• Coupled systems mechanics
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• v.7 no.6
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• pp.707-729
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• 2018

The semi-active optimal vibration control of nonlinear torsion-bar suspension vehicle systems under random road excitations is an important research subject, and the boundedness of MR dampers and the uncertainty of vehicle systems are necessary to consider. In this paper, the differential equations of motion of the coupling torsion-bar suspension vehicle system with MR damper under random road excitation are derived and then transformed into strongly nonlinear stochastic coupling vibration equations. The dynamical programming equation is derived based on the stochastic dynamical programming principle firstly for the nonlinear stochastic system. The semi-active bounded parametric optimal control law is determined by the programming equation and MR damper dynamics. Then for the uncertain nonlinear stochastic system, the minimax dynamical programming equation is derived based on the minimax stochastic dynamical programming principle. The worst-case disturbances and corresponding semi-active bounded parametric optimal control are obtained from the programming equation under the bounded disturbance constraints and MR damper dynamics. The control strategy for the nonlinear stochastic vibration of the uncertain torsion-bar suspension vehicle system is developed. The good effectiveness of the proposed control is illustrated with numerical results. The control performances for the vehicle system with different bounds of MR damper under different vehicle speeds and random road excitations are discussed.

• Structural Engineering and Mechanics
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• v.15 no.6
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• pp.669-683
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• 2003

The stochastic optimal nonlinear control of coupled adjacent building structures is studied based on the stochastic dynamical programming principle and the stochastic averaging method. The coupled structures with control devices under random seismic excitation are first condensed to form a reduced-order structural model for the control analysis. The stochastic averaging method is applied to the reduced model to yield stochastic differential equations for structural modal energies as controlled diffusion processes. Then a dynamical programming equation for the energy processes is established based on the stochastic dynamical programming principle, and solved to determine the optimal nonlinear control law. The seismic response mitigation of the coupled structures is achieved through the structural energy control and the dimension of the optimal control problem is reduced. The seismic excitation spectrum is taken into account according to the stochastic dynamical programming principle. Finally, the nonlinear controlled structural response is predicted by using the stochastic averaging method and compared with the uncontrolled structural response to evaluate the control efficacy. Numerical results are given to demonstrate the response mitigation capabilities of the proposed stochastic optimal control method for coupled adjacent building structures.

• Smart Structures and Systems
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• v.5 no.1
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• pp.69-79
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• 2009

A non-clipped semi-active stochastic optimal control strategy for nonlinear structural systems with MR dampers is developed based on the stochastic averaging method and stochastic dynamical programming principle. A nonlinear stochastic control structure is first modeled as a semi-actively controlled, stochastically excited and dissipated Hamiltonian system. The control force of an MR damper is separated into passive and semi-active parts. The passive control force components, coupled in structural mode space, are incorporated in the drift coefficients by directly using the stochastic averaging method. Then the stochastic dynamical programming principle is applied to establish a dynamical programming equation, from which the semi-active optimal control law is determined and implementable by MR dampers without clipping in terms of the Bingham model. Under the condition on the control performance function given in section 3, the expressions of nonlinear and linear non-clipped semi-active optimal control force components are obtained as well as the non-clipped semi-active LQG control force, and thus the value function and semi-active nonlinear optimal control force are actually existent according to the developed strategy. An example of the controlled stochastic hysteretic column is given to illustrate the application and effectiveness of the developed semi-active optimal control strategy.

• 제어로봇시스템학회:학술대회논문집
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• 1993.10a
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• pp.264-269
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• 1993

In this paper, we develop the basic robot commands on the level of VAL robot language and the integrated environment software of the robot management system to give users an easy way of programming and running the robot. The developed software is designed to support Korean language and to be run by the pop-up menus for programming commands and inputs. Geometrical and dynamical features