analysis of 3 d rotation fitting computational techniques for fitting a 3 d rotation to 3 d data are recapitulated in a refined form as minimization over proper rotations extending three existing methods the method of singular value decomposition the method of polar decomposition and the method of quaternion representation then we describe the problem of 3 d motion estimation in this new light finally we define the covariance matrix of a rotation and analyze the statistical behavior of errors in 3 d rotation fitting

uncertainty characterization of the orthogonal procrustes problem with arbitrary covariance matrices abstract this paper addresses the weighted orthogonal procrustes problem of matching stochastically perturbed point clouds formulated as an optimization problem with a closed form solution a novel uncertainty characterization of the solution of this problem is proposed resorting to perturbation theory concepts which admits arbitrary transformations between point clouds and individual covariance and cross covariance matrices for the points of each cloud the method is thoroughly validated through extensive monte carlo simulations and particularly interesting cases where nonlinearities may arise are further analyzed

least squares estimation of transformation parameters between two point patterns in many applications of computer vision the following problem is encountered two point patterns sets of points x sub i and x sub i i 1 2 n are given in m dimensional space and the similarity transformation parameters rotation translation and scaling that give the least mean squared error between these point patterns are needed recently k s arun et al 1987 and b k p horn et al 1987 presented a solution of this problem their solution however sometimes fails to give a correct rotation matrix and gives a reflection instead when the data is severely corrupted the proposed theorem is a strict solution of the problem and it always gives the correct transformation parameters even when the data is corrupted

indecomposable representations of the nonlinear lie algebras on the two state heisenberg weyl basis the indecomposable representations of the nonlinear lie algebras of vector type r 0 1 one of which is generated by two angular momentum operators j0 j2 and any component of an irreducible tensor operator of rank 1 t 1 0 1 of an so 3 group are studied in detail we give the explicit expressions for the infinite dimensional indecomposable representations of r which further subduce the infinite dimensional indecomposable representations on the invariant subspaces and induce the finite dimensional or infinite dimensional indecomposable irreducible representations on the quotient spaces as special cases the standard angular momentum representations of r are given also

dt refind diffusion tensor registration with exact finite strain differential in this paper we propose the dt refind algorithm for the diffeomorphic nonlinear registration of diffusion tensor images unlike scalar images deforming tensor images requires choosing both a reorientation strategy and an interpolation scheme current diffusion tensor registration algorithms that use full tensor information face difficulties in computing the differential of the tensor reorientation strategy and consequently these methods often approximate the gradient of the objective function in the case of the finite strain fs reorientation strategy we borrow results from the pose estimation literature in computer vision to derive an analytical gradient of the registration objective function by utilizing the closed form gradient and the velocity field representation of one parameter subgroups of diffeomorphisms the resulting registration algorithm is diffeomorphic and fast we contrast the algorithm with a traditional fs alternative that ignores the reorientation in the gradient computation we show that the exact gradient leads to significantly better registration at the cost of computation time independently of the choice of euclidean or log euclidean interpolation and sum of squared differences dissimilarity measure the exact gradient achieves better alignment over an entire spectrum of deformation penalties alignment quality is assessed with a battery of metrics including tensor overlap fractional anisotropy inverse consistency and closeness to synthetic warps the improvements persist even when a different reorientation scheme preservation of principal directions is used to apply the final deformations

adaptive neural tracking control for stochastic nonlinear strict feedback systems with unknown input saturation in this paper the problem of adaptive neural tracking control is considered for a class of single input single output siso strict feedback stochastic nonlinear systems with input saturation to deal with the non smooth input saturation nonlinearity a smooth nonaffine function of the control input signal is used to approximate the input saturation function classical adaptive technique and backstepping are used for control synthesis based on the mean value theorem a novel adaptive neural control scheme is systematically derived without requiring the prior knowledge of bound of input saturation it is shown that under the action of the proposed adaptive controller all the signals of the closed loop system remain bounded in probability and the tracking error converges to a small neighborhood around the origin in the sense of mean quartic value two simulation examples are provided to demonstrate the effectiveness of the presented results

