Higher Order Derivative Information Research Articles

Multilevel Latent Differential Structural Equation Model with Short Time Series and Time-Varying Covariates: A Comparison of Frequentist and Bayesian Estimators

Continuous-time modeling using differential equations is a promising technique to model change processes with longitudinal data. Among ways to fit this model, the Latent Differential Structural Equation Modeling (LDSEM) approach defines latent derivative variables within a structural equation modeling (SEM) framework, thereby allowing researchers to leverage advantages of the SEM framework for model building, estimation, inference, and comparison purposes. Still, a few issues remain unresolved, including performance of multilevel variations of the LDSEM under short time lengths (e.g., 14 time points), particularly when coupled multivariate processes and time-varying covariates are involved. Additionally, the possibility of using Bayesian estimation to facilitate the estimation of multilevel LDSEM (M-LDSEM) models with complex and higher-dimensional random effect structures has not been investigated. We present a series of Monte Carlo simulations to evaluate three possible approaches to fitting M-LDSEM, including: frequentist single-level and two-level robust estimators and Bayesian two-level estimator. Our findings suggested that the Bayesian approach outperformed other frequentist approaches. The effects of time-varying covariates are well recovered, and coupling parameters are the least biased especially using higher-order derivative information with the Bayesian estimator. Finally, an empirical example is provided to show the applicability of the approach.

Generalized Eigenvalue Proximal Support Vector Machine for Functional Data Classification

Functional data analysis has become a research hotspot in the field of data mining. Traditional data mining methods regard functional data as a discrete and limited observation sequence, ignoring the continuity. In this paper, the functional data classification is addressed, proposing a functional generalized eigenvalue proximal support vector machine (FGEPSVM). Specifically, we find two nonparallel hyperplanes in function space, a positive functional hyperplane, and a functional negative hyperplane. The former is closest to the positive functional data and furthest from the negative functional data, while the latter has the opposite properties. By introducing the orthonormal basis, the problem in function space is transformed into the ones in vector space. It should be pointed out that the higher-order derivative information is applied from two aspects. We apply the derivatives alone or the weighted linear combination of the original function and the derivatives. It can be expected that to improve the classification accuracy by using more data information. Experiments on artificial datasets and benchmark datasets show the effectiveness of our FGEPSVM for functional data classification.

Inverse dynamics of parallel manipulators in the presence of drive singularities

At drive singularities of parallel manipulators the actuators lose control of the end-effector in certain directions. It is shown that if certain conditions related to the consistency of the dynamic equations are satisfied by a proper design of the trajectory, the manipulator can pass through the singular positions while the actuator forces and the system motion remain stable. To find the values of the actuator forces in the neighborhood of the drive singularities, the dynamic equations are modified by using higher order derivative information.

INVERSE DYNAMICS CONTROL OF CONSTRAINED ROBOTS IN THE PRESENCE OF JOINT FLEXIBILITY

An inverse dynamics control algorithm for constrained flexible-joint robots is developed. It is shown that in a flexible-joint robot, the acceleration level inverse dynamic equations are singular because of the elastic media. Implicit numerical integration methods that account for the higher order derivative information are utilized for solving the singular set of differential equations. The control law proposed linearizes and decouples the system and achieves simultaneous and asymptotically stable trajectory tracking control of the end-effector motion and contact forces. Together with the integrators for improving robustness due to modelling errors and disturbances, a fifth order position error dynamics and a third order contact force error dynamics are obtained. A 3R spatial robot with all joints flexible is simulated to illustrate the performance of the method.

Stability of control forces in redundant multibody systems

In this paper inverse dynamics of redundant multibody systems using a minimum number of control forces is formulated. It is shown that the control forces and the task accelerations may become noncausal at certain configurations, yielding the dynamical equation set of the system to be singular. For a given set of tasks, each different set of actuators leads to a different system motion and also to different singular configurations. To avoid the singularities in the numerical solution, the dynamical equations are modified in the neighborhoods of the singular configurations by utilizing higher order derivative information. The modification is made easier by transforming the equations of motion to the null space of the control force direction matrix. The conditions for the existence of solution are also discussed. A redundant planar manipulator is analyzed to illustrate the methods proposed.

Open-loop flexibility control in multibody systems dynamics

In this paper inverse dynamics of flexible multibody systems for the realization of the prescribed motion tasks is formulated. The number of actuators is equal to the dimension of the task space which is usually equal to the rigid body degrees of freedom. Since the control forces and the prescribed accelerations are noncausal due to the elastic media, the dynamical equation set of the system becomes singular. To avoid the singularities in the numerical solution higher order derivative information are utilized. The conditions for the existence of solution and for the control force directions are also presented. A flexible manipulator is analyzed to illustrate the methods proposed.

An Interior-Point Algorithm for Linearly Constrained Optimization

This paper describes an algorithm for optimization of a smooth function subject to general linear constraints. An algorithm of the gradient projection class is used, with the important feature that the “projection” at each iteration is performed by using a primal–dual interior-point method for convex quadratic programming. Convergence properties can be maintained even if the projection is done inexactly in a well-defined way. Higher-order derivative information on the manifold defined by the apparently active constraints can be used to increase the rate of local convergence.