• Journal of the Korean Mathematical Society
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• v.60 no.2
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• pp.375-393
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• 2023

Rabinowitz action functional is the Lagrange multiplier functional of the negative area functional to a constraint given by the mean value of a Hamiltonian. In this note we show that on a symplectization there is a one-to-one correspondence between gradient flow lines of Rabinowitz action functional and gradient flow lines of the restriction of the negative area functional to the constraint. In the appendix we explain the motivation behind this result. Namely that the restricted functional satisfies Chas-Sullivan additivity for concatenation of loops which the Rabinowitz action functional does in general not do.

• Journal of Mechanical Science and Technology
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• v.16 no.8
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• pp.1072-1078
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• 2002

The constrained motion requires the determination of constraint force acting on unconstrained systems for satisfying given constraints. Most of the methods to decide the force depend on numerical approaches such that the Lagrange multiplier method, and the other methods need vector analysis or complicated intermediate process. In 1992, Udwadia and Kalaba presented the generalized inverse method to describe the constrained motion as well as to calculate the constraint force. The generalized inverse method has the advantages which do not require any linearization process for the control of nonlinear systems and can explicitly describe the motion of holonomically and/or nongolonomically constrained systems. In this paper, an explicit equation to describe the constrained motion is derived by minimizing the performance index, which is a function of constraint force vector, with respect to the constraint force. At this time, it is shown that the positive-definite weighting matrix in the performance index must be the inverse of mass matrix on the basis of the Gauss's principle and the derived differential equation coincides with the generalized inverse method. The effectiveness of this method is illustrated by means of two numerical applications.

• Journal of Sensor Science and Technology
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• v.28 no.2
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• pp.81-87
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• 2019

One of the major issues in inertial and magnetic measurement unit (IMMU)-based 3D orientation estimation is compensation for magnetic disturbances in magnetometer signals, as the magnetic disturbance is a major cause of inaccurate yaw estimation. In the proposed approach, a kinematic constraint is used to provide a measurement equation in addition to the accelerometer and magnetometer signals to mitigate the disturbance effect on the orientation estimation. Although a Kalman filter (KF) is the most popular framework for IMMU-based orientation estimation, a complementary filter (CF) has its own advantages over KF in terms of mathematical simplicity and ease of implementation. Accordingly, this paper introduces a quaternion-based CF with a constraint-combined correction equation. Furthermore, the weight of the constraint relative to the magnetometer signal is adjusted to adapt to magnetic environments to optimally deal with the magnetic disturbance. In the results of our validation experiments, the average and maximum of yaw errors were $1.17^{\circ}$ and $1.65^{\circ}$ from the proposed CF, respectively, and $8.88^{\circ}$ and $14.73^{\circ}$ from the conventional CF, respectively, showing the superiority of the proposed approach.

• IEMEK Journal of Embedded Systems and Applications
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• v.8 no.2
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• pp.111-119
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• 2013

This paper proposes one method on photometric stereo calibration using the constraint on light source directions in which the light sources have the unknown tilt and slant angles but the slant angles are the same. First, the constraint is analyzed based on the equation of linear ambiguity which leads to the conclusion that another constraint should be added to solve the calibration completely. Later, the combination of constraint on light source directions and the constraint that there exists at least six surface patches having known albedos is exploited to resolve the linear ambiguity up to an accurate and close-form solution. The effective performance of the proposed method is demonstrated through experiment results.

• Proceedings of the IEEK Conference
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• 2001.09a
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• pp.91-94
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• 2001

Recently a constant-norm constraint equation-error method was proposed to solve the bias problem in adaptive IIR filtering. However, the method adopts a fixed step-size and thus results in slow convergence for a small step-size and significant misadjustment error for a largestep-size. In this paper, we propose a variable step-size (VSS) algorithm that greatly improves convergence properties of the constant-norm constraint equation-error method. The analysis and the simulation results show that the proposed method indeed achieves both fast convergence and small misadjustment error.

• Proceedings of the KSME Conference
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• 2001.06b
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• pp.488-494
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• 2001

Many literatures, so far, have concentrated on approaches employing dependent coordinates set resulting in computational burden of constraint forces, which is needless in many cases. Some researchers developed methods to remove or calculate it efficiently. But systematic generation of the motion equation using independent coordinates set by Kane's equation is possible for any closed loop system. Independent velocity transformation method builds the smallest size of motion equation, but needs practically more complicated code implementation. In this study, dependent velocity matrix is systematically transformed into independent one using dependent-independent transformation matrix of each body group, and then motion equation free of constraint force is constructed. This method is compared with the other approach by counting the number of multiplications for car model with 15 d.o.f..

• Journal of the Korean Society for Aeronautical & Space Sciences
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• v.48 no.11
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• pp.881-888
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• 2020

In this paper, research on estimation of states of a target of interest using Line Of Sight(LOS) angle measurement is performed. Target's position, velocity, and acceleration are chosen to be the states of interests. The LOS measurement is known to be highly non-linear, making target dynamic modeling hard to be implemented into a filter. To solve this issue, the Pseudomeasurement equation was applied to the LOS measurement equation. With the help of this equation, 3D variable turn target dynamic model is applied to the filter model. For better performance, Kinematic Constraint is also implemented into the filter model. As for the filter, Bias Compensation Pseudomeasurement Filter (BCPMF) is used which is known for its robustness to initial conditions. Moreover, Two-Stage Kalman Filter (TSKF) form was also implemented to benefit from the parallel computation. As a result, TBCPMF 3DVT-KC is proposed and simulated to assess performance.

• Journal of applied mathematics & informatics
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• v.27 no.1_2
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• pp.1-12
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• 2009

Iterative algorithms are proposed for the least-squares symmetric solution of AXB = E with a submatrix constraint. We characterize the linear mappings from their independent element space to the constrained solution sets, study their properties and use these properties to propose two matrix iterative algorithms that can find the minimum and quasi-minimum norm solution based on the classical LSQR algorithm for solving the unconstrained LS problem. Numerical results are provided that show the efficiency of the proposed methods.

• Bulletin of the Korean Mathematical Society
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• v.23 no.2
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• pp.141-148
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• 1986

In [1], M. Guignard considered a constraint set in a Banach space, which is similar to that in [2] and gave a first order necessary optimality condition which generalized the Kuhn-Tucker conditions [3]. Sufficiency is proved for objective functions which is either pseudoconcave [5] or quasi-concave [6] where the constraint sets are taken pseudoconvex. In this note, we consider a psedoconvex programming problem in a Hilbert space. Constraint set in a Hillbert space being pseudoconvex and the objective function is restrained by an operator equation. Then we use the methods similar to that in [1] and [6] to obtain a necessary and sufficient optimality condition.

• Journal of the korean Society of Automotive Engineers
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• v.14 no.3
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• pp.43-56
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• 1992

This task is to derive the Hamiltonian equations of motion for BMW 323i vehicle. The kinematic relationships are defined. The cut constraint equations are derived. The cut constraint equations are stabilized. The stabilized constraint equations are used to derive the relationships between the independent and dependent coordinates. The Hamiltonian equations of motion are reduced only in terms of the independent generalized coordinates.