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A new three-dimensional chaotic system with a hidden attractor, circuit design and application in wireless mobile robot

Sundarapandian Vaidyanathan Aceng Sambas Mustafa Mamat Mada Sanjaya Ws

Archives of Control Sciences | 2017 | No 4 | DOI: 10.1515/acsc-2017-0032

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Abstract

Abstract This research work proposes a new three-dimensional chaotic system with a hidden attractor. The proposed chaotic system consists of only two quadratic nonlinearities and the system possesses no critical points. The phase portraits and basic qualitative properties of the new chaotic system such as Lyapunov exponents and Lyapunov dimension have been described in detail. Finally, we give some engineering applications of the new chaotic system like circuit simulation and control of wireless mobile robot.

Authors and Affiliations

Sundarapandian Vaidyanathan

Aceng Sambas

Mustafa Mamat

Mada Sanjaya Ws

Adaptive robust simultaneous stabilization controller with tuning parameters design for two dissipative Hamiltonian systems

Zhong Cao Xiaorong Hou Wenjing Zhao

Archives of Control Sciences | 2017 | No 4 | DOI: 10.1515/acsc-2017-0030

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Abstract

Abstract This paper investigates the problem of adaptive robust simultaneous stabilization (ARSS) of two dissipative Hamiltonian systems (DHSs), and proposes a number of results on the controller parameterization design. Firstly, an adaptive H∞ control design approach is presented by using the dissipative Hamiltonian structural for the case that there are both external disturbances and parametric uncertainties in two DHSs. Secondly, an algorithm for solving tuning parameters of the controller is proposed using symbolic computation. The proposed controller parameterization method avoids solving Hamilton-Jacobi-Issacs (HJI) equations and the obtained controller is easier as compared to some existing ones. Finally, an illustrative example is presented to show that the ARSS controller obtained in this paper works very well.

Authors and Affiliations

Zhong Cao

Xiaorong Hou

Wenjing Zhao

On optimal control problem subject to fractional order discrete time singular systems

Tirumalasetty Chiranjeevi Raj Kumar Biswas Ramesh Devarapalli Naladi Ram Babu Fausto Pedro García Márquez

Archives of Control Sciences | 2021 | vol. 31 | No 4 | 849-863 | DOI: 10.24425/acs.2021.139733

Keywords fractional optimal control problem discrete time singular system fractional derivative Hamiltonian technique

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Abstract

In this work, we present optimal control formulation and numerical algorithm for fractional order discrete time singular system (DTSS) for fixed terminal state and fixed terminal time endpoint condition. The performance index (PI) is in quadratic form, and the system dynamics is in the sense of Riemann-Liouville fractional derivative (RLFD). A coordinate transformation is used to convert the fractional-order DTSS into its equivalent non-singular form, and then the optimal control problem (OCP) is formulated. The Hamiltonian technique is used to derive the necessary conditions. A solution algorithm is presented for solving the OCP. To validate the formulation and the solution algorithm, an example for fixed terminal state and fixed terminal time case is presented.

Bibliography

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[26] R.K. Biswas and S. Sen: Fractional optimal control within Caputo’s derivative. In: Proceedings of the ASME IDETC/CIE Conference, (2012), 353– 360, DOI: 10.1115/DETC2011-48045.
[27] T. Chiranjeevi, R.K. Biswas, and C. Sethi: Optimal control of fractional order singular system. The International Journal of Electrical Engineering & Education, p. 0020720919833031, (2019), DOI: 10.1177/0020720919833031.
[28] T. Chiranjeevi and R.K. Biswas: Numerical approach to the fractional optimal control problem of continuous-time singular system. In: Advances in Electrical Control and Signal Systems, Singapore, (2020), 239–248, DOI: 10.1007/978-981-15-5262-5_16.
[29] T. Chiranjeevi and R.K. Biswas: Linear quadratic optimal control problem of fractional order continuous-time singular system. Procedia Computer Science, 171 (2020), 1261–1268, DOI: 10.1016/j.procs.2020.04.134.
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[33] T. Chiranjeevi and R.K. Biswas: Computational method based on reflection operator for solving a class of fractional optimal control problem. Procedia Computer Science, 171 (2020), 2030–2039, DOI: 10.1016/j.procs.2020.04.218.
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Authors and Affiliations