barrier lyapunov functions based adaptive control for a class of nonlinear pure feedback systems with full state constraints in this study an adaptive control technique is developed for a class of uncertain nonlinear parametric systems the considered systems can be viewed as a class of nonlinear pure feedback systems and the full state constraints are strictly required in the systems one remarkable advantage is that only less adjustable parameters are used in the design this advantage is first to take into account the pure feedback systems with the full state constraints the characteristics of the considered systems will lead to a difficult task for designing a stable controller to this end the mean value theorem is employed to transform the pure feedback systems to a strict feedback structure but non affine terms still exist for the transformed systems a novel recursive design procedure is constructed to remove the difficulties for avoiding non affine terms and guarantee that the full state constraints are not violated by introducing barrier lyapunov function blf with the error variables moreover it is proved that all the signals in the closed loop system are global uniformly bounded and the tracking error is remained in a bounded compact set two simulation studies are worked out to show the effectiveness of the proposed approach

robust adaptive control of uncertain nonlinear systems in the presence of input saturation and external disturbance in this technical note we consider adaptive control of single input uncertain nonlinear systems in the presence of input saturation and unknown external disturbance by using backstepping approaches two new robust adaptive control algorithms are developed by introducing a well defined smooth function and using a nussbaum function the nussbaum function is introduced to compensate for the nonlinear term arising from the input saturation unlike some existing control schemes for systems with input saturation the developed controllers do not require assumptions on the uncertain parameters within a known compact set and a priori knowledge on the bound of the external disturbance besides showing global stability transient performance is also established and can be adjusted by tuning certain design parameters

adaptive backstepping fuzzy control for nonlinearly parameterized systems with periodic disturbances a novel function approximator is constructed by combining a fuzzy logic system with a fourier series expansion in order to model unknown periodically disturbed system functions then an adaptive backstepping tracking control scheme is developed where the dynamic surface control approach is used to solve the problem of explosion of complexity in the backstepping design procedure and the time varying parameter dependent integral lyapunov function is used to analyze the stability of the closed loop system the semiglobal uniform ultimate boundedness of all closed loop signals is guaranteed and the tracking error is proved to converge to a small residual set around the origin two simulation examples are provided to illustrate the effectiveness of the control scheme designed in this paper

the quantum group suq 2 and a q analogue of the boson operators a new realisation of the quantum group suq 2 is constructed by means of a q analogue to the jordan schwinger mapping determining thereby both the complete representation structure and q analogues to the wigner and racah operators to achieve this realisation a new elementary object is defined a q analogue to the harmonic oscillator the uncertainty relation for position and momentum in a q harmonic oscillator is quite unusual

nonlinear lie algebra and ladder operators for orbital angular momentum based on the nonlinear lie algebra a new framework is put forward to treat the problem of angular momentum from this framework the ladder operators for the orbital angular momentum can be solved as simultaneous eigenvectors of the lie derivations ad l2 and ad l2 in an operator space the ladder operators for solvable central potentials can also be found in a united way

adaptive fuzzy fault tolerant control with guaranteed tracking performance for nonlinear strict feedback systems in this study we propose two backstepping based adaptive fuzzy fault tolerant control ftc methods for a class of nonlinear strict feedback systems with actuator failures first a traditional ftc tftc method is considered our analysis shows that tftc has poor tracking performance due to the existence of approximation errors and external disturbances inspired by the idea that the magnitudes of control inputs decrease as the error of the last step decreases in the backstepping procedure we propose a new prescribed performance ftc npp ftc method based on the improved error transformation technique compared with previous methods where only the output tracking error is guaranteed within the prescribed performance bound ppb we show that the state tracking error for each step between the intermediate control and virtual control remains within the ppb regardless of actuator faults the main advantage of the npp ftc method is that the tracking errors and magnitudes of the control inputs can be reduced by adjusting the ppb parameters of the errors in the first and last steps our simulation results demonstrate the effectiveness of the proposed npp ftc method

