non self adjoint hamiltonians defined by riesz bases we discuss some features of non self adjoint hamiltonians with real discrete simple spectrum under the assumption that the eigenvectors form a riesz basis of hilbert space among other things we give conditions under which these hamiltonians can be factorized in terms of generalized lowering and raising operators

brief paper adaptive control in robotic systems with h tracking performance the problem of the adaptive model reference tracking control with a guaranteed h performance is solved for rigid robotic systems with unknown parameters and external disturbances a novel model for disturbance signals is introduced to improve the ability of disturbance rejection in the proposed robotic adaptive tracking control design the proposed h adaptive tracking control design consists of an adaptive disturbance attenuation algorithm and an adaptive internal model compensation algorithm so that the tracking error can asymptotically converge to zero in the presence of disturbances the proposed h adaptive tracking control is smooth as well as global and suitable for practical robotic control design finally a simulation example is given to exhibit the tracking performance of a two link robotic manipulator with the proposed h adaptive control algorithm

non self adjoint hamiltonians defined by generalized riesz bases bagarello inoue and trapani j math phys 55 033501 2014 investigated some operators defined by the riesz bases these operators connect with quasi hermitian quantum mechanics and its relatives in this paper we introduce a notion of generalized riesz bases which is a generalization of riesz bases and investigate some operators defined by the generalized riesz bases by changing the frameworks of the operators defined in the work of bagarello inoue and trapani

regular biorthogonal pairs and pseudo bosonic operators the first purpose of this paper is to show a method of constructing a regular biorthogonal pair based on the commutation rule ab ba i for a pair of operators a and b acting on a hilbert space h with inner product here sequences n and n in a hilbert space h are biorthogonal if n m nm n m 0 1 and they are regular if both d span n and d span n are dense in h indeed the assumptions to construct the regular biorthogonal pair coincide with the definition of pseudo bosons as originally given in f bagarello pseudobosons riesz bases and coherent states j math phys 51 023531 2010 furthermore we study the connections between the pseudo bosonic operators a b a b and the pseudo bosonic operators defined by a regular biorthogonal pair n n and an onb e of h in h inoue general theory of regular biorthogonal pairs and its physical applications e print arxiv math ph 1604 01967 the second purpose is to define and study the notion of d p

composite learning from adaptive dynamic surface control in the conventional adaptive control a stringent condition named persistent excitation pe must be satisfied to guarantee parameter convergence this technical note focuses on adaptive dynamic surface control for a class of strict feedback nonlinear systems with parametric uncertainties where a novel technique coined composite learning is developed to guarantee parameter convergence without the pe condition in the composite learning online recorded data together with instantaneous data are applied to generate prediction errors and both tracking errors and prediction errors are utilized to update parametric estimates the proposed approach is also extended to an output feedback case by using a nonlinear separation principle the distinctive feature of the composite learning is that parameter convergence can be guaranteed by an interval excitation condition which is much weaker than the pe condition such that the control performance can be improved from practical asymptotic stability to practical exponential stability an illustrative example is used for verifying effectiveness of the proposed approach

stability and exponential stability of an adaptive control scheme for plants of any relative degree relying on a new adaptive pole assignment control scheme for plants with unknown relative degree and uncertain order which can be made minimum phase by means of a relative degree one first order parallel compensator a new adaptation mechanism is proposed in this note in order to tackle with the problem of the attainment of an exponentially stable behavior of the output error in particular the connection between exponential stability and persistent excitation is outlined and a complete stability analysis is performed

hamiltonians defined by biorthogonal sets in some recent papers studies on biorthogonal riesz bases have found renewed motivation because of their connection with pseudo hermitian quantum mechanics which deals with physical systems described by hamiltonians that are not self adjoint but may still have real point spectra also their eigenvectors may form riesz not necessarily orthonormal bases for the hilbert space in which the model is defined those riesz bases allow a decomposition of the hamiltonian as already discussed in some previous papers however in many physical models one has to deal not with orthonormal bases or with riesz bases but just with biorthogonal sets here we consider the more general concept of quasi basis and we show a series of conditions under which a definition of non self adjoint hamiltonian with purely point real spectra is still possible

