC is that this method can be applied to constrained output systems. Unlike other ILC methods the COILC method employs an algorithm that stops the iteration before the occurrence of a violation in any of the state space constraints. This way COILC resolves both the hard constraints in the non-linear state space and the transient growth problem. The convergence of the proposed numerical procedure is proved in this paper. The performance of the method is evaluated through a computer simulation and the obtained results are compared to the BEA method for controlling non-linear systems. The numerical experiments demonstrate that COILC is more computationally effective and provides better overall performance. The robustness and convergence of the method make it suitable for solving constrained state space problems of non-linear systems in robotics.

**keywords:** constrained output systems, convergence analysis, iterative learning control, robot manipulators

Exact and approximate distributed controllability of processes described by KdV and Boussinesq equations: The Green’s function approach

Jerzy Klamka(Silesian University of Technology, Poland) | Ara S. Avetisyan(National Academy of Sciences of Armenia) | Asatur Zh. Khurshudyan(National Academy of Sciences of Armenia, Shanghai Jiao TongUniversity, China) |

In this paper, we study the constrained exact and approximate controllability of traveling wave solutions of Korteweg-de Vries (third order) and Boussinesq (fourth order) semi-linear equations using the Green’s function approach. Control is carried out by a moving external source. Representing the general solution of those equations in terms of the Frasca’s short time expansion, system of constraints on the distributed control is derived for both types of controllability. Due to the possibility of explicit solution provided by the heuristic method, the controllability analysis becomes straightforward. Numerical analysis confirms theoretical derivations.

**keywords:** KdV equation, Boussinesq equation, Frasca?s method, short time expansion, traveling wave, heuristic method, distributed control, constrained controllability

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