Some new results on iterative learning control of noninteger order

Iterativno upravljanje putem učenja (ILC) predstavlja jedno od važnih oblasti u teoriji upravljanja i ono je moćan koncept upravljanja koji na iterativan način poboljšava ponašanje procesa koji su po prirodi ponovljivi. ILC je pogodno za upravljanje šire klase mehatroničkih sistema i posebno su pogodni za upravljanje na primer kretanja robotskih sistema koji imaju važnu ulogu u tehničkim sistemima koji uključuju sisteme upravljanja, primenu u vojnoj industriji itd. Ovaj se rad bavi problemom ILC upravljanja za nelinearne sisteme necelog reda sa vremenskim kašnjenjem. Posebno, ovde se proučavaju sistemi necelog reda sa nepoznatim ograničenim vremenskim kašnjenjem u prostoru stanja kao i slučaj vremenski promenljivog kašnjenja. Pri tome, dovoljni uslovi za konvergenciju u vremenskom domenu predloženog PDα ILC upravljanja za datu klasu necelog reda sistema sa kašnjenjem su prezentovani i dati u vremenskom domenu.Takođe, robusno PDα ILC upravljanje u direktnoj-povratnoj sprezi za dati sistem sa kašnjenjem je razmatrano.Posebno, razmatra se sistem necelog reda sa nepoznatim ali ograničenim konstantnim vremenskim kašnjenjem. Dovoljni uslovi za konvergenciju u vremenskom domenu predloženog PDα ILC upravljanja su dati odgovarajućom teoremom sa pratećim dokazom. Konačno, simulacioni primer pokazuje izvodljivost i efikasnost predloženog pristupa.Iterative learning control (ILC) is one of the recent topics in control theories and it is a powerful control concept that iteratively improves the behavior of processes repetitive in their nature. ILC is suitable for controlling a wider class of mechatronic systems - it is especially suitable for the motion control of robotic systems that attract and hold an important position in technical systems involving control applications, military industry, etc. This paper addresses the problem of iterative learning control (ILC) for fractional nonlinear time delay systems. Particularly, we study fractional order time delay systems in the state space form with unknown bounded constant time delay as well as time-varying delay. Sufficient conditions for the convergence of a proposed PDα type of a learning control algorithm for a class of fractional state space time delay systems are presented in the time domain. Also, a feedback-feed forward PDα type robust iterative learning control (ILC) of the given fractional order uncertain time delay system is considered. We consider fractional order time delay systems in the state space form with uncertain bounded constant time delay in particular. Sufficient conditions for the convergence in the time domain of the proposed PDα ILC are given by the corresponding theorem together with its proof. Finally, a simulation example shows the feasibility and effectiveness of the proposed approach