Tirumalasetty Chiranjeevi

1

Raj Kumar Biswas

2

Ramesh Devarapalli

3

e-mail:

ORCID:

Naladi Ram Babu

2

Fausto Pedro García Márquez

4

Department of Electrical Engineering, Rajkiya Engineering College Sonbhadra, U. P., India
Department of Electrical Engineering, National Institute of Technology, Silchar, India
Department of Electrical Engineering, BIT Sindri, Dhanbad 828123, Jharkhand, India
Ingenium Research Group, University of Castilla-La Mancha, Spain

Offset-free nonlinear Model Predictive Control with state-space process models

Piotr Tatjewski

Archives of Control Sciences | 2017 | No 4 | DOI: 10.1515/acsc-2017-0035

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Abstract

Abstract Offset-free model predictive control (MPC) algorithms for nonlinear state-space process models, with modeling errors and under asymptotically constant external disturbances, is the subject of the paper. The main result of the paper is the presentation of a novel technique based on constant state disturbance prediction. It was introduced originally by the author for linear state-space models and is generalized to the nonlinear case in the paper. First the case with measured state is considered, in this case the technique allows to avoid disturbance estimation at all. For the cases with process outputs measured only and thus the necessity of state estimation, the technique allows the process state estimation only - as opposed to conventional approach of extended process-and-disturbance state estimation. This leads to simpler design with state observer/filter of lower order and, moreover, without the need of a decision of disturbance placement in the model (under certain restrictions), as in the conventional approach. A theoretical analysis of the proposed algorithm is provided, under applicability conditions which are weaker than in the conventional approach. The presented theory is illustrated by simulation results of nonlinear processes, showing competitiveness of the proposed algorithms.

Authors and Affiliations

Piotr Tatjewski

Application of maximum principle to optimization of production and storage costs

Liviu Popescu Ramona Dimitrov

Archives of Control Sciences | 2021 | vol. 31 | No 4 | 865-881 | DOI: 10.24425/acs.2021.139734

Keywords optimal control Pontryagin Maximum Principle controllability production and storage

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Abstract

A problem of optimization for production and storge costs is studied. The problem consists in manufacture of n types of products, with some given restrictions, so that the total production and storage costs are minimal. The mathematical model is built using the framework of driftless control affine systems. Controllability is studied using Lie geometric methods and the optimal solution is obtained with Pontryagin Maximum Principle. It is proved that the economical system is not controllable, in the sense that we can only produce a certain quantity of products. Finally, some numerical examples are given with graphical representation.

Bibliography

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Authors and Affiliations

Liviu Popescu

1

Ramona Dimitrov

1

University of Craiova, Faculty of Economics and Business Administration, Department of Statistics and Economic Informatics, Al. I. Cuza st., No. 13, Craiova 200585, Romania

On dynamically consistent Jacobian inverse for non-holonomic robotic systems

Joanna Ratajczak Krzysztof Tchoń

Archives of Control Sciences | 2017 | No 4 | DOI: 10.1515/acsc-2017-0033

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Abstract

Abstract This paper presents the dynamically consistent Jacobian inverse for non-holonomic robotic system, and its application to solving the motion planning problem. The system’s kinematics are represented by a driftless control system, and defined in terms of its input-output map in accordance with the endogenous configuration space approach. The dynamically consistent Jacobian inverse (DCJI) has been introduced by means of a Riemannian metric in the endogenous configuration space, exploiting the reduced inertia matrix of the system’s dynamics. The consistency condition is formulated as the commutativity property of a diagram of maps. Singular configurations of DCJI are studied, and shown to coincide with the kinematic singularities. A parametric form of DCJI is derived, and used for solving example motion planning problems for the trident snake mobile robot. Some advantages in performance of DCJI in comparison to the Jacobian pseudoinverse are discovered.

