Sharif Digital Repository

This paper studies unamped oscillations of fractional-order Duffing system. Stability theorems for fractional order systems are used to determine the characteristic polynomial of the system in order to find the parametric ranges for undamped oscillations in this system. We also derive relations for estimating the frequency and the amplitude of the oscillations in this system using a describing function method. Finally numerical simulation results are provided to justify the analysis  

This paper studies fractional-order systems of retarded type with two independent delays, and determines the stability regions in spaces of delays. In this approach, an auxiliary polynomial is employed to calculate all purely imaginary roots of the characteristic equation of the system on the imaginary axis. Since roots of the characteristic equation are continuous with respect to delays, these purely imaginary roots determine the stability regions in delay space. Also, the necessary and sufficient condition for stability independent of delays is developed for the systems. Furthermore, a simple inequality constraint is established to obtain pure imaginary poles of the scalar systems.... 

This paper deals with a refined analysis and modification of existing results on the flocking algorithms proposed for the second order dynamic agents. In the present work, the limiting condition of ever connectivity is removed and it is proved that the flocking can be reached if only the union of the network proximity graphs during nonoverlapping time intervals becomes connected frequently enough. Also, it is proved that including a static virtual leader cannot model the group objective of achieving the desired velocity and it will stop eventually at a predefined point in the space. The convergence rate to this fixed point is determined too. The last contribution of this paper is definition... 

A fractional order PID controller is designed to stabilize fractional delay systems with commensurate orders and multiple commensurate delays, where the time delays in the system may belong to several distinct intervals. Moreover, the controller parameters should belong to given intervals. In order to stabilize the system, the D-subdivision method is employed to choose the stabilizing set of the controller parameters from their available values. Furthermore, the nearest values of the obtained stabilizing set to their mean values are selected as the controller parameters so that a non-fragile controller is concluded. Two numerical examples evaluate the proposed control design method  

The practicality of robust model predictive control of systems with model uncertainties depends on the time consumed for solving a defined optimization problem. This paper presents a method for the computational complexity reduction in a robust model predictive control. First a scaled state vector is defined such that the objective function contours in the defined optimization problem become vertical or horizontal ellipses or circles, and then the control input is determined at each sampling time as a state feedback that minimizes the infinite horizon objective function by solving some linear matrix inequalities. The simulation results show that the number of iterations to solve the problem... 

This paper deals with the synchronization of two Lur'e differential inclusions containing sector nonlinearity. Lyapunov stability theorem is employed to design the control inputs. The controllers are designed considering three important practical features in physical systems. First, differential equation part of the Lur'e differential inclusion is assumed to be convex. Second, it is presumed that parameters of the Lur'e differential inclusion are not completely known. Third, sector nonlinearities are considered on control inputs applied to the Lur'e differential inclusions. To assess performance and effectiveness of the proposed controllers, synchronization of two rotor dynamic systems is... 

This paper studies flocking algorithms for multi-agent systems with directed switching velocity interaction topologies. It is assumed that the position information of each agent is available for agents within its neighborhood region of radius r, however, they communicate the velocity information between each other through unidirectional links modeled by a particular class of directed topologies. A new energy function is defined to analyze the global stability and a sufficient condition is derived for asymptotic flocking in the face of switching topologies. The proposed control strategy guarantees the achievement of desired formations, while avoiding collisions among agents. It also ensures... 

In this paper, three fundamental properties of a potential field-based flocking algorithm, i.e. merging of neighbouring graphs during the system evolution, collision avoidance and convergence of position of the centre of mass of informed agents to that of virtual leader are discussed. Next, these properties are utilized to determine required number of informed agents based on initial position of uninformed ones and consequently reduce the domain of search in optimization problems defined for finding the optimal number of required informed agents. Finally, a new optimization framework is proposed, which benefits Voronoi diagrams in order to reduce the number of informed agents required for... 

In this study, a fractional-order adaptive-sliding mode control (SMC) scheme is proposed to stabilise commensurate fractional-order polytopic non-linear differential inclusion systems containing sector and dead-zone nonlinearities in the control inputs and unknown bounded disturbances. The suggested control method is composed of fractional-order sliding surfaces, adaptive-SMC inputs and adaptation laws for unknown bounds of disturbances. The Lyapunov stability theorem is used to prove the stability of the closed-loop system. A practical system and two numerical examples are simulated to show the effectiveness and performance of the proposed control technique  

The undamped oscillations of a scalar fractional neutral system are studied in this paper. For this purpose, it is proved that this kind of systems can have the oscillatory behavior. The necessary and sufficient condition is proposed to determine that there exists a delay value for which the system oscillates. The frequency, amplitude and required delay for the undamped oscillations depend on the fractional order. However, the behavior of dependencies is not specified. Indeed, when the system has oscillatory behavior, it is bounded-input bounded-output stable for delay less than the required delay. Moreover, when the order is approaching to an integer value, the necessary and sufficient... 