Some new results on iterative learning control of noninteger order

Iterativno upravljanje putem učenja (ILC) predstavlja jedno od važnih oblasti u teoriji upravljanja i ono je moćan koncept upravljanja koji na iterativan način poboljšava ponašanje procesa koji su po prirodi ponovljivi. ILC je pogodno za upravljanje šire klase mehatroničkih sistema i posebno su pogodni za upravljanje na primer kretanja robotskih sistema koji imaju važnu ulogu u tehničkim sistemima koji uključuju sisteme upravljanja, primenu u vojnoj industriji itd. Ovaj se rad bavi problemom ILC upravljanja za nelinearne sisteme necelog reda sa vremenskim kašnjenjem. Posebno, ovde se proučavaju sistemi necelog reda sa nepoznatim ograničenim vremenskim kašnjenjem u prostoru stanja kao i slučaj vremenski promenljivog kašnjenja. Pri tome, dovoljni uslovi za konvergenciju u vremenskom domenu predloženog PDα ILC upravljanja za datu klasu necelog reda sistema sa kašnjenjem su prezentovani i dati u vremenskom domenu.Takođe, robusno PDα ILC upravljanje u direktnoj-povratnoj sprezi za dati sistem sa kašnjenjem je razmatrano.Posebno, razmatra se sistem necelog reda sa nepoznatim ali ograničenim konstantnim vremenskim kašnjenjem. Dovoljni uslovi za konvergenciju u vremenskom domenu predloženog PDα ILC upravljanja su dati odgovarajućom teoremom sa pratećim dokazom. Konačno, simulacioni primer pokazuje izvodljivost i efikasnost predloženog pristupa.Iterative learning control (ILC) is one of the recent topics in control theories and it is a powerful control concept that iteratively improves the behavior of processes repetitive in their nature. ILC is suitable for controlling a wider class of mechatronic systems - it is especially suitable for the motion control of robotic systems that attract and hold an important position in technical systems involving control applications, military industry, etc. This paper addresses the problem of iterative learning control (ILC) for fractional nonlinear time delay systems. Particularly, we study fractional order time delay systems in the state space form with unknown bounded constant time delay as well as time-varying delay. Sufficient conditions for the convergence of a proposed PDα type of a learning control algorithm for a class of fractional state space time delay systems are presented in the time domain. Also, a feedback-feed forward PDα type robust iterative learning control (ILC) of the given fractional order uncertain time delay system is considered. We consider fractional order time delay systems in the state space form with uncertain bounded constant time delay in particular. Sufficient conditions for the convergence in the time domain of the proposed PDα ILC are given by the corresponding theorem together with its proof. Finally, a simulation example shows the feasibility and effectiveness of the proposed approach

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)

Iterative learning control of integer and noninteger order: An overview

Ovaj rad daje pregledni prikaz nedavno prezentiranih i objavljenih rezultata autora koji se odnose na primenu iterativnog upravljanja putem učenja (ILC) i to celog reda kao i necelog reda. ILC predstavlja jedno od važnih oblasti u teoriji upravljanja i ono je moćan koncept upravljanja koji na iterativan način poboljšava ponašanje procesa koji su po prirodi ponovljivi. ILC je pogodno za upravljanje šire klase mehatroničkih sistema i posebno su pogodni za upravljanje kretanja robotskih sistema koji imaju važnu ulogu u biomehatroničkim, tehničkim sistemima koji uključuju primenu i vojnoj industriju itd. U prvom delu rada predstavljeni su rezultati koji se odnose na primenu višeg celobrojnog reda PD tipa sa pratećom numeričkom simulacijom. Takođe, još jedna druga ILC šema celobrojnog reda je predložena za dati robotski sistem sa tri stepena slobode u rešavanju zadatka praćenja što je i verifikovano kroz simulacioni primer. U drugom delu, predstavljeni su rezultati koji se odnose na primenu ILC frakcionog reda gde je prvo PDα tip predložen za linearni sistem frakcionog reda. Pokazano je da se pod odredjenim dovoljnim uslovima koji uključuju operatore učenja konvergencija datog sistema može biti garantovana. Takodje, PIβDα tip ILC upravljanja je predložen za linearni sistem frakcionog reda sa kašnjenjem. Konačno, dovoljni uslovi za konvergenciju u vremenskom domenu predloženog ILC upravljanja su dati odgovarajućom teoremom sa pratećim dokazom.This paper provides an overview of the recently presented and published results relating to the use of iterative learning control (ILC) based on and integer and fractional order. ILC is one of the recent topics in control theories and it is a powerful control concept that iteratively improves the behavior of processes that are repetitive in nature. ILC is suitable for controlling a wider class of mechatronic systems - it is especially suitable for motion control of robotic systems that attract and hold an important position in biomechatronical, technical systems involving the application, military industry, etc. The first part of the paper presents the results relating to the application of higher integer order PD type ILC with numerical simulation. Also, another integer order ILC scheme is proposed for a given robotic system with three degrees of freedom for task-space trajectory tracking where the effectiveness of the suggested control is demonstrated through a simulation procedure. In the second part, the results related to the application of the fractional order of ILC are presented where PDα type of ILC is proposed firstly, for a fractional order linear time invariant system. It is shown that under some sufficient conditions which include the learning operators, convergence of the learning system can be guaranteed. Also, PIβDα type of ILC is suggested for a fractional order linear time delay system. Finally, sufficient conditions for the convergence in the time domain of the proposed ILC were given by the corresponding theorem together with its proof