tracking for fully actuated mechanical systems a geometric framework we present a general framework for the control of lagrangian systems with as many inputs as degrees of freedom relying on the geometry of mechanical systems on manifolds we propose a design algorithm for the tracking problem the notions of error function and transport map lead to a proper definition of configuration and velocity error these are the crucial ingredients in designing a proportional derivative feedback and feedforward controller the proposed approach includes as special cases a variety of results on control of manipulators pointing devices and autonomous vehicles our design provides particular insight into both aerospace and underwater applications where the configuration manifold is a lie group

brief paper composite adaptive control for euler lagrange systems with additive disturbances in a typical adaptive update law the rate of adaptation is generally a function of the state feedback error ideally the adaptive update law would also include some feedback of the parameter estimation error the desire to include some measurable form of the parameter estimation error in the adaptation law resulted in the development of composite adaptive update laws that are functions of a prediction error and the state feedback in all previous composite adaptive controllers the formulation of the prediction error is predicated on the critical assumption that the system uncertainty is linear in the uncertain parameters lp uncertainty the presence of additive disturbances that are not lp would destroy the prediction error formulation and stability analysis arguments in previous results in this paper a new prediction error formulation is constructed through the use of a recently developed robust integral of the sign of the error rise technique the contribution of this design and associated stability analysis is that the prediction error can be developed even with disturbances that do not satisfy the lp assumption e g additive bounded disturbances a composite adaptive controller is developed for a general mimo euler lagrange system with mixed structured i e lp and unstructured uncertainties a lyapunov based stability analysis is used to derive sufficient gain conditions under which the proposed controller yields semi global asymptotic tracking experimental results are presented to illustrate the approach

symmetries first integrals and the inverse problem of lagrangian mechanics deals with the following question given a symmetry vector field y of a system of second order ordinary differential equations and an associated constant of the motion f is it possible to find a lagrangian l for the system such that y becomes a noether symmetry with respect to l and f its implied noether constant for one degree of freedom systems the answer to this question is affirmative in addition attention is paid to the construction of a suitable constant of the motion f for given symmetry y and vice versa several examples are discussed

pt symmetric quantum mechanics this paper proposes to broaden the canonical formulation of quantum mechanics ordinarily one imposes the condition h h on the hamiltonian where represents the mathematical operation of complex conjugation and matrix transposition this conventional hermiticity condition is sufficient to ensure that the hamiltonian h has a real spectrum however replacing this mathematical condition by the weaker and more physical requirement h h where represents combined parity reflection and time reversal pt one obtains new classes of complex hamiltonians whose spectra are still real and positive this generalization of hermiticity is investigated using a complex deformation h p2 x2 ix e of the harmonic oscillator hamiltonian where e is a real parameter the system exhibits two phases when e 0 the energy spectrum of h is real and positive as a consequence of pt symmetry however when 1 e 0 the spectrum contains an infinite number of complex eigenvalues and a finite number of real positive eigenvalues b

modular adaptive control of uncertain euler lagrange systems with additive disturbances a novel adaptive nonlinear control design is developed which achieves modularity between the controller and the adaptive update law modularity between the controller update law design provides flexibility in the selection of different update laws that could potentially be easier to implement or used to obtain faster parameter convergence and or better tracking performance for a general class of linear in the parameters lp uncertain euler lagrange systems subject to additive bounded non lp disturbances the developed controller uses a model based feedforward adaptive term in conjunction with the recently developed robust integral of the sign of the error rise feedback term modularity in the adaptive feedforward term is made possible by considering a generic form of the adaptive update law and its corresponding parameter estimate this generic form of the update law is used to develop a new closed loop error system and stability analysis that does not depend on nonlinear damping to yield the modular adaptive control result

