Sharif Digital Repository

The main point of this paper is to present a time domain strategy for drug dosage to treat psychiatric disorders. A time domain model of emotion is obtained from an extension of a recently developed fractional nonlinear dynamic model of happiness. First, the Fractional Optimal Control law for incommensurate multi state systems is obtained. It will be then applied as an optimal drug administration procedure in the line of psychiatric disorders treatment. Results of this paper show that optimal control scheme is a proper approach to face the difficulties of analysis and control the incommensurate systems. It can be also clearly seen from the simulation results that this approach is very... 

The main purpose of this paper is to use variational calculus and Pontryagin's minimum principle to propose a solution scheme for time optimal control problem stated on the fractional systems defined in the sense of Caputo. After deriving the necessary optimality conditions, a novel numerical solution is used to solve the problem. Afterwards, a simple case study shows the effectiveness of the proposed method. © 2017  

When an integer order linear time invariant system possesses unrepeated pure imaginary poles it can generate oscillatory response which is represented by invariant closed contours in the phase plane. In linear time invariant fractional order systems with the same property, due to their special characteristics, this behavior will be more complicated and the contours would not be invariant. In this paper we will investigate the behavior of fractional order systems under such conditions  

In this paper, a chaos-based communication system in the presence of unknown transmission delay is studied. First, under master/slave configurations, two chaotic Chen systems as the slaves are synchronized with a master one via unidirectional coupling. Then at the transmitter, information of an image is embedded within a slave-one signal and the resultant signal along with another one which is used to determine the transmission delay is transmitted to the receiver. At the receiver, using the received signals and the slave-two counterpart signal, the image is recovered. The performance of the proposed method is experimentally illustrated  

In this paper, the behavior of a fractional order Van der Pol-like oscillator is investigated using a describing function method. A parametric function for the boundary between oscillatory and nonoscillatory regions of this system is extracted. The analytical results are evaluated by numerical simulations which demonstrate sufficient reliability of the proposed analyzing method  

In this paper, issues related to the identifiability of a fractional order system having its input and output frequency contents are discussed. The effects of the commensurate order α in the identifiability of the model structure and model parameters are analytically studied. It is shown that both identifiabilities (model structure and model parameters) are reduced remarkably for smaller values of α. This phenomenon is observed even though the input signals are rich enough and system belongs to the model set. Our understanding is that the problem arises since differences among different members of the model set fall beyond the practically recognizable precision range. The issue is more... 

This paper deals with a new fractional calculus based method to stabilize fixed points of single-input 3D systems. In the proposed method, the control signal is determined by fractional order integration of a linear combination of the system linearized model states. The tuning rule for this method is based on the stability theorems in the incommensurate fractional order systems. The introduced technique can be used in suppression of chaotic oscillations. To evaluate the performance of the proposed technique in practical applications, it has been experimentally applied to control chaos in two chaotic circuits  

A simple fractional differentiator-based controller is proposed to suppress chaos in a 3D single input chaotic system by stabilizing some of the fixed points. The tuning procedure for the proposed controller is based on the stability concepts in the incommensurate fractional order systems. To show the efficiency of the controller, some numerical simulations are given. Also, to evaluate the practical capability of the proposed controller, we experimentally apply it to control chaos in a chaotic circuit. Moreover, some mathematical analyses are presented to show the applicability of the proposed controller, when its structure is not exactly implementable. © Birkhäuser Boston 2009  

Synchronization of two coupled Chen systems through one of their variables is experimentally studied in this paper. We explore the chaotic behavior of the rescaled Chen system by the bifurcation analysis and computing its Lyapunov exponents which these results are also verified by circuitry realization of the system. Also, using 0-1 test, the chaotic manner of the circuit signals is validated. Finally, we synchronize two Chen circuits using unidirectional continues coupling with only one state variable and show despite the presence of the noise and the fact that two implemented circuits are not completely identical; the circuits achieve complete synchronization. © ICROS  

This paper proposes a fractional order controller to stabilize saddle points of index 2 in a chaotic system. The proposed controller has a simple structure and can be tuned to stabilize fixed points when unstructured norm bounded perturbations exist on the model of the chaotic system. Numerical simulations confirm the ability of the controller to stabilize the fixed points in uncertain chaotic systems. Also, to illustrate the practical capability of the proposed controller, it is experimentally applied to control chaos in a chaotic circuit. © IMechE 2008  

This paper studies the robust stability of the fractional-order (FO) LTI systems with polytopic uncertainty. Generally, the characteristic polynomial of the system dynamic matrix is not an affine function of the uncertain parameters. Consequently, the robust stability of the uncertain system cannot be evaluated by well-known approaches including LMIs or exposed edges theorem. Here, an over-parameterization technique is developed to convert the main characteristic polynomial into a set of local over-parameterized characteristic polynomials (LOPCPs). It is proved that the robust stability of LOPCPs implies the robust stability of the uncertain system. Then, an algorithm is proposed to explore... 