Iterative learning control of integer and noninteger order: An overview

Ovaj rad daje pregledni prikaz nedavno prezentiranih i objavljenih rezultata autora koji se odnose na primenu iterativnog upravljanja putem učenja (ILC) i to celog reda kao i necelog reda. ILC predstavlja jedno od važnih oblasti u teoriji upravljanja i ono je moćan koncept upravljanja koji na iterativan način poboljšava ponašanje procesa koji su po prirodi ponovljivi. ILC je pogodno za upravljanje šire klase mehatroničkih sistema i posebno su pogodni za upravljanje kretanja robotskih sistema koji imaju važnu ulogu u biomehatroničkim, tehničkim sistemima koji uključuju primenu i vojnoj industriju itd. U prvom delu rada predstavljeni su rezultati koji se odnose na primenu višeg celobrojnog reda PD tipa sa pratećom numeričkom simulacijom. Takođe, još jedna druga ILC šema celobrojnog reda je predložena za dati robotski sistem sa tri stepena slobode u rešavanju zadatka praćenja što je i verifikovano kroz simulacioni primer. U drugom delu, predstavljeni su rezultati koji se odnose na primenu ILC frakcionog reda gde je prvo PDα tip predložen za linearni sistem frakcionog reda. Pokazano je da se pod odredjenim dovoljnim uslovima koji uključuju operatore učenja konvergencija datog sistema može biti garantovana. Takodje, PIβDα tip ILC upravljanja je predložen za linearni sistem frakcionog reda sa kašnjenjem. Konačno, dovoljni uslovi za konvergenciju u vremenskom domenu predloženog ILC upravljanja su dati odgovarajućom teoremom sa pratećim dokazom.This paper provides an overview of the recently presented and published results relating to the use of iterative learning control (ILC) based on and integer and fractional order. ILC is one of the recent topics in control theories and it is a powerful control concept that iteratively improves the behavior of processes that are repetitive in nature. ILC is suitable for controlling a wider class of mechatronic systems - it is especially suitable for motion control of robotic systems that attract and hold an important position in biomechatronical, technical systems involving the application, military industry, etc. The first part of the paper presents the results relating to the application of higher integer order PD type ILC with numerical simulation. Also, another integer order ILC scheme is proposed for a given robotic system with three degrees of freedom for task-space trajectory tracking where the effectiveness of the suggested control is demonstrated through a simulation procedure. In the second part, the results related to the application of the fractional order of ILC are presented where PDα type of ILC is proposed firstly, for a fractional order linear time invariant system. It is shown that under some sufficient conditions which include the learning operators, convergence of the learning system can be guaranteed. Also, PIβDα type of ILC is suggested for a fractional order linear time delay system. Finally, sufficient conditions for the convergence in the time domain of the proposed ILC were given by the corresponding theorem together with its proof

Iterative Solution of Fractional Diffusion Equation Modelling Anomalous Diffusion

In this article, we study the fractional diffusion equation with spatial Riesz fractional derivative. The continuation of the solution of this fractional equation to the solution of the corresponding integer order equation is proved. The series solution is obtained based on properties of Riesz fractional derivative operator and utilizing the optimal homotopy analysis method (OHAM). Numerical simulations are presented to validate the method and to show the effect of changing the fractional derivative parameter on the solution behavior

An Updated Vision of Continuous-Time Fractional Models

A few days before the end of the revision procedure, my friend J. Tenreiro Machado had a sudden cardio-respiratory arrest and died. Here I want to express my gratitude and tribute to a great man and scientist. He was a very friendly and helpful person, with an unusual work capacity that allowed him to publish interesting articles on a wide range of topics.This paper presents the continuous-time fractional linear systems and their main properties. Two particular classes of models are introduced: the fractional autoregressive-moving average type and the tempered linear system. For both classes, the computations of the impulse response, transfer function, and frequency response are discussed. It is shown that such systems can have integer and fractional components. From the integer component we deduce the stability. The fractional order component is always stable. The initial-condition problem is analyzed and it is verified that it depends on the structure of the system. For a correct definition and backward compatibility with classic systems, suitable fractional derivatives are also introduced. The Grünwald-Letnikov and Liouville derivatives, as well as the corresponding tempered versions, are formulated.authorsversionpublishe