In this paper, we propose and analyze flocking algorithms in a network of second-order agents with bounded control inputs and nonlinear intrinsic dynamics. We consider a general switching network topology, for velocity information exchange, rather than undirected or fixed directed network topology with a directed spanning tree. The proposed adaptive controller architecture applies a leader-following strategy in which the pinning scheme is defined based on the interaction topology. Finally, some examples are presented to illustrate the theoretical results  

In a multi-agent system, the number and initial position of informed agents play a major role in the convergence of uninformed agents. In this paper, three different patterns of informed agents' initial positions are studied to see how the convergence percentage can be affected by the number of informed agents. The proposed initial locations are intuitive and inferred from the collective behavior in humans. To evaluate efficiency of the proposed methods and to compare them from different points of view, large number of computer simulations is performed and results are analyzed  

This paper considers flocking to the virtual leader in network of agents with double-integrator. A locally linear algorithm is employed which guarantees exponential flocking to the virtual leader. A lower bound for flocking rate is calculated which is independent of the initial conditions. Simulations are provided to validate the result and it is shown that the calculated rate is not over bound the actual convergence rate. The effect of coefficients of algorithm is investigated and it is shown that the similar results can be inferred from the calculated formula for the convergence rate. Copyright  

This paper presents a new method for assessing the bounded input bounded output stability of a class of fractional delay systems with commensurate orders and multiple commensurate delays of retarded type. In the proposed method, first, by mapping the principal sheet of the Riemann surface and a pseudo-delay transformation, an auxiliary polynomial is generated. Then, this auxiliary polynomial is employed to find roots of the characteristic equation on the imaginary axis. The properties of the root path close to these roots are used to identify intervals of delay values, in which the system is stable. The obtained results are illustrated via some numerical examples  

Five different approaches are presented to assign characteristic ratios for commensurate fractional order systems having order in (0,0.5]. Through the indirect methods, a closed-loop or plant transfer function is converted to a commensurate order one with an order greater than 0.5 so that the previously designed CRA method by the authors is applicable. The first method among the proposed direct ones is based on increasing the order of the desired closed-loop transfer function that allows the employment of positive characteristic ratios. In the second method the closed-loop response is sped up by augmenting an appropriate zero. The final method uses negative characteristic ratios to reach the... 

This paper considers a closed-loop system consisting of a fractional/integer order system and a fractional PID controller. Assuming that the uncertain coefficients of the fractional PID controller lie in some known intervals independently (i.e. that controller is a member of an interval family), the paper presents some easy to use theorems to investigate the robust bounded-input bounded-output stability of the resultant closed-loop system. Moreover, a finite frequency bound required in drawing the related graphs has also been provided. Finally, some numerical examples are presented to illustrate the results  

The time delay equations are frequently used to model real systems since they can describe the after-effect phenomenon. It is usually difficult to analyze the properties of time delay systems. Thus it would be beneficial to make the systems as simple as possible. For this purpose, the decomposition of the systems into some separate or cascaded sub-systems with smaller dimension is introduced as the solution of the mentioned complex task. The decomposition of the time delay systems with one delay is directly related to simultaneous similarity of two matrices. In this regard, necessary and sufficient conditions are derived for the existence of a common similar block diagonal or triangular form... 

This paper deals with the existence and the characteristics of the limit cycles in the fractional-order Arneodo system. The analysis is done using the describing function method. Our focus is on a special case where two limit cycles exist. The parametric range for the case of interest is derived, and the frequency and the amplitude of the oscillation are predicted. Numerical simulation results are presented to further demonstrate the reliability of the analysis  

In this paper, we develop control algorithms for addressing second-order consensus problems in intrinsically second-order nonlinear multi-agent dynamical systems with switching topologies. The proposed adaptive controller applies a leader-following strategy in which all agents are assumed to be informed of the leader's state. Another feature of this work which specifically distinguishes it from others is that the proposed controller uses undirected and directed graphs to accommodate for a full range of possible graph information topologies without limitations of bidirectional communication  

In this paper, we present sufficient conditions to address a larger class of digraphs, including balanced ones, whose members' Laplacian (L) makes L 1L + LTL1 to be positive semi-definite, where L1 is the Laplacian associated with a fully connected equally-edged weighted graphs. This property can be later utilized to introduce an appropriate energy function for stability analysis of flocking algorithms in a larger class of networks with switching directed information flow. Also, some of their properties are investigated in the line of matrix theory and graph theory