Authors and Affiliations

Joanna Ratajczak

Krzysztof Tchoń

Explicit modeling of multi-period setup times in proportional lot-sizing and scheduling problem with variable capacity

Waldemar Kaczmarczyk

Archives of Control Sciences | 2021 | vol. 31 | No 4 | 883-812 | DOI: 10.24425/acs.2021.139735

Keywords production lot-sizing and scheduling mixed-integer programming

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Abstract

Small bucket models with many short fictitious micro-periods ensure high-quality schedules in multi-level systems, i.e., with multiple stages or dependent demand. In such models, setup times longer than a single period are, however, more likely. This paper presents new mixedinteger programming models for the proportional lot-sizing and scheduling problem (PLSP) with setup operations overlapping multiple periods with variable capacity.
A new model is proposed that explicitly determines periods overlapped by each setup operation and the time spent on setup execution during each period. The model assumes that most periods have the same length; however, a few of them are shorter, and the time interval determined by two consecutive shorter periods is always longer than a single setup operation. The computational experiments showthat the newmodel requires a significantly smaller computation effort than known models.

Bibliography

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[15] W.Kaczmarczyk: Explicit modelling of multi-period setup times in proportional lot-sizing problem with constant capacity. (2021), Preprint available at Research Square, DOI: 10.21203/rs.3.rs-1086310/v1.
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Authors and Affiliations

Waldemar Kaczmarczyk

1

Department of Strategic Management, AGH University of Science and Technology, Al.Mickiewicza 30, 30-059, Kraków, Poland

Position-force control of mobile manipulator – nonadaptive and adaptive case

Mirela Kaczmarek Wojciech Domski Alicja Mazur

Archives of Control Sciences | 2017 | No 4 | DOI: 10.1515/acsc-2017-0029

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Abstract

Abstract This article presents a control algorithm for nonholonomic mobile manipulators with a simple, geometric holonomic constraint imposed on the robot’s arm. A mathematical model in generalized, auxiliary and linearized coordinates is presented, as well as the constrained dynamics of the robotic system. A position-force control law is proposed, both for the fully known robot’s model, as well as for the model with parametric uncertainty in the dynamics. Theoretical considerations are supported by the results of computer simulations.

Authors and Affiliations

Mirela Kaczmarek

Wojciech Domski

Alicja Mazur

Contents

Archives of Control Sciences | 2021 | vol. 31 | No 4

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Stabilization of discrete-time LTI positive systems

Dušan Krokavec Anna Filasová

Archives of Control Sciences | 2017 | No 4 | DOI: 10.1515/acsc-2017-0034

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Abstract

Abstract The paper mitigates the existing conditions reported in the previous literature for control design of discrete-time linear positive systems. Incorporating an associated structure of linear matrix inequalities, combined with the Lyapunov inequality guaranteing asymptotic stability of discrete-time positive system structures, new conditions are presented with which the state-feedback controllers and the system state observers can be designed. Associated solutions of the proposed design conditions are illustrated by numerical illustrative examples.

Authors and Affiliations

Dušan Krokavec

Anna Filasová

Vibration control in semi-active suspension of the experimental off-road vehicle using information about suspension deflection

Jerzy Kasprzyk Piotr Krauze Sebastian Budzan Jarosław Rzepecki

Archives of Control Sciences | 2017 | No 2 | DOI: 10.1515/acsc-2017-0016

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Abstract

Abstract The efficiency of vibration control in an automotive semi-active suspension system depends on the quality of information from sensors installed in the vehicle, including information about deflection of the suspension system. The control algorithm for vibration attenuation of the body takes into account its velocity as well as the relative velocity of the suspension. In this paper it is proposed to use the Linear Variable Differential Transformer (LVDT) unit to measure the suspension deflection and then to estimate its relative velocity. This approach is compared with a typical solution implemented in such applications, where the relative velocity is calculated by processing signals acquired from accelerometers placed on the body and on the chassis. The experiments performed for an experimental All-Terrain Vehicle (ATV) confirm that using LVDT units allows for improving ride comfort by better vibration attenuation of the body.