Advanced Parameterisation of Online Handwriting in Writers with Graphomotor Disabilities

Grafomotorick© obt­e (GD) vraznÄ ovlivuj­ kvalitu ivota koln­m vÄkem poÄ­naj­c, kde se vyv­jej­ grafomotorick© schopnosti, a do dchodov©ho vÄku. VÄasn diagnza tÄchto obt­­ a terapeutick zsah maj­ velk vznam k jejich zlepen­. Vzhledem k tomu, e GD souvis­ z v­cermi symptomy v oblasti kinematiky, zkladn­ kinematick© parametry jako rychlost, zrychlen­ a vih prokzaly efektivn­ kvantizaci tÄchto symptom. Objektivn­ vpoÄetn­ syst©m podpory rozhodovn­ pro identifikaci a vyeten­ GD vak nen­ dostupn. A proto je hlavn­m c­lem m© disertaÄn­ prce vzkum pokroÄil© metody parametrizace online p­sma pro analzu GD se speciln­m zamÄen­m na vyuit­ metod zlomkov©ho kalkulu. Tato prce je prvn­, kter experimentuje s vyuit­m derivac­ neceloÄ­seln©ho du (FD) pro analzu GD pomoc­ online p­sma z­skan©ho od pacient s Parkinsonovou nemoc­ a u dÄt­ koln­ho vÄku. Byla navrena a evaluovna nov metoda parametrizace online p­sma zaloena na FD vyuit­m Grnwald-Letnikova p­stupu. Bylo dokzno, e navren metoda vznamnÄ zlepuje diskriminaÄn­ s­lu a deskriptivn­ schopnosti v oblasti Parkinsonick© dysgrafie. StejnÄ tak metoda pozitivnÄ ovlivnila i nejmodernÄj­ techniky v oblasti analzy GD u dÄt­ koln­ho vÄku. Vyvinut parametrizace byla optimalizovna s ohledem na vpoÄetn­ nroÄnost (a o 80 %) a tak© na vyladÄn­ du FD. Ke konci prce byly porovnny v­cer© p­stupy vpoÄtu FD, jmenovitÄ Riemann-Liouvillv, Caputv spoleÄnÄ z Grnwald-Letnikovm p­stupem za Äelem identifikace tÄch nejvhodnÄj­ch pro jednotliv© oblasti analzy GD.Graphomotor disabilities (GD) significantly affect the quality of life beginning from the school-age, when the graphomotor skills are developed, until the elderly age. The timely diagnosis of these difficulties and therapeutic interventions are of great importance. As GD are associated with several symptoms in the field of kinematics, the basic kinematic features such as velocity, acceleration, and jerk were proved to effectively quantify these symptoms. Nevertheless, an objective computerized decision support system for the identification and assessment of GD is still missing. Therefore, the main objective of my dissertation is the research of an advanced online handwriting parametrization utilized in the field of GD analysis, with a special focus on methods based on fractional calculus. This work is the first to experiment with fractional-order derivatives (FD) in the GD analysis by online handwriting of Parkinsonâs disease (PD) patients and school-age children. A new online handwriting parametrization technique based on the Grnwald-Letnikov approach of FD has been proposed and evaluated. In the field of PD dysgraphia, a significant improvement in the discrimination power and descriptive abilities was proven. Similarly, the proposed methodology improved current state-of-the-art techniques of GD analysis in school-aged children. The newly designed parametrization has been optimized in the scope of the computational performance (up to 80 %) as well as in FD order fine-tuning. Finally, various FD-approaches were compared, namely Riemann-Liouville, Caputoâs, together with Grnwald-Letnikov approximation to identify the most suitable approach for particular areas of GD analysis.