nonlinear deformations of su 2 and su 1 1 generalizing witten s algebra nonlinear deformations of su 2 and su 1 1 involving two deforming functions f j0 and g j0 are considered for g j0 1 they reduce to some algebras first studied by polychronakos 1990 and rocek 1991 spatial emphasis is laid on the case where g j0 is a linear function of j0 it is shown that for any lambda 2 3 there exist lambda 1 parameter algebras that are deformations of su 2 or su 1 1 respectively and for which f j0 is a polynomial of degree lambda for lambda 2 such algebras are equivalent to witten s 1990 first deformation of su 2 or su 1 1 for any lambda the spectrum of j0 is exponential instead of linear as in the case where g j0 1

dynamic surface control using neural networks for a class of uncertain nonlinear systems with input saturation in this paper a dynamic surface control dsc scheme is proposed for a class of uncertain strict feedback nonlinear systems in the presence of input saturation and unknown external disturbance the radial basis function neural network rbfnn is employed to approximate the unknown system function to efficiently tackle the unknown external disturbance a nonlinear disturbance observer ndo is developed the developed ndo can relax the known boundary requirement of the unknown disturbance and can guarantee the disturbance estimation error converge to a bounded compact set using ndo and rbfnn the dsc scheme is developed for uncertain nonlinear systems based on a backstepping method using a dsc technique the problem of explosion of complexity inherent in the conventional backstepping method is avoided which is specially important for designs using neural network approximations under the proposed dsc scheme the ultimately bounded convergence of all closed loop signals is guaranteed via lyapunov analysis simulation results are given to show the effectiveness of the proposed dsc design using ndo and rbfnn

on some nonlinear extensions of the angular momentum algebra deformations of the lie algebras so 4 so 3 1 and e 3 that leave their so 3 subalgebra undeformed and preserve their coset structure are considered it is shown that such deformed algebras are associative for any choice of the deformation parameters their casimir operators are obtained and some of their unitary irreducible representations are constructed for vanishing deformation the unitary irreducible representations of the deformed algebras transform into those of the corresponding lie algebras that contain each of the so 3 unitary irreducible representations at most once it is also proved that similar deformations of the lie algebras su 3 sl 3 r and of the semidirect sum of an abelian algebra t 5 and so 3 do not lead to associative algebras

observer based fuzzy adaptive control for strict feedback nonlinear systems in this paper a new fuzzy adaptive control approach is developed for a class of siso strict feedback nonlinear systems with unmeasured states using fuzzy logic systems to approximate the unknown nonlinear functions a fuzzy adaptive observer is introduced for state estimation as well as system identification under the framework of the backstepping design fuzzy adaptive output feedback control is constructed recursively it is proven that the proposed fuzzy adaptive control approach guarantees the semi global boundedness property for all the signals and the tracking error to a small neighborhood of the origin simulation studies are included to illustrate the effectiveness of the proposed approach

disturbance observer based adaptive fuzzy control for nonlinear state constrained systems with input saturation and input delay abstract in this paper the problem of disturbance observer based adaptive fuzzy control is studied for nonlinear systems with full state constraints input constraints and unknown external disturbance compared with existing results the unknown compound disturbance is estimated by nonlinear disturbance observer ndo and the input delay is effectively processed by pade approximation different from the mean value theorem and nussbaum function method an auxiliary variable is introduced to obtain the actual control input which reduces the conservativeness of controller design in order to solve the difficulties caused by input saturation and state constraints the auxiliary design functions and barrier lyapunov functions blfs are employed respectively by utilizing adaptive backstepping technique and lyapunov stability theorem a ndo based novel controller is developed it is proved that all the signals of the closed loop systems are semi globally uniformly ultimately bounded sguub the disturbance estimation errors and the tracking errors converge on a small neighborhood of the origin and the full state constraints are not violated simulation results are provided to demonstrate the effectiveness of the proposed method

generalized deformed oscillator and nonlinear algebras the harmonic oscillator is deformed arbitrarily and the properties of the deformed oscillator algebra are studied the eigenstates and eigenvalues of the deformed oscillator are calculated this generalized deformed oscillator algebra is used to create nonlinear deformation of the classical su 2 algebra the deformed boson realizations of an arbitrary nonlinear su 2 algebra are calculated the algebra of the q deformed oscillator is a special case of the generalized deformed oscillator algebra