energy based approach to sliding composite adaptive control for rigid robots with finite error convergence time in this paper a terminal sliding mode adaptive control scheme for robotic manipulators designed following an energybased approach is presented the control comprises two basic terms a composite adaptive term which implements a feedback law for compensating the modelled dynamics and a non linear sliding mode term for overcoming the unmodelled dynamics and perturbations the resulting closed loop system is proved to be stable and it is also shown that the trajectory tracking error converges to zero in finite time moreover an upper bound of this error convergence time is calculated finally the design is evaluated by means of simulations

general theory of regular biorthogonal pairs and its physical operators in this paper we introduce a general theory of regular biorthogonal sequences and its physical operators biorthogonal sequences n and n in a hilbert space h are said to be regular if span n and span n are dense in h the first purpose is to show that there exists a non singular positive self adjoint operator tf in h defined by an orthonormal basis onb f fn in h such that n tffn and n tf 1fn n 0 1 and such an onb f is unique the second purpose is to define and study the lowering operators af and bf the raising operators bf and af and the number operators nf and nf determined by the non singular positive self adjoint operator tf these operators connect with quasi hermitian quantum mechanics and its relatives this paper clarifies and simplifies the mathematical structure of this framework and minimizes the required assumptions

brief paper adaptive inverse dynamics control of robots with uncertain kinematics and dynamics it has been about two decades since the first globally convergent adaptive tracking controller was derived for robots with dynamic uncertainties however not until recently has the problem of concurrent adaptation to both the kinematic and dynamic uncertainties found its solution this adaptive controller belongs to passivity based control though passivity based controllers have many attractive properties in general they are not able to guarantee the uniform performance of the robot over the entire workspace even in the ideal case of perfect knowledge of the manipulator parameters the closed loop system remains nonlinear and coupled thus the closed loop tracking performance is difficult to quantify while the inverse dynamics controllers can overcome these deficiencies therefore in this work we will develop a new adaptive jacobian tracking controller based on the inverse manipulator dynamics using the lyapunov approach we have proved that the end effector motion tracking errors converge asymptotically to zero simulation results are presented to show the performance of the proposed controller

an improved dynamic neurocontroller based on christoffel symbols in this paper a dynamic neurocontroller for positioning of robots based on static and parametric neural networks nns has been developed this controller is based on christoffel symbols of first kind in order to carry out coriolis centripetal matrix structural properties of robots and kronecker product has been taken into account to develop nns to approximate nonlinearities the weight updating laws have been obtained from a nonlinear strategy based on lyapunov energy that guarantees both stability and boundedness of signals and weights the nn weights are tuned online with no offline learning phase and are initialized to zero the neurocontroller improves the implementation with respect to other dynamic nns used in the literature

adaptive vision based control of a motor toggle mechanism simulations and experiments the dynamic motion of an adaptive visual servoing feedback controlled punching machine which is made up by a toggle mechanism driven by a permanent magnet pm synchronous servomotor is studied numerically and experimentally first hamilton s principle lagrange multiplier geometric constraints and partitioning method are employed to derive its dynamic equations for numerical simulations to satisfy the demand of the machine performance adaptive controller by using stability analysis with inertia related lyapunov function is designed to control the slider responses different from the previous studies the vision servo system of a non contact measurement of a charge coupled device ccd camera is employed to measure the shape patterns as output states instead of using the expensive linear scale or encoder of the motor mechanism system finally the stable and robust control performances of an adaptive controller by the lyapunov stable theory for a motor toggle mechanism with external disturbances are proposed a combination of the visual servoing measurement system and the motion control system are established experimentally for the motor toggle mechanism system from the agreements between numerical simulations and experimental results it is demonstrated that the proposed controller by use of machine vision is robust to external disturbances for a punching machine system

trajectory tracking control of port controlled hamiltonian systems via generalized canonical transformations this paper addresses trajectory tracking control of port controlled hamiltonian systems via generalized canonical transformations and passivity based control the main strategy adopted in this paper is to construct an error system which describes the dynamics of the tracking error by a passive port controlled hamiltonian system after obtaining the error system tracking control of the original system can be achieved by stabilizing the error system via passivity based approach first a fundamental framework is provided for constructing the error system via generalized canonical transformations then a concrete design procedure is derived for a class of electro mechanical systems furthermore the proposed method is applied to a magnetic levitation system and laboratory experiments demonstrate its effectiveness

