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JACOBIAN MATRIX AND p-BASIS

open access: yesJACOBIAN MATRIX AND p-BASIS
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Toeplitz Jacobian Matrix for Nonlinear Periodic Vibration

Journal of Applied Mechanics, 1995
The main difference between a linear system and a nonlinear system is in the non-uniqueness of solutions manifested by the singular Jacobian matrix. It is important to be able to express the Jacobian accurately, completely, and efficiently in an algorithm to analyze a nonlinear system.
Leung, A. Y. T., Ge, T.
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Approximate Jacobian robot control with adaptive Jacobian matrix

42nd IEEE International Conference on Decision and Control (IEEE Cat. No.03CH37475), 2004
In this paper, we present approximate Jacobian feedback control laws for setpoint control of robot with uncertain kinematics from joint space to task space. An adaptive law is proposed to update the approximate Jacobian matrix to improve the performance.
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Network Observability Analysis Through Measurement Jacobian Matrix Reduction

IEEE Power Engineering Review, 1987
A method of observability analysis for the state estimation in power systems is presented. The method is based on a symbolic reduction of the measurement Jacobian matrix without its actual computation. The algorithm is characterized as being extremely simple and fast.
Ilya W. Slutsker, Jon M. Scudder
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A Random Matrix Approach to Manipulator Jacobian

Volume 3: Nonlinear Estimation and Control; Optimization and Optimal Control; Piezoelectric Actuation and Nanoscale Control; Robotics and Manipulators; Sensing; System Identification (Estimation for Automotive Applications, Modeling, Therapeutic Control in Bio-Systems); Variable Structure/Sliding-Mode Control; Vehicles and Human Robotics; Vehicle Dynamics and Control; Vehicle Path Planning and Collision Avoidance; Vibrational and Mechanical Systems; Wind Energy Systems and Control, 2013
Traditional kinematic analysis of manipulators, built upon a deterministic articulated kinematic modeling often proves inadequate to capture uncertainties affecting the performance of the real robotic systems. While a probabilistic framework is necessary to characterize the system response variability, the random variable/vector based approaches are ...
Javad Sovizi   +2 more
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