least squares fitting of two 3 d point sets two point sets pi and p i i 1 2 n are related by p i rpi t ni where r is a rotation matrix t a translation vector and ni a noise vector given pi and p i we present an algorithm for finding the least squares solution of r and t which is based on the singular value decomposition svd of a 3 3 matrix this new algorithm is compared to two earlier algorithms with respect to computer time requirements

fuzzy adaptive quantized output feedback tracking control for switched nonlinear systems with input quantization in this paper the problem of adaptive fuzzy quantized output feedback control is investigated for a class of uncertain switched nonlinear systems in strict feedback form the considered switched systems contain unknown nonlinearities hysteretic quantized input and without requiring the system states being available for measurement fuzzy logic systems are utilized to approximate the unknown nonlinear functions and a switched fuzzy state observer is designed to estimate the unmeasured states the hysteretic quantized input is implemented to avoid the oscillation caused by logarithmic quantizer and decomposed into two bounded nonlinear functions based on the estimated states and using the backstepping design principle an adaptive fuzzy quantized output feedback control scheme is developed it is proved that whole adaptive fuzzy quantized control scheme can guarantee that all the variables in the closed loop system are bounded under a class of switching signals with average dwell time and also that the system output can track a given reference signal as closely as possible the simulation results are given to check the effectiveness of the proposed approach

estimation of optimal fiducial target registration error in the presence of heteroscedastic noise we study the effect of point dependent heteroscedastic and identically distributed anisotropic fiducial localization noise on fiducial target registration error tre we derive an analytic expression based on the concept of mechanism spatial stiffness for predicting tre the accuracy of the predicted tre is compared to simulated values where the optimal registration transformation is computed using the heteroscedastic errors in variables algorithm the predicted values are shown to be contained by the 95 confidence intervals of the root mean square tre obtained from the simulations

first order error propagation of the procrustes method for 3d attitude estimation the well known procrustes method determines the optimal rigid body motion that registers two point clouds by minimizing the square distances of the residuals in this paper we perform the first order error analysis of this method for the 3d case fully specifying how directional noise in the point clouds affects the estimated parameters of the rigid body motion these results are much more specific than the error bounds which have been established in numerical analysis we provide an intuitive understanding of the outcome to facilitate direct use in applications

relaxed stability conditions for continuous time t s fuzzy control systems via augmented multi indexed matrix approach this paper is concerned with the problem of developing an advanced strategy to reduce the conservatism in stability analysis and control synthesis of continuous time takagi sugeno t s fuzzy systems a novel augmented multi indexed matrix approach is proposed to implement new right hand side slack variables technique for the homogenous polynomial setting combining with the finsler lemma with homogenous matrix lagrange multipliers convergent linear matrix inequality lmi relaxations for stability analysis are proposed by using the generalization of the polya theorem for the case of positive polynomials with matrix valued coefficients a new type of state feedback controller namely the homogeneous polynomially nonquadratic control law hpnqcl is developed to conceive less conservative stabilization conditions the obtained stability and stabilization conditions are further relaxed by using the proposed right hand side slack variables technique moreover the advantages over the existing control schemes are certificated in theory three numerical examples are also provided to illustrate the effectiveness of the proposed methods

barrier lyapunov functions for the control of output constrained nonlinear systems in this paper we present control designs for single input single output siso nonlinear systems in strict feedback form with an output constraint to prevent constraint violation we employ a barrier lyapunov function which grows to infinity when its arguments approach some limits by ensuring boundedness of the barrier lyapunov function in the closed loop we ensure that those limits are not transgressed besides the nominal case where full knowledge of the plant is available we also tackle scenarios wherein parametric uncertainties are present asymptotic tracking is achieved without violation of the constraint and all closed loop signals remain bounded under a mild condition on the initial output furthermore we explore the use of an asymmetric barrier lyapunov function as a generalized approach that relaxes the requirements on the initial conditions we also compare our control with one that is based on a quadratic lyapunov function and we show that our control requires less restrictive initial conditions a numerical example is provided to illustrate the performance of the proposed control