This paper presents two different stabilization methods based on the fractional-calculus theory. The first method is proposed via using the fractional differentiator, and the other is constructed based on using the fractional integrator. It has been shown that the proposed techniques can be used to suppress chaotic oscillations in 3-D chaotic systems. To show the practical capability of the methods, some experimental results on the control of chaos in chaotic circuits are presented. © 2008 IEEE  

In this paper, we address global non-fragile control and synchronization of a new fractional order chaotic system. First we inspect the chaotic behavior of the fractional order system under study and also find the lowest order (2.49) for the introduced dynamics to remain chaotic. Then, a necessary and sufficient condition which can be easily extended to other fractional-order systems is proposed in terms of Linear Matrix Inequality (LMI) to check whether the candidate state feedback controller with parameter uncertainty can guarantee zero convergence of error or not. In addition, the proposed method provides a global zero attraction of error that guarantees stability around all existing... 

Control input energy efficiency is an important issue which should be considered in designing any control system. Due to the importance of this subject, in the present paper fractional order control systems are studied in the viewpoint of control input energy efficiency. In this study, the divergent terms of the control input energy function of fractional order control systems are obtained. It is shown that these terms have a significant role in the amount of the energy injected to the plant by the controller. Finally, two examples are provided to demonstrate the usefulness of the presented results in the paper  

In this paper, the concept of minimal state space realization for a fractional order system is defined from the inner dimension point of view. Some basic differences of the minimal realization concept in the fractional and integer order systems are discussed. Five lower bounds are obtained for the inner dimension of a minimal state space realization of a fractional order transfer function. Also, the concept of optimal realization, which can be a helpful concept in practice, is introduced for transfer functions having rational orders. An algorithm is suggested to obtain the optimal realizations of rational order transfer functions. The introduced concept might be used to get minimal... 

In this paper, firstly a four-parameter fractional order model structure is introduced to approximate processes having S-shaped step responses. Three different strategies are presented in order to determine the parameters of the proposed model. In a special case where the proposed model is not satisfactory, another fractional order model structure with five free parameters is introduced to improve the model approximation. Also in this case, a procedure is provided to estimate the parameters of the introduced five-parameter model. Then, some common classical integer order control design approaches are modified or extended to their fractional order counterparts in order to incorporate the... 

This paper deals with the stabilization of the feasible equilibrium point of a special class of nonlinear quadratic systems known as Lotka-Volterra (LV) systems, in the presence of interval uncertainty via a fixed linear state feedback (FLSF). It is well known that for a linear time-invariant system with interval uncertainty, stability at the vertices of a polytope implies stability in the interior of the whole polytope. It has been shown that this idea can be extended to examine the stability of LV systems in the presence of interval uncertainty, recently. In fact, it has been proved that in spite of nonlinear nature of the system, stability at a special vertex guarantees stability at all... 

In this paper, relation between the inner dimension of a fractional order LTI system and the maximum number of frequencies which exist in oscillations generated by the system is investigated. The considered system is defined in pseudo state space form and the orders of its involved fractional derivatives are rational numbers between zero and one. First, an upper bound is derived for the maximum number of frequencies. Then, using the restricted difference bases concept, a new method is introduced to design a multifrequency oscillatory fractional order system. Finally, based on the proposed method some lower bounds are derived for the maximum number of frequencies obtainable in solutions of a... 

This paper deals with a fractional calculus based control strategy for chaos suppression in the 3D chaotic systems. It is assumed that the structure of the controlled chaotic system has only one control input. In the proposed strategy, the controller has three tuneable parameters and the control input is constructed as fractional-order integration of a linear combination of linearized model states. The tuning procedure is based on the stability theorems in the incommensurate fractional-order systems. To evaluate the performance of the proposed controller, the design method is applied to suppress chaotic oscillations in a 3D chaotic oscillator and in the Chen chaotic system. © 2008 Springer...