Fractional calculus approach to modeling and control of (bio)mechanical systems

Recently, an increasing attention has been paid to fractional calculus (FC) and its application in control and modeling of fractional order (bio)mechanical system. Fractional derivatives and integrals may have a wide application in describing complex properties of materials including long-term memory, non-locality of power law type and fractality [1]. In this presentation we applied the concept of fractional order for biomehanical modeling of human arm dynamics as well as soft tissues, specially human skin as well as human blood. Besides, it is also presented the connection between fractional order differintegral operators and behavior of the memsystems which can be used for modeling dynamics of (bio)mechanical systems. Further, we present robust feedback-(feedforward) loop fractional-order iterative learning control [2] for regular and singular fractional order system. Particularly, a feedback-(feedforward) PDalpfa / PIbetaDalpfa type iterative learning control (ILC) of fractional order system- (regular and degenerate type) which includes time delay are considered [3]. Sufficient conditions for the convergence of a proposed PD alpha type of learning control algorithm for a class of fractional state space time delay system are given in time domain. Finally, a simulation results show the feasibility and effectiveness of the suggested approach

Optimal control of a fractional order epidemic model with application to human respiratory syncytial virus infection

A human respiratory syncytial virus surveillance system was implemented in Florida in 1999, to support clinical decision-making for prophylaxis of premature newborns. Recently, a local periodic SEIRS mathematical model was proposed in [Stat. Optim. Inf. Comput. 6 (2018), no.1, 139--149] to describe real data collected by Florida's system. In contrast, here we propose a non-local fractional (non-integer) order model. A fractional optimal control problem is then formulated and solved, having treatment as the control. Finally, a cost-effectiveness analysis is carried out to evaluate the cost and the effectiveness of proposed control measures during the intervention period, showing the superiority of obtained results with respect to previous ones.Comment: This is a preprint of a paper whose final and definite form is with 'Chaos, Solitons & Fractals', available from [http://www.elsevier.com/locate/issn/09600779]. Submitted 23-July-2018; Revised 14-Oct-2018; Accepted 15-Oct-2018. arXiv admin note: substantial text overlap with arXiv:1801.0963

Biologically inspired control and modeling of (bio)robotic systems and some applications of fractional calculus in mechanics

U ovom radu, prezentovane su primene biološki inspirisanog modeliranja i upravljanja (bio)mehaničkim (ne)redundantnim mehanizmima, kao i novodobijeni rezultati autora u oblasti primenjene mehanike koji su zasnovani na primeni računa necelobrojnog reda. Prvo, predloženo je korišćenje biološkog analogona-sinergije zahvaljujući postojanju nepromenljivih odlika u izvršavanju funkcionalnih pokreta. Drugo, model (bio)mehaničkog sistema može se dobiti primenom drugog biološkog koncepta poznatim pod nazivom distribuirano pozicioniranje (DP), koji je zasnovan na inercijalnim svojstva i pokretanju zglobova razmatranog mehaničkog sistema. Takođe,predlaže se korišćenje drugih bioloških principa kao što su: princip minimalne interakcije, koji ima glavnu ulogu u hijerarhijskoj strukturi upravljanja i princip samopodešavanja (uvodi lokalne pozitivnu/negativnu povratnu spregu u upravljačkoj petlji i to sa velikim pojačanjem), koji omogućava efikasno ostvarivanje upravljanja na bazi iterativnog prirodnog učenja. Takođe, novi, nedavno publikovani rezultati autora su takođe predstavljeni u oblasti stabilnosti, elektro-viskoelastičnosti i teoriji upravljanja a koji su zasnovani na korišćenju računa necelobrojnog reda.In this paper, the applications of biologically inspired modeling and control of (bio)mechanical (non)redundant mechanisms are presented, as well as newly obtained results of author in mechanics which are based on using fractional calculus. First, it is proposed to use biological analog-synergy due to existence of invariant features in the execution of functional motion. Second, the model of (bio)mechanical system may be obtained using another biological concept called distributed positioning (DP), which is based on the inertial properties and actuation of joints of considered mechanical system. In addition, it is proposed to use other biological principles such as: principle of minimum interaction, which takes a main role in hierarchical structure of control and self-adjusting principle (introduce local positive/negative feedback on control with great amplifying), which allows efficiently realization of control based on iterative natural learning. Also, new, recently obtained results of the author in the fields of stability, electroviscoelasticity, and control theory are presented which are based on using fractional calculus (FC)