an indirect adaptive robot controller abstract indirect adaptive control of robot manipulators represents an approach parallel to direct and composite adaptive methods this paper develops a new globally convergent indirect adaptive controller which requires neither measurements of joint acceleration nor inversion of the estimated inertia matrix several aspects of this paper such as new parameter estimators with desirable properties and a physically based technique for guaranteeing the uniform positive definiteness of the estimated inertia matrix along with the related convexity proof are also of interest in their own right

moyal products a new perspective on quasi hermitian quantum mechanics the rationale for introducing non hermitian hamiltonians and other observables is reviewed and open issues identified we present a new approach based on moyal products to compute the metric for quasi hermitian systems this approach is not only an efficient method of computation but also suggests a new perspective on quasi hermitian quantum mechanics which invites further exploration in particular we present some first results which link the berry connection and curvature to non perturbative properties and the metric

adaptive control for robot manipulators using discrete time identification an adaptive control scheme is proposed for rigid link robots where the control signal computations are performed continuously and the control coefficient computations are performed in discrete time a global boundedness result is established for the resulting scheme independent of the sampling rate it is also shown that the position velocity and acceleration tracking errors are of the order of the sampling period furthermore it is shown that if the reference trajectory is persistently exciting in a continuous time sense then for a sufficiently fast sampling rate the tracking errors decay to zero

non self adjoint hamiltonians defined by sesquilinear forms and their physical applications in this paper we introduce a theory of sesquilinear forms with respect to a non self adjoint hamiltonian and its physical operators in particular we discuss some features of non self adjoint operators and sesquilinear forms which are defined starting from biorthogonal sequences that are not riesz bases generalized riesz systems d quasi bases and d e quasi bases

composite adaptive control of robot manipulators abstract adaptive control of linear time invariant single input single output systems has been extensively studied and a number of globally convergent controllers have been derived while extensions of the results to non linear or multivariable systems have rarely been achieved similar global convergence properties can indeed be obtained in the case of robot manipulators an important and unique class of non linear multi input multi output dynamic systems based on the observation that the parameter uncertainty is reflected in both the tracking error in joint motion and the prediction error in the joint torques or the power input we recently proposed a new class of adaptive robot controllers the parameter adaptation of which is driven by both tracking error and prediction error in this paper following a brief review of our earlier globally convergent direct adaptive controller we provide a detailed analysis of these composite adaptive controllers results on global asymptotic and exponential tracking convergence are established and confirmed by simulation

exponential convergence of adaptive identification and control algorithms output and equation error adaptive identification algorithms are shown to be exponentially convergent under a deterministic or stochastic persistently exciting or spanning condition on the system inputs together with several other standard conditions an adaptive control algorithm is shown to be exponentially convergent under a deterministic or stochastic persistently exciting condition on the reference trajectory together with some standard conditions

the algorithm for computing nonmonic second order multivariable systems abstract an efficient method for computing impulse response matrices of nonmonic multivariable second order systems is proposed a procedure has been developed which uses some properties of regular matrix polynomials p s s 2 a 2 sa 1 a 0 with a 2 identically singular an algorithm suitable for computer use is established and its applications can be effectively controlled via the newly introduced special graphical scheme it produces simultaneously the adjoint and determinant of the matrix polynomial p s and avoids the inversion of any matrix moreover all computations can be performed on constant matrices and coefficients only it is shown that substantial economy may be achieved in computation time and storage when solving large order problems characteristic of many physical plants and engineering structures

generalized swanson models and their solutions we analyse a class of non hermitian quadratic hamiltonians which are of the form where are real constants with and and are generalized creation and annihilation operators respectively thus these hamiltonians may be classified as generalized swanson models it is shown that the eigenenergies are real for a certain range of values of the parameters a similarity transformation mapping the non hermitian hamiltonian h to a hermitian one h is also obtained it is shown that h and h share identical energies as explicit examples the solutions of a couple of models based on the trigonometric rosen morse i and the hyperbolic rosen morse ii type potentials are obtained we also study the case where the non hermitian hamiltonian is symmetric