Authors and Affiliations

Jerzy Kasprzyk

Piotr Krauze

Sebastian Budzan

Jarosław Rzepecki

A new 3-D jerk chaotic system with two cubic nonlinearities and its adaptive backstepping control

Sundarapandian Vaidyanathan

Archives of Control Sciences | 2017 | No 3 | DOI: 10.1515/acsc-2017-0026

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Abstract

Abstract This paper presents a new seven-term 3-D jerk chaotic system with two cubic nonlinearities. The phase portraits of the novel jerk chaotic system are displayed and the qualitative properties of the jerk system are described. The novel jerk chaotic system has a unique equilibrium at the origin, which is a saddle-focus and unstable. The Lyapunov exponents of the novel jerk chaotic system are obtained as L1 = 0:2974, L2 = 0 and L3 = −3:8974. Since the sum of the Lyapunov exponents of the jerk chaotic system is negative, we conclude that the chaotic system is dissipative. The Kaplan-Yorke dimension of the new jerk chaotic system is found as DKY = 2:0763. Next, an adaptive backstepping controller is designed to globally stabilize the new jerk chaotic system with unknown parameters. Moreover, an adaptive backstepping controller is also designed to achieve global chaos synchronization of the identical jerk chaotic systems with unknown parameters. The backstepping control method is a recursive procedure that links the choice of a Lyapunov function with the design of a controller and guarantees global asymptotic stability of strict feedback systems. MATLAB simulations are shown to illustrate all the main results derived in this work.

Authors and Affiliations

Sundarapandian Vaidyanathan

An interval observer design for uncertain nonlinear systems based on the T-S fuzzy model

Yamina Menasria Hichem Bouras Nasreddine Debbache

Archives of Control Sciences | 2017 | No 3 | DOI: 10.1515/acsc-2017-0025

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Abstract

Abstract A new approach to build an interval observer for nonlinear uncertain systems is presented in this paper. Nonlinear systems modeled in the Takagi-Sugeno (T-S) form are studied. A T-S proportional observer is first issued by pole-placement and LMI tools. Secondly, time-varying change of coordinates for each dynamic state estimation error is used to design an interval observer. The system state bounds are then directly deduced.

Authors and Affiliations

Yamina Menasria

Hichem Bouras

Nasreddine Debbache

Dual hesitant pythagorean fuzzy Hamacher aggregation operators in multiple attribute decision making

Guiwu Wei Mao Lu

Archives of Control Sciences | 2017 | No 3 | DOI: 10.1515/acsc-2017-0024

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Abstract

Abstract In this paper, we investigate the multiple attribute decision making (MADM) problem based on the Hamacher aggregation operators with dual Pythagorean hesitant fuzzy information. Then, motivated by the ideal of Hamacher operation, we have developed some Hamacher aggregation operators for aggregating dual hesitant Pythagorean fuzzy information. The prominent characteristic of these proposed operators are studied. Then, we have utilized these operators to develop some approaches to solve the dual hesitant Pythagorean fuzzy multiple attribute decision making problems. Finally, a practical example for supplier selection in supply chain management is given to verify the developed approach and to demonstrate its practicality and effectiveness.

Authors and Affiliations

Guiwu Wei

Mao Lu

Relationship between the observability of standard and fractional linear systems

Tadeusz Kaczorek

Archives of Control Sciences | 2017 | No 3 | DOI: 10.1515/acsc-2017-0027

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Abstract

Abstract The relationship between the observability of standard and fractional discrete-time and continuous-time linear systems are addressed. It is shown that the fractional discrete-time and continuous-time linear systems are observable if and only if the standard discrete-time and continuous-time linear systems are observable.