Comparison of smoothing filters in analysis of EEG data for the medical diagnostics purposes

This paper covers a brief review of both the advantages and disadvantages of the implementation of various smoothing filters in the analysis of electroencephalography (EEG) data for the purpose of potential medical diagnostics. The EEG data are very prone to the occurrence of various internal and external artifacts and signal distortions. In this paper, three types of smoothing filters were compared: smooth filter, median filter and Savitzky-Golay filter. The authors of this paper compared those filters and proved their usefulness, as they made the analyzed data more legible for diagnostic purposes. The obtained results were promising, however, the studies on finding perfect filtering methods are still in progress.Web of Science203art. no. 80

Fractional order modelling of contact with the environment in flexible robot applications

[Abstract] The control of flexible robots that interact with the environment presents some difficulties because the mechanical environment is unknown. In this kind of applications, force robust control rather than position control is required. The purpose of this paper is to model the mechanical impedance of the environment contacted by a flexible link based on the well-known spring-damper system typically used in the literature, considering models of both integer and fractional order. In particular, four models are identified: 1) linear regression model, 2) spring-damper model, 3) spring-damper model that also includes a spring for the robotic arm, and 4) fractional order extension of spring-damper model. Experimental results (impacts with ten different objects) are given to identify the parameters of the considered models. The goodness of the adjustment is analyzed by a set of performance indices. The results show that fractional models may have better performance in comparison with classical alternatives proposed in the literature for the objects used in this study.[Resumen] El control de robots flexibles que interactúan con el entorno presenta algunas dificultades porque se desconoce el entorno mecánico. En este tipo de aplicaciones, se requiere un control robusto en lugar de un control de posición. El propósito de este trabajo es modelar la impedancia mecánica del entorno contactado por un enlace flexible basado en el conocido sistema de amortiguador de resortes que se usa típicamente en la literatura, considerando modelos de orden entero y fraccional. En particular, se identifican cuatro modelos: 1) modelo de regresión lineal, 2) modelo de amortiguador de resorte, 3) modelo de amortiguador de resorte que también incluye un resorte para el brazo robótico, y 4) extensión de orden fraccional del modelo de amortiguador de resorte. Se dan resultados experimentales (impactos con diez objetos diferentes) para identificar los parámetros de los modelos considerados. La bondad del ajuste se analiza mediante un conjunto de índices de rendimiento. Los resultados muestran que los modelos fraccionarios pueden tener un mejor rendimiento en comparación con las alternativas clásicas propuestas en la literatura para los objetos utilizados en este estudio.Ministerio de Economía y Competitividad; DPI2016-80547-

Fractional-Order Iterative Learning Control for Robotic Arm-(PDD alpha)-D-2 Type

In this paper, a new open-loop (PDDa)-D-2 type a fractional order iterative learning control (ILC) is studied for joint space trajectory tracking control of a linearized uncertain robotic arm. The robust convergent analysis of the tracking errors has been done in time domain where it is theoretically proven that the boundednesses of the tracking error are guaranteed in the presence of model uncertainty. The convergence of the proposed open-loop ILC law is proven mathematically using Gronwall integral inequality for a linearized robotic system and sufficient conditions for convergence and robustness are obtained

Fractional-Order Iterative Learning Control for Robotic Arm-(PDD alpha)-D-2 Type

In this paper, a new open-loop (PDDa)-D-2 type a fractional order iterative learning control (ILC) is studied for joint space trajectory tracking control of a linearized uncertain robotic arm. The robust convergent analysis of the tracking errors has been done in time domain where it is theoretically proven that the boundednesses of the tracking error are guaranteed in the presence of model uncertainty. The convergence of the proposed open-loop ILC law is proven mathematically using Gronwall integral inequality for a linearized robotic system and sufficient conditions for convergence and robustness are obtained