the fredholm index of a pair of commuting operators ii this paper concerns fredholm theory in several variables and its applications to hilbert spaces of analytic functions one feature is the introduction of ideas from commutative algebra to operator theory specifically we introduce a method to calculate the fredholm index of a pair of commuting operators to achieve this we define and study the hilbert space analogs of samuel multiplicities in commutative algebra then the theory is applied to the symmetric fock space in particular our results imply a satisfactory answer to arveson s program on developing a fredholm theory for pure d contractions when d 2 including both the fredholmness problem and the calculation of indices we also show that arveson s curvature invariant is in fact always equal to the samuel multiplicity for an arbitrary pure d contraction with finite defect rank it follows that the curvature is a similarity invariant

the numerical analysis of ordinary differential equations runge kutta and general linear methods mathematical and computational introduction the euler method and its generalizations analysis of runge kutta methods general linear methods bibliography

indirect adaptive fuzzy control for a nonholonomic underactuated wheeled inverted pendulum vehicle based on a data driven trajectory planner in this study we investigate an error data based trajectory planner and indirect adaptive fuzzy control for a class of wheeled inverted pendulum vehicle systems based on the error dynamics the closed loop trajectory planner can generate the desired velocity values using the virtual acceleration input for the tilt angle subsystem composite control for the rotational and longitudinal subsystems can be constructed via indirect adaptive fuzzy and sliding mode control approaches to achieve simultaneous velocity tracking and tilt angle stabilization we rigorously prove the system stability and convergence of the tracking error signals using the lyapunov theory and lasalle s invariance theorem the results of our numerical simulations demonstrated the efficiency of the proposed control strategies and the implementations of the algorithms

invariant subspaces dilation theory and the structure of the predual of a dual algebra i on etudie la structure des preduaux d algebres d operateurs on obtient un nouveau theoreme de sous espace invariant on trouve des proprietes concernant le treillis sous espace invariant de l operateur decalage de bergman

an additive formula for samuel multiplicities on hilbert spaces of analytic functions abstract we establish a short exact sequence to relate the germ model of invariant subspaces of a hilbert space of vector valued analytic functions and the sheaf model of the corresponding coinvariant subspaces as a consequence we obtain an additive formula for samuel multiplicities as an application we give a different proof for a formula relating the fibre dimension and the samuel multiplicity which is first proved in fang 2005 11 the feature of the new proof is that the analytic arguments in fang 2005 11 are now subsumed by algebraic machinery

synthesized design of a fuzzy logic controller for an underactuated unicycle in this paper we propose synthesized design of a fuzzy logic controller flc for control of an underactuated unicycle system the flc objective is velocity control of the wheel while keeping the pendulum upright which is an unstable equilibrium the synthesized design consists of three phases first the flc structures including the number of rules membership functions inference and parametric relations are chosen based on heuristic knowledge about the unicycle second on the basis of a linearized model and linear feedback the flc output parameters are determined quantitatively for stabilization of the unicycle third the flc output parameters are tuned using an iterative learning tuning ilt algorithm which minimizes an objective function that specifies the desired unicycle performance the rationale for the synthesized flc design is full utilization of the available information which is achieved by combining model based and model free designs and hence improves the flc performance we minimize the number of flc rules and fuzzy labels six rules are used for regulation or setpoint tasks whereas 10 rules are used with extra integral control to eliminate steady state errors induced by system uncertainties and disturbances only two fuzzy labels are adopted for each fuzzy variable the ilt process consists of two phases exploration for stabilization and exploitation for better performance the effectiveness of the proposed flc is validated using intensive simulations and comparisons

design of a parallel distributed fuzzy lqr controller for the twin rotor multi input multi output system in this paper a helicopter like twin rotor multi input multi output system trms is decoupled and is fuzzy takagi sugeno modeled with the complex nonlinear functions simplified as the propositional combination of linear functions the design procedures of the fuzzy takagi sugeno model of trms are detailed based on the derived fuzzy takagi sugeno model parallel distributed fuzzy lqr controller are designed to control the positions of the pitch and yaw angles in trms the stability of the trms system with the proposed fuzzy controllers is discussed moreover simulation results are included to indicate the effectiveness of the presented parallel distributed fuzzy lqr controllers for the trms

hilbert polynomials and arveson s curvature invariant abstract we define and study hilbert polynomials for certain holomorphic hilbert spaces we obtain several estimates for these polynomials and their coefficients our estimates inspire us to investigate the connection between the leading coefficients of hilbert polynomials for invariant subspaces of the symmetric fock space and arveson s curvature invariant for coinvariant subspaces we are able to obtain some formulas relating the curvature invariant with other invariants in particular we prove that arveson s version of the gauss bonnet chern formula is true when the invariant subspaces are generated by any polynomials

stable adaptive fuzzy pd plus pi controller for nonlinear uncertain systems abstract this paper presents an improved version of the stable fuzzy adaptive control structure which comprises an approximation of the ideal controller and a supervisory controller wang 1993 2 the proposed adaptive controller cancels the nonlinear function using a fuzzy system whose inputs are the feedback error signals instead of the state variables by using the feedback errors as the inputs to the fuzzy system improved control and disturbance rejection performance may be achieved as the controller is made more sensitive to the presence of tracking errors another useful feature of this structure is that the supervisory controller can be designed without the need of prior knowledge about the plant furthermore the computational burden of on line tuning can be reduced by disabling on line adaptation without incurring stability problems the efficiency of the proposed adaptive fuzzy system is demonstrated through simulation studies