basic definition and properties of bessel multipliers this paper introduces the concept of bessel multipliers these operators are defined by a fixed multiplication pattern which is inserted between the analysis and synthesis operators the proposed concept unifies the approach used for gabor multipliers for arbitrary analysis synthesis systems which form bessel sequences like wavelet or irregular gabor frames the basic properties of this class of operators are investigated in particular the implications of summability properties of the symbol for the membership of the corresponding operators in certain operator classes are specified as a special case the multipliers for riesz bases are examined and it is shown that multipliers in this case can be easily composed and inverted finally the continuous dependence of a bessel multiplier on the parameters i e the involved sequences and the symbol in use is verified using a special measure of similarity of sequences

second order consensus of networked thrust propelled vehicles on directed graphs this technical note addresses the second order consensus problem of multiple underactuated thrust propelled vehicles tpvs on directed graphs containing a directed spanning tree we propose an adaptive control approach to resolve this problem and the proposed controller does not rely on the commonly used backstepping methodology and the exact knowledge of the mass properties of the tpvs in addition the resultant complexity is reduced and the requirement on the interaction graph is relaxed using an input output analysis we show that the proposed controller realizes second order consensus of the tpvs i e the position and velocity consensus errors between the tpvs converge to zero and moreover the velocities of the tpvs converge to the weighted average of their initial values the performance of the proposed control approach is shown by a numerical simulation

application of the hamilton jacobi method to linear nonconservative vibration theory in this paper it is shown how linear strictly nonconservative oscillatory systems with one and many degrees of freedom may be analyzed by application of the theory of hamilton and jacobi

biorthogonal vectors sesquilinear forms and some physical operators continuing the analysis undertaken in previous articles we discuss some features of non self adjoint operators and sesquilinear forms which are defined starting from two biorthogonal families of vectors like the so called generalized riesz systems enjoying certain properties in particular we discuss what happens when they forms two d quasi bases

dealing with time varying parameter problem of robot manipulators performing path tracking tasks using the properties of the element by element or hadamard product of matrices the authors obtain the robot dynamics in parameter isolated form from which a new control scheme is developed the controller proposed yields zero asymptotic tracking errors when applied to robotic systems with time varying parameters by using a switching type control law the results obtained are global in the initial state of the robot and can be applied to rapidly varying systems

brief paper tracking and disturbance rejection for fully actuated mechanical systems in this paper we solve the tracking and disturbance rejection problem for fully actuated passive mechanical systems we assume that the reference signal r and its first two derivatives r r are available to the controller and the disturbance signal d can be decomposed into a finite superposition of sine waves of arbitrary but known frequencies and an arbitrary l 2 signal we combine the internal model principle with the ideas behind the slotine li adaptive controller the internal model based adaptive controller that we propose causes the closed loop state trajectories to be bounded and the tracking error and its derivative to converge to zero without any prior knowledge of the plant parameters an important part of our results is that we prove the existence and uniqueness of the state trajectories of the closed loop system

space of state vectors in symmetric quantum mechanics the space of states of symmetric quantum mechanics is examined the requirement that eigenstates with different eigenvalues must be orthogonal leads to the conclusion that eigenfunctions belong to a space with an indefinite metric self consistent expressions for the probability amplitude and the average value of operator are suggested further specification of the space of state vectors yields a superselection rule redefining the notion of the superposition principle an expression for the probability current density satisfying the equation of continuity and vanishing for the bound state is proposed

composite model reference adaptive control with parameter convergence under finite excitation a new parameter estimation method is proposed in the framework of composite model reference adaptive control for improved parameter convergence without persistent excitation the regressor filtering scheme is adopted to perform the parameter estimation with signals that can be obtained easily a new framework for residual signal construction is proposed the incoming data are first accumulated to build the information matrix and then its quality is evaluated with respect to a chosen measure to select and store the best one the information matrix is built to have full rank after sufficient but not persistent excitation in this way the exponential convergence of both tracking error and parameter estimation error can be guaranteed without persistent oscillation in the external command which drives the system numerical simulations are performed to verify the theoretical findings and to demonstrate the advantages of the proposed adaptation law over the standard direct adaptation law

prediction error based adaptive jacobian tracking of robots with uncertain kinematics and dynamics in this note we have proposed a prediction error based adaptive jacobian controller to solve the problem of concurrent adaptation to both uncertain kinematics and dynamics this controller is composed of a modified computed torque controller and two cushion floor least square estimators and in ideal case of perfect knowledge of the robot parameters it leads to linear and decoupled error dynamics the kinematic and dynamic parameters adaptations are driven by prediction errors using input output stability analysis we show that the end effector motion tracking errors converge asymptotically we have also derived an alternative adaptive jacobian controller that does not require the invertibility of the estimated inertia matrix simulation results are presented to show the performance of the proposed controllers

hybrid adaptive fuzzy identification and control of nonlinear systems we present a combined direct and indirect adaptive control scheme for adjusting an adaptive fuzzy controller and adaptive fuzzy identification model parameters first using adaptive fuzzy building blocks with a common set of parameters we design and study an adaptive controller and an adaptive identification model that have been proposed for a general class of uncertain structure nonlinear dynamic systems we then propose a hybrid adaptive ha law for adjusting the parameters the ha law utilizes two types of errors in the adaptive system the tracking error and the modeling error performance analysis using a lyapunov synthesis approach proves the superiority of the ha law over the direct adaptive da method in terms of faster and improved tracking and parameter convergence furthermore this is achieved at negligible increased implementation cost or computational complexity we prove a theorem that shows the properties of this hybrid adaptive fuzzy control system i e bounds for the integral of the squared errors and the conditions under which these errors converge asymptotically to zero are obtained finally we apply the hybrid adaptive fuzzy controller to control a chaotic system and the inverted pendulum system

lyapunov design for convergence rate improvement in adaptive control this note deals with the improvement of the convergence rate and robust properties in an adaptive error model a new adaptive control algorithm is presented which includes both the estimate of the prediction error to drive the parameter adaptation and the proportional integral or integral relay adjustment law to prevent unbounded growth of feedback gains a least squares gain update is used the adaptive controller is constructed using measurements of state variables only the design is based on the lyapunov function method and a new general form of the lyapunov function was found as a result exponential convergence of the lyapunov function in the presence of persistent excitation is obtained

transition elements for a non hermitian quadratic hamiltonian the non hermitian quadratic hamiltonian h a a a2 a 2 is analyzed where a and a are harmonic oscillator creation and annihilation operators and and are real constants for the case that 2 4 0 it is shown using operator techniques that the hamiltonian possesses real and positive eigenvalues a generalized bogoliubov transformation allows the energy eigenstates to be constructed from the algebra and states of the harmonic oscillator the eigenstates are shown to possess an imaginary norm for a large range of the parameter space finding the orthonormal dual space allows the inner product to be redefined using the complexification procedure of bender et al for non hermitian hamiltonians transition probabilities governed by h are shown to be manifestly unitary when the complexification procedure is followed a specific transition element between harmonic oscillator states is evaluated for both the hermitian and non hermitian cases to identify the differences in time evolution

adaptive visual tracking for robotic systems without image space velocity measurement in this paper we investigate the visual tracking problem for robotic systems without image space velocity measurement simultaneously taking into account the uncertainties of the camera model and the manipulator kinematics and dynamics we propose a new image space observer that exploits the image space velocity information contained in the unknown kinematics upon which we design an adaptive controller without using the image space velocity signal where the adaptations of the depth rate independent kinematic parameter and depth parameter are driven by both the image space tracking errors and observation errors the major superiority of the proposed observer based adaptive controller lies in its simplicity and the separation of the handling of multiple uncertainties in visually servoed robotic systems thus avoiding the overparametrization problem of the existing work using lyapunov analysis we demonstrate that the image space tracking errors converge to zero asymptotically the performance of the proposed adaptive control scheme is illustrated by a numerical simulation