implicit finite difference approximation for time fractional diffusion equations time fractional diffusion equations are used when attempting to describe transport processes with long memory where the rate of diffusion is inconsistent with the classical brownian motion model in this paper we develop an implicit unconditionally stable numerical method to solve the one dimensional linear time fractional diffusion equation formulated with caputo s fractional derivative on a finite slab several numerical examples of interest are also included

brief paper spacecraft coordination control in 6dof integrator backstepping vs passivity based control in this paper we present three nonlinear control solutions for 6dof spacecraft formation control adopted from euler lagrange system theory the quaternion parametrization results in dual equilibrium points in the closed loop system and the controllers are proved to render these uniformly asymptotically stable we also present a theoretical comparison of the three control solutions together with simulation results to visualize the performance of the controllers

asymptotic stabilization of passive systems without damping injection a sampled integral technique passivity in physical systems is a restatement of energy balancing and therefore is a ubiquitous property in engineering applications under some weak conditions the unique equilibrium state of passive systems is stable however to ensure asymptotic stability strict output passivity and a detectability property are required although strict output passivity may be enforced via a damping injection that feeds back the passive output this signal may be noisy or unmeasurable the paradigmatic example being velocity in mechanical systems in this paper a sampled integral stabilization sis technique for the asymptotic regulation of passive systems that requires only the knowledge of the time integral of the passive output i e position in mechanical systems is proposed as a generalization of the previous result it is shown that sis is applicable to cascade connections of passive systems measuring only the storage function of the second one several examples including a planar elbow manipulator and the rigid body dynamics are shown to satisfy the assumptions for the application of sis

application of subival in solving initial value problems with fractional derivatives abstract the application of a numerical method for the approximation of the fractional derivative in riemann liouville and caputo definitions in initial value problems is discussed the method previously known as the subinterval based method is now referred to by its acronym subival for simpler future references it is dependent on subinterval partitions performed according to a proposed algorithm interpolations using selected time axis nodes i e nodes where solutions have been computed and analytical monomial integrodifferentiation formulae two exemplary circuit problems have been introduced as a test for the method these problems have analytical solutions available in literature the evaluations of these solutions have been compared with results obtained through an adaptive step size predictor corrector scheme where the core computations relied on the proposed numerical method subival has been implemented into an activex dynamic link library dll the paper contains instructions on how the predictor corrector algorithm can be implemented into a computer algebra system where the subival library is applied for the fractional derivative approximation examples of this are given in the form of scripts in matlab and mathematica these scripts generally allow to solve systems of fractional order state equations to which the introduced circuit examples can be brought to

fractional pseudospectral integration differentiation matrix and fractional differential equations abstract in this paper we present a new pseudospectral integration matrix which can be used to compute n f o l d integrals of function f for any n r also it can be used to calculate the derivatives of f for any non integer order 1 1 less computational complexity and programming much higher rate in running calculating the integral derivative of fractional order and its extraordinary accuracy are advantages of this method in comparison with other known methods we apply two approaches by using this matrix to solve some fractional differential equations with high accuracy some numerical examples are presented

numerical computation of sign indefinite linear quadratic differential games for weakly coupled large scale systems in this paper n player linear quadratic differential games that are sign indefinite for infinite horizon weakly coupled large scale systems are discussed after establishing the asymptotic structure and local uniqueness of the solution for cross coupled sign indefinite algebraic riccati equations csare a new algorithm for solving csare is provided it is shown that the proposed algorithm attains linear convergence moreover in order to reduce the computational workspace the recursive algorithm is combined finally a high order approximation strategy based on the proposed iterative solutions is described as a result it was recently proved that the numerical strategy achieves a high order approximation of the equilibrium value as another important feature when the small parameters are unknown a parameter independent strategy is developed

congestion control as a stochastic control problem with action delays we consider the design of explicit rate based congestion control for high speed communication networks and show that this can be formulated as a stochastic control problem where the controls of different users enter the system dynamics with different delays we discuss the existence derivation and the structure of the optimal controller as well as of suboptimal controllers of the certainty equivalent type a terminology that is precisely defined in the paper for the specific context of the congestion control problem considered we consider in particular two certainty equivalent controllers which are easy to implement and show that they are stabilizing i e they lead to bounded infinite horizon average cost and stable queue dynamics further these controllers perform well in simulations

a topological obstruction to continuous global stabilization of rotational motion and the unwinding phenomenon we show that a continuous dynamical system on a state space that has the structure of a vector bundle on a compact manifold possesses no globally asymptotically stable equilibrium this result is directly applicable to mechanical systems having rotational degrees of freedom in particular the result applies to the attitude motion of a rigid body in light of this result we explain how attitude stabilizing controllers obtained using local coordinates lead to unwinding instead of global asymptotic stability

analytical solution of a time fractional navier stokes equation by adomian decomposition method abstract the aim of the present analysis is to apply adomian decomposition method for the solution of a time fractional navier stokes equation in a tube by using an initial value the explicit solution of the equation has been presented in the closed form and then its numerical solution has been represented graphically the present method performs extremely well in terms of efficiency and simplicity

high order finite element methods for time fractional partial differential equations the aim of this paper is to develop high order methods for solving time fractional partial differential equations the proposed high order method is based on high order finite element method for space and finite difference method for time optimal convergence rate o dt 2 a n r is proved for the r 1 th order finite element method r 2

robust control for nonlinear systems using passivity based robust right coprime factorization the robust control for nonlinear feedback system with unknown perturbations is discussed based on the robust right coprime factorization and passivity property firstly based on passivity property the right factorization of the perturbed plant is realized secondly a robust control scheme is proposed considering the tracking property for the nonlinear system with nominal plant and perturbed plant finally we show the connection between the passivity and robust right coprime factorization for the obtained nonlinear system a numerical example is given to show the effectiveness of the proposed design scheme

unit dual quaternion based feedback linearization tracking problem for attitude and position dynamics abstract this paper provides a unified solution for the attitude and position tracking problem of a rigid body in 3 dimensional space using the concept of the unit dual quaternion the error dynamics described by a unit dual quaternion are deduced after the dual quaternion based dynamics of a single rigid body are given then by utilizing the feedback linearization principle a unit dual quaternion based tracker is proposed based on the error dynamics which is proven to render the equilibrium point of the closed loop system asymptotically stable and includes the attitude and position regulation problems as particular cases furthermore to solve the two equilibria problem a switching parameter is introduced to improve the tracker which causes the system to converge to the nearer equilibrium with a shorter path both the trackers uniquely deal with the rotational and translational dynamics simultaneously with non singularity and maintain the interconnection between rotation and translation finally the proposed control schemes with applications to the regulation problem and the tracking problem are simulated to illustrate the theoretical results

solving the time fractional diffusion equation via sinc haar collocation method expanding the approximation with the elements of sinc and haar functions an efficient algorithm with exponential convergence rate computational speed is high due to using the haar operational matrices to improve the accuracy by increasing the number of collocation points the present study investigates the sinc haar collocation method for the solution of the time fractional diffusion equation the advantages of this technique are that not only the convergence rate of sinc approximation is exponential but the computational speed also is high due to the use of the haar operational matrices this technique is used to convert the problem to the solution of linear algebraic equations via expanding the required approximation based on the elements of sinc functions in space and haar functions in time with unknown coefficients the effectiveness of the proposed method is examined by comparing the numerical results with the exact solutions

finite difference spectral approximations for the time fractional diffusion equation in this paper we consider the numerical resolution of a time fractional diffusion equation which is obtained from the standard diffusion equation by replacing the first order time derivative with a fractional derivative of order a with 0 a 1 the main purpose of this work is to construct and analyze stable and high order scheme to efficiently solve the time fractional diffusion equation the proposed method is based on a finite difference scheme in time and legendre spectral methods in space stability and convergence of the method are rigourously established we prove that the full discretization is unconditionally stable and the numerical solution converges to the exact one with order o dt 2 a n m where dt n and m are the time step size polynomial degree and regularity of the exact solution respectively numerical experiments are carried out to support the theoretical claims

on the stability and stabilization of quaternion equilibria of rigid bodies we study attitude control of rigid bodies on quaternion coordinates under three mathematically different perspectives depending on how the system dynamics are assumed to evolve in the first case we suppose that one equilibrium point is chosen a priori and a continuous controller is used under the assumption that the rigid body always spins in the same direction in the second case we relax the assumption that the sense of rotation is constant finally a third scenario is considered in which hybrid switching control is used to choose the direction in which to spin that is both equilibria are continuously considered with regard to less energy consumption it is showed that each of three scenarios must be treated in a different theoretical setting a comparative study in simulations is also provided

rigid body attitude stabilization with attitude and angular rate constraints abstract in this paper a solution to the problem of rest to rest three axis attitude reorientation of a fully actuated rigid body under multiple attitude constraint zones and angular velocity limits is presented based on the unit quaternion parameterized attitude constrained zones a quadratic potential function is developed with a global minimum locating at the desired attitude and high potential closing to the constrained zones in addition to limit the magnitude of the angular velocity another logarithmic potential function is also designed using these two potential functions and sliding mode control technique a nonlinear attitude control law is obtained to guarantee asymptotic convergence of the closed loop system with consideration of attitude and angular rate constraints and external disturbances the effectiveness of the constrained attitude control method is demonstrated through numerical simulation

haar wavelet operational matrix of fractional order integration and its applications in solving the fractional order differential equations haar wavelet operational matrix has been widely applied in system analysis system identification optimal control and numerical solution of integral and differential equations in the present paper we derive the haar wavelet operational matrix of the fractional order integration and use it to solve the fractional order differential equations including the bagley torvik ricatti and composite fractional oscillation equations the results obtained are in good agreement with the existing ones in open literatures and it is shown that the technique introduced here is robust and easy to apply

finite time output feedback position and attitude tracking of a rigid body the position and attitude tracking of a rigid body without velocity measurements is addressed dual quaternions are used to describe the coupled rotational and translational motions of the rigid body yielding compact forms of the kinematics and dynamics suitable for control law synthesis an output feedback pose position and attitude tracking controller is then designed by integrating techniques from passivity and homogeneity more precisely a passivity enabling auxiliary system is proposed to provide necessary damping instead of velocity feedback and a homogeneous method is used to ensure finite time convergence the proposed controller guarantees uniform almost global finite time stability of the closed loop system and produces a well defined vector field on the attitude configuration manifold thus avoiding the unwinding phenomenon moreover it can be split to obtain velocity free controllers with finite time convergence for the cases of translation only or rotation only control numerical examples verify the effectiveness of the proposed method

asymptotic solutions to weakly coupled stochastic teams with nonclassical information the authors develop a new iterative approach toward the solution of a class of two agent dynamic stochastic teams with nonclassical information when the coupling between the agents is weak either through the state dynamics or through the information channel in each case the weak coupling is characterized in terms of a small perturbation parameter when this parameter value say in is set equal to zero the original fairly complex dynamic team with a nonclassical information pattern is decomposed into or converted to relatively simple stochastic control or team problems the solution of which makes up the zeroth order approximation in a function space to the team optical solution of the original problem the fact that the zeroth order solution approximates the optimal cost up to at least o in is shown it is also shown that approximations of all orders can be obtained by solving a sequence of stochastic control and or simpler team problems

analytical approximate solution for fractional heat like and wave like equations with variable coefficients using the decomposition method abstract the time fractional heat like and wave like equations with variable coefficients are obtained by replacing the first order and second order time derivative by a fractional derivative of order 0 2 the applications of the decomposition method were extended to derive analytical solutions in the form of a series with easily computed terms for these generalized fractional equation some examples are presented to show the efficiency and simplicity of the method

comparison between the homotopy perturbation method and the variational iteration method for linear fractional partial differential equations in this article the homotopy perturbation method proposed by j h he is adopted for solving linear fractional partial differential equations the fractional derivatives are described in the caputo sense comparison of the results obtained by the homotopy perturbation method with those obtained by the variational iteration method reveals that the present methods are very effective and convenient

numerical solution of stochastic nash games with state dependent noise for weakly coupled large scale systems abstract this paper discusses the infinite horizon stochastic nash games with state dependent noise after establishing the asymptotic structure along with the positive semidefiniteness for the solutions of the cross coupled stochastic algebraic riccati equations csares a new algorithm that combines newton s method with two fixed point algorithms for solving the csares is derived as a result it is shown that the proposed algorithm attains quadratic convergence and the reduced order computations for sufficiently small parameter e as another important feature the high order approximate strategy that is based on the iterative solutions is proposed using such strategy the degradation of the cost functional is investigated finally in order to demonstrate the efficiency of the proposed algorithms computational examples are provided

the sinc collocation method for solving the thomas fermi equation a numerical technique for solving nonlinear ordinary differential equations on a semi infinite interval is presented we solve the thomas fermi equation by the sinc collocation method that converges to the solution at an exponential rate this method is utilized to reduce the nonlinear ordinary differential equation to some algebraic equations this method is easy to implement and yields very accurate results

a novel method for nonlinear fractional partial differential equations combination of dtm and generalized taylor s formula in this article a novel numerical method is proposed for nonlinear partial differential equations with space and time fractional derivatives this method is based on the two dimensional differential transform method dtm and generalized taylor s formula the fractional derivatives are considered in the caputo sense several illustrative examples are given to demonstrate the effectiveness of the present method results obtained using the scheme presented here agree well with the analytical solutions and the numerical results presented elsewhere results also show that the numerical scheme is very effective and convenient for solving nonlinear partial differential equations of fractional order

large population cost coupled lqg problems with nonuniform agents individual mass behavior and decentralized varepsilon nash equilibria we consider linear quadratic gaussian lqg games in large population systems where the agents evolve according to nonuniform dynamics and are coupled via their individual costs a state aggregation technique is developed to obtain a set of decentralized control laws for the individuals which possesses an epsiv nash equilibrium property a stability property of the mass behavior is established and the effect of inaccurate population statistics on an isolated agent is also analyzed by variational techniques