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

Advanced fractional order modeling and control of dynamics of complex systems: recent results

In this presentation, we provide some applications of memristors and mem-systems with a particular focus on electromechanical systems and analogies that holds great promise for advanced modeling and control of complex objects and processes. In science and engineering, the ideas and concepts developed in one branch of science and engineering are often transferred to other branches. In addition to the analogy between mechanical and electrical systems, it was observed that phenomena from other physical domains exhibit similar properties, [1]. Representative example is nonlinear element -memristor which was postulated by Chua in 1971 [1] by analyzing mathematical relations between pairs of fundamental circuit variables. Besides, the relation between current and voltage which defines a memristive system, the relation between charge and voltage also specifies a memcapacitive system, and the flux-current relation gives rise to a meminductive system [2]. Here, we give a short review of available mem-systems integer order. In addition, important property of fractional operators is that they capture the history of all past events which means that fractional order systems [3] have intrinsically a memory of the previous dynamical evolution. Particularly, we present the connection between fractional order differintegral operators and behavior of the mem-systems which can be used for modeling dynamics of complex systems. Several potential applications of electromechanical analogies of integer and fractional order are discussed. Further, we investigate and suggest an open-closed-loop P/PDalpha type iterative learning control (ILC) [4] of fractional order singular complex system [5]. Particularly, we discuss fractional order linear singular systems in pseudo state space form. Sufficient conditions for the convergence in time domain of the proposed fractional order ILC for a class of fractional order singular system are given by the corresponding theorem together with its proof. Finally, numerical example is presented to illustrate the effectiveness of the proposed open-closed ILC scheme of fractional order for a class of fractional order singular complex system

Closed-loop iterative learning control for fractional-order linear singular time-delay system: PDα-type

U ovom radu razmatrano je iterativno upravljanje učenjem u zatvorenoj petlji (ILC) - PDα tip linearnim singularnim sistemom sa kašnjenjem necelog reda. Dati su dovoljni uslovi za konvergenciju u vremenskom domenu predloženog PD-alfa tipa ILC za datu klasu linearnog singularnog sistema sa kašnjenjem necelog reda zajedno sa odgovarajućom teoremom i dokazom. Takođe, po prvi put je u ovom radu predloženi tip PDα ILC primenjen za datu klasu linearnih singularnih sistema sa kašnjenjem necelog reda sa neizvesnošću. Konačno, valjanost predloženog ILC algoritma upravljanja za razmatranu klasu singularnih sistema je potvrđena sa adekvatnom numeričkom simulacijom.In this paper a closed-loop PDα - type iterative learning control (ILC) of fractional order linear singular time-delay system is considered. The sufficient conditions for the convergence in time domain of the proposed PD-alpha type ILC for a class of fractional order singular system are given by the corresponding theorem together with its proof. Also, for the first time, we proposed a proposed ILC PDα type for a given class of uncertain, fractional order, singular systems. Finally, the validity of the proposed PDα ILC scheme for a class of fractional order singular time-delay system is verified by a numerical example

Hyperspectral Unmixing Overview: Geometrical, Statistical, and Sparse Regression-Based Approaches

Imaging spectrometers measure electromagnetic energy scattered in their instantaneous field view in hundreds or thousands of spectral channels with higher spectral resolution than multispectral cameras. Imaging spectrometers are therefore often referred to as hyperspectral cameras (HSCs). Higher spectral resolution enables material identification via spectroscopic analysis, which facilitates countless applications that require identifying materials in scenarios unsuitable for classical spectroscopic analysis. Due to low spatial resolution of HSCs, microscopic material mixing, and multiple scattering, spectra measured by HSCs are mixtures of spectra of materials in a scene. Thus, accurate estimation requires unmixing. Pixels are assumed to be mixtures of a few materials, called endmembers. Unmixing involves estimating all or some of: the number of endmembers, their spectral signatures, and their abundances at each pixel. Unmixing is a challenging, ill-posed inverse problem because of model inaccuracies, observation noise, environmental conditions, endmember variability, and data set size. Researchers have devised and investigated many models searching for robust, stable, tractable, and accurate unmixing algorithms. This paper presents an overview of unmixing methods from the time of Keshava and Mustard's unmixing tutorial [1] to the present. Mixing models are first discussed. Signal-subspace, geometrical, statistical, sparsity-based, and spatial-contextual unmixing algorithms are described. Mathematical problems and potential solutions are described. Algorithm characteristics are illustrated experimentally.Comment: This work has been accepted for publication in IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensin

Fractional-order iterative learning control for singular fractional- order system: (P) - PDa type

Iterativno upravljanje putem učenja (ILC) predstavlja jedno od važnih oblasti u teoriji upravljanja i pogodno je za upravljanje šire klase mehatroničkih sistema, a posebno su pogodni za upravljanje kretanjem robotskih sistema. Ovaj se rad bavi problemom primene frakcionog reda ILC upravljanja za singularne sisteme frakcionog reda. Posebno, ovde se proučavaju singularni sistemi necelog reda u prostoru pseduo-stanja. U povratnoj sprezi frakcionog reda PDa tip ILC upravljanje za singularni sistem frakcionog reda je istraživano. Takođe, frakcionog reda P-PDa tip ILC upravljanje u direktnoj-povratnoj sprezi je razmatrano. Dovoljni uslovi za konvergenciju u vremenskom domenu predloženih šema ILC upravljanja su data odgovarajućim teoremama i koja su dokazana. Konačno, numeričke simualcije na primer pokazuje izvodljivost i efikasnost predloženog pristupa.Iterative learning control (ILC) is one of the recent topics in control theories and it is suitable for controlling a wider class of mechatronic systems - it is especially suitable for the motion control of robotic systems. This paper addresses the problem of application of fractional order ILC for fractional order singular system. Particularly, we study fractional order singular systems in the pseudo-state space. An closed-loop fractional order PDalpha type ILC of the fractional-order singular system is investigated. Also, open-closed loop of the fractional order P-PDa type ILC is considered. Sufficient conditions for the convergence in the time domain of the proposed ILC schemes are given by the corresponding theorems and proved. Finally, numerical simulations show the feasibility and effectiveness of the proposed approach