Authors and Affiliations

Tadeusz Kaczorek

Stabilization of a certain class of fuzzy control systems with uncertainties

Nizar Hadj Taieb Mohamed Ali Hammami François Delmotte

Archives of Control Sciences | 2017 | No 3 | DOI: 10.1515/acsc-2017-0028

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Abstract

Abstract In this paper, we investigate the global uniform practical exponential stability for a class of uncertain Takagi-Sugeno fuzzy systems. The uncertainties are supposed uniformly to be bounded by some known integrable functions to obtain an exponential convergence toward a neighborhood of the origin. Therefore, we use common quadratic Lyapunov function (CQLF) and parallel distributed compensation (PDC) controller techniques to show the global uniform practical exponential stability of the closed-loop system. Numeric simulations are given to validate the proposed approach.

Authors and Affiliations

Nizar Hadj Taieb

Mohamed Ali Hammami

François Delmotte

A New Fuzzy Iterative Learning Control Algorithm for Single Joint Manipulator

Meng Wang Guangrong Bian Hongsheng Li

Archives of Control Sciences | 2016 | No 3 | DOI: 10.1515/acsc-2016-0017

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Abstract

Abstract This paper present a new fuzzy iterative learning control design to solve the trajectory tracking problem and performing repetitive tasks for rigid robot manipulators. Several times’ iterations are needed to make the system tracking error converge, especially in the first iteration without experience. In order to solve that problem, fuzzy control and iterative learning control are combined, where fuzzy control is used to tracking trajectory at the first learning period, and the output of fuzzy control is recorded as the initial control inputs of ILC. The new algorithm also adopts gain self-tuning by fuzzy control, in order to improve the convergence rate. Simulations illustrate the effectiveness and convergence of the new algorithm and advantages compared to traditional method.

Authors and Affiliations

Meng Wang

Guangrong Bian

Hongsheng Li

Analysis, Adaptive Control and Synchronization of a Novel 4-D Hyperchaotic Hyperjerk System via Backstepping Control Method

Sundarapandian Vaidyanathan

Archives of Control Sciences | 2016 | No 3 | DOI: 10.1515/acsc-2016-0018

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Abstract

Abstract A hyperjerk system is a dynamical system, which is modelled by an nth order ordinary differential equation with n ≥ 4 describing the time evolution of a single scalar variable. Equivalently, using a chain of integrators, a hyperjerk system can be modelled as a system of n first order ordinary differential equations with n ≥ 4. In this research work, a 4-D novel hyperchaotic hyperjerk system with two nonlinearities has been proposed, and its qualitative properties have been detailed. The novel hyperjerk system has a unique equilibrium at the origin, which is a saddle-focus and unstable. The Lyapunov exponents of the novel hyperjerk system are obtained as L1 = 0.14219, L2 = 0.04605, L3 = 0 and L4 = −1.39267. The Kaplan-Yorke dimension of the novel hyperjerk system is obtained as DKY = 3.1348. Next, an adaptive controller is designed via backstepping control method to stabilize the novel hyperjerk chaotic system with three unknown parameters. Moreover, an adaptive controller is designed via backstepping control method to achieve global synchronization of the identical novel hyperjerk systems with three unknown parameters. MATLAB simulations are shown to illustrate all the main results derived in this research work on a novel hyperjerk system.

Authors and Affiliations

Sundarapandian Vaidyanathan

Equitable Coloring of Graphs. Recent Theoretical Results and New Practical Algorithms

Hanna Furmańczyk Andrzej Jastrzębski Marek Kubale

Archives of Control Sciences | 2016 | No 3 | DOI: 10.1515/acsc-2016-0016

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Abstract

Abstract In many applications in sequencing and scheduling it is desirable to have an underlaying graph as equitably colored as possible. In this paper we survey recent theoretical results concerning conditions for equitable colorability of some graphs and recent theoretical results concerning the complexity of equitable coloring problem. Next, since the general coloring problem is strongly NP-hard, we report on practical experiments with some efficient polynomial-time algorithms for approximate equitable coloring of general graphs.

Authors and Affiliations

Hanna Furmańczyk

Andrzej Jastrzębski

Marek Kubale

Explicit Finite-Difference Scheme for the Numerical Solution of the Model Equation of Nonlinear Hereditary Oscillator with Variable-Order Fractional Derivatives

Roman I. Parovik

Archives of Control Sciences | 2016 | No 3 | DOI: 10.1515/acsc-2016-0023

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Abstract

Abstract The paper deals with the model of variable-order nonlinear hereditary oscillator based on a numerical finite-difference scheme. Numerical experiments have been carried out to evaluate the stability and convergence of the difference scheme. It is argued that the approximation, stability and convergence are of the first order, while the scheme is stable and converges to the exact solution.

Authors and Affiliations

Roman I. Parovik

Lyapunov Matrices Approach to the Parametric Optimization of a System with Two Delays

Jozef Duda

Archives of Control Sciences | 2016 | No 3 | DOI: 10.1515/acsc-2016-0020

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Abstract

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

Authors and Affiliations

Jozef Duda

Membership Functions for Fuzzy Focal Elements

Sebastian Porębski Ewa Straszecka

Archives of Control Sciences | 2016 | No 3 | DOI: 10.1515/acsc-2016-0022

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Abstract

Abstract The paper presents a study on data-driven diagnostic rules, which are easy to interpret by human experts. To this end, the Dempster-Shafer theory extended for fuzzy focal elements is used. Premises of the rules (fuzzy focal elements) are provided by membership functions which shapes are changing according to input symptoms. The main aim of the present study is to evaluate common membership function shapes and to introduce a rule elimination algorithm. Proposed methods are first illustrated with the popular Iris data set. Next experiments with five medical benchmark databases are performed. Results of the experiments show that various membership function shapes provide different inference efficiency but the extracted rule sets are close to each other. Thus indications for determining rules with possible heuristic interpretation can be formulated.

Authors and Affiliations

Sebastian Porębski

Ewa Straszecka

Optimal and Suboptimal Control of a Standard Brownian Motion

Mario Lefebvre

Archives of Control Sciences | 2016 | No 3 | DOI: 10.1515/acsc-2016-0021

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Abstract

Abstract The problem of optimally controlling a standard Brownian motion until a fixed final time is considered in the case when the final cost function is an even function. Two particular problems are solved explicitly. Moreover, the best constant control as well as the best linear control are also obtained in these two particular cases.

Authors and Affiliations

Mario Lefebvre

Tools and Methods for RTCP-Nets Modeling and Verification

Marcin Szpyrka Jerzy Biernacki Agnieszka Biernacka

Archives of Control Sciences | 2016 | No 3 | DOI: 10.1515/acsc-2016-0019

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Abstract

Abstract RTCP-nets are high level Petri nets similar to timed colored Petri nets, but with different time model and some structural restrictions. The paper deals with practical aspects of using RTCP-nets for modeling and verification of real-time systems. It contains a survey of software tools developed to support RTCP-nets. Verification of RTCP-nets is based on coverability graphs which represent the set of reachable states in the form of directed graph. Two approaches to verification of RTCP-nets are considered in the paper. The former one is oriented towards states and is based on translation of a coverability graph into nuXmv (NuSMV) finite state model. The later approach is oriented towards transitions and uses the CADP toolkit to check whether requirements given as μ-calculus formulae hold for a given coverability graph. All presented concepts are discussed using illustrative examples

Authors and Affiliations

Marcin Szpyrka

Jerzy Biernacki

Agnieszka Biernacka

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