• Journal of applied mathematics & informatics
• /
• v.16 no.1_2
• /
• pp.515-524
• /
• 2004

We prove the local existence of solution for nonconvex-valued differential inclusion under time-varying state constraints.

• Journal of Mechanical Science and Technology
• /
• v.20 no.6
• /
• pp.770-781
• /
• 2006

This paper defined design constraints for the compound CVTs (continuously variable trans-missions) by combining power-circulation-mode CVTs and power-split-mode CVTs, which were proposed for connecting 2K-H I-type differential gear to V-belt-type CVU (Continuously Variable Unit). The design constraints are the necessary and sufficient conditions to avoid geometrical interferences among elements in the compound CVTs, and to guarantee smooth assembly between the power-circulation-mode CVT and power-split-mode CVT Two com-pound CVTs were designed and manufactured in accordance with the design constraints. With these compound CVTs, theoretical analysis and performance experiments were conducted. The results showed that the design constraints were valid and effective design method, and that the designed compound CVTs had the improved performance.

• Communications of the Korean Mathematical Society
• /
• v.19 no.3
• /
• pp.557-567
• /
• 2004

We prove the sufficient conditions for optimality in differential inclusion problem by using the value function. For this purpose, we assume at first that the value function is locally Lipschitz. Secondly, without this assumption, we use the viability theory.

• Journal of applied mathematics & informatics
• /
• v.19 no.1_2
• /
• pp.215-229
• /
• 2005

In this paper, constraint aggregation is combined with the adjoint and multiple shooting strategies for optimal control of differential algebraic equations (DAE) systems. The approach retains the inherent parallelism of the conventional multiple shooting method, while also being much more efficient for large scale problems. Constraint aggregation is employed to reduce the number of nonlinear continuity constraints in each multiple shooting interval, and its derivatives are computed by the adjoint DAE solver DASPKADJOINT together with ADIFOR and TAMC, the automatic differentiation software for forward and reverse mode, respectively. Numerical experiments demonstrate the effectiveness of the approach.

• International Journal of Control, Automation, and Systems
• /
• v.6 no.3
• /
• pp.401-412
• /
• 2008

This paper discusses a design methodology of cooperative path planning for dynamical multi-agent systems with spatial and temporal constraints. The cooperative behavior of the multi-agent systems is specified in terms of the objective function in an optimization formulation. The path of achieving cooperative tasks is then generated by the optimization formulation constructed based on a differential flatness approach. Three scenarios of multi-agent tasking are proposed at the cooperative task planning framework. Given agent dynamics, both spatial and temporal constraints are considered in the path planning. The path planning algorithm first finds trajectory curves in a lower-dimensional space and then parameterizes the curves by a set of B-spline representations. The coefficients of the B-spline curves are further solved by a sequential quadratic programming solver to achieve the optimization objective and satisfy these constraints. Finally, several illustrative examples of cooperative path/task planning are presented.

• Journal of the Korean Operations Research and Management Science Society
• /
• v.14 no.2
• /
• pp.97-104
• /
• 1989

This paper extends the existence proofs of a Nash equilibrium to a more general class of differentila game models with constraints on the control spaces. With the assumptions of continuity, convexity, and compactness, the existence is proved using Kakutani Theorem and via a path-following approach. Furthermore, the proof for a period-by-period optimization of multi-period problems provides an insight to a numerical solution algorithm to differential game models with constraints.

• Structural Engineering and Mechanics
• /
• v.16 no.3
• /
• pp.259-274
• /
• 2003

In this paper, a novel numerical solution technique, the differential cubature method is employed to study the buckling problems of thick plates with arbitrary quadrilateral planforms and non-uniform boundary constraints based on the first order shear deformation theory. By using this method, the governing differential equations at each discrete point are transformed into sets of linear homogeneous algebraic equations. Boundary conditions are implemented through discrete grid points by constraining displacements, bending moments and rotations of the plate. Detailed formulation and implementation of this method are presented. The buckling parameters are calculated through solving a standard eigenvalue problem by subspace iterative method. Convergence and comparison studies are carried out to verify the reliability and accuracy of the numerical solutions. The applicability, efficiency, and simplicity of the present method are demonstrated through solving several sample plate buckling problems with various mixed boundary constraints. It is shown that the differential cubature method yields comparable numerical solutions with 2.77-times less degrees of freedom than the differential quadrature element method and 2-times less degrees of freedom than the energy method. Due to the lack of published solutions for buckling of thick rectangular plates with mixed edge conditions, the present solutions may serve as benchmark values for further studies in the future.

• Proceedings of the Korean Society of Precision Engineering Conference
• /
• 2000.11a
• /
• pp.670-673
• /
• 2000

This paper attempt analysis and computer simulation of dynamics of a set of dual multi-joint fingers with soft-deformable tips which are grasping. Firstly, a set of differential equation describing dynamics of the fingers and object together with geometric constraint of tight area-contacts is formulated by Euler-Lagrange's formalism. Secondly, problems of controlling both the internal force and the rotation angle of the grasped object under the constraints of area-contacts of tight area-contacts are discussed. The effect of geometric constraints of area-contacts on motion of the overall system is analyzed and a method of computer simulation for overall system of differential-algebraic equations is presented. Finally, simulation results are shown and the effects of geometric constraints of area-contact is discussed.

• 제어로봇시스템학회:학술대회논문집
• /
• 2001.10a
• /
• pp.132.6-132
• /
• 2001

This paper aims to derive a mathematical model of the dynamics of handling tasks in field robot which stable grasping and manipulates a rigid object with some dexterity. Firstly, a set of differential equation describing dynamics of the manipulators and object together with geometric constraint of tight area-contacts is formulated by Lagrange equation. Secondly, problems of controlling both the internal force and the rotation angle of the grasped object under the constraints of area-contacts of tight area-contacts are discussed. The effect of geometric constraints of area-contacts on motion of the overall system is analyzed and a method of computer simulation for overall system of differential-algebraic equations is presented. Thirdly, simulation results are shown and the effects of geometric constraints of area-contact is discussed.

• Structural Engineering and Mechanics
• /
• v.5 no.3
• /
• pp.283-295
• /
• 1997

This paper presents a high precision integration method for the dynamic response analysis of structures with holonomic constraints. A detail recursive scheme suitable for algebraic and differential equations (ADEs) which incorporates generalized forces is established. The matrix exponential involved in the scheme is calculated precisely using $2^N$ algorithm. The Taylor expansions of the nonlinear term concerned with state variables of the structure and the generalized constraint forces of the ADEs are derived and consequently, their particular integrals are obtained. The accuracy and effectiveness of the present method is demonstrated by two numerical examples, a plane truss with circular slot at its tip point and a slewing flexible cantilever beam which is currently interesting in optimal control of robot manipulators.