sliding mode control of underactuated multibody systems and its application to shape change control in this article we introduce an approach based on sliding mode control to design full state feedback controllers for stabilisation of underactuated non linear multibody systems we define first order sliding surfaces as a linear combination of actuated and unactuated coordinate tracking errors lyapunov stability analysis guarantees that all system trajectories reach and remain on the sliding surfaces however stability of the sliding surfaces depends on the equilibrium manifold if the system has isolated equilibrium points it is linearly controllable and asymptotic stability can be guaranteed under certain conditions otherwise the control system fails brockett s necessary condition for existence of a smooth stabilising feedback in the latter case if the total momentum is conserved the closed loop control system will be marginally stable consequently a procedure is proposed to achieve an asymptotically stable discontinuous control law through sliding surface redefinition and shape changes it i

samuel multiplicity and the structure of semi fredholm operators abstract two numerical invariants refining the fredholm index are introduced for any semi fredholm operator in such a way that their difference calculates the fredholm index these two invariants are inspired by samuel multiplicity in commutative algebra and can be regarded as the stabilized dimension of the kernel and cokernel a geometric interpretation of these invariants leads naturally to a 4 4 uptriangular matrix model for any semi fredholm operator on a separable hilbert space this model can be regarded as a refined local version of the apostol s 3 3 triangular representation for arbitrary operators some classical results such as gohberg s punctured neighborhood theorem can be read off directly from our matrix model banach space operators are also considered

parametric motion of complex time singularity toward real collapse abstract motion of complex time singularities for solutions of a system of three interacting point vortices is studied by varying initial conditions until collapse occurs when collapse occurs the complex time singularities converge to a point on the real axis a heuristic scaling law between the initial displacement of one vortex and the position of the nearest complex time singularity to the origin is tested numerically the exponent of the scaling law is related to one of the eigenvalues of the linearized stability problem for the motion of the vortices in a regularized blown up frame

a rescaling algorithm for the numerical calculation of blowing up solutions on presente un algorithme a invariance d echelle pour le calcul numerique des solutions a singularites explosives des equations d evolution non lineaires

tracing complex singularities with spectral methods abstract a numerical method for investigating the possibility of blow up after a finite time is introduced for a large class of nonlinear evolution problems with initial data analytic in the space variable s the solutions have for any t 0 complex space singularities at the edge of an analyticity strip of width t loss of regularity corresponds to the vanishing of t numerical integration by high resolution spectral methods reveals the large wavenumber behavior of the fourier transform of the solutions from which t is readily obtained its time evolution can be traced down to about one mesh length by extrapolation of t such numerical experiments provide evidence suggesting finite time blow up or all time regularity the method is tested on the inviscid and viscous burgers equations and is applied to the one dimensional nonlinear schrodinger equation with quartic potential and to the two dimensional incompressible euler equation all with periodic boundary conditions in the latter case evidence is found suggesting that existing all time regularity results can be substantially sharpened

fuzzy hierarchical swing up and sliding position controller for the inverted pendulum cart system in this paper a fuzzy hierarchical swing up and sliding position controller is proposed for the swing up and position controls of an inverted pendulum cart system the proposed fuzzy hierarchical swing up and sliding position controller includes a fuzzy switching controller a fuzzy swing up controller and a twin fuzzy sliding position controller the fuzzy switching controller is designed to smoothly switch between the swing up and position controls with the inverted pendulum cart system decomposed into a pendulum subsystem and a cart subsystem fuzzy sliding position controllers are presented to robustly balance the pendulum and cart at the desired positions the sliding mode and stability of the fuzzy sliding position control systems are guaranteed moreover an adaptive mechanism is provided to on line adjust the parameters in the fuzzy sliding position controllers simulation results are included to illustrate the effectiveness of the proposed fuzzy hierarchical swing up and sliding position controller

adaptive fuzzy logic control of dynamic balance and motion for wheeled inverted pendulums in this paper adaptive fuzzy logic control of dynamic balance and motion is investigated for wheeled inverted pendulums with parametric and functional uncertainties the proposed adaptive fuzzy logic control based on physical properties of wheeled inverted pendulums makes use of a fuzzy logic engine and a systematic online adaptation mechanism to approximate the unknown dynamics based on lyapunov synthesis the fuzzy control ensures that the system outputs track the given bounded reference signals to within a small neighborhood of zero and guarantees semi global uniform boundedness of all closed loop signals the effectiveness of the proposed control is verified through extensive simulations

h and mixed h2 h control of discrete time t s fuzzy systems with local nonlinear models abstract this paper addresses the h and mixed h 2 h control synthesis problems of nonlinear discrete time systems which are represented by a new type of t s fuzzy models the fuzzy systems consist of local nonlinear models and are with fewer fuzzy rules than the conventional t s fuzzy systems with local linear models a fuzzy control scheme with local nonlinear feedbacks is proposed and h and mixed h 2 h control synthesis conditions are given in terms of solutions to a set of linear matrix inequalities lmis in contrast to the existing conditions for designing fuzzy controllers the new ones can be used to design fuzzy controllers based on fewer control rules as well as are with less computational burden in particular the new methods can also give less conservative results a numerical example is given to illustrate the effectiveness of the proposed methods

deciphering singularities by discrete methods we consider the problem of estimating numerically the parameters of singularities of solutions of differential equations we propose a novel approach which is based on discretizing the governing equation and timestepping in the complex domain some applications to ordinary and partial differential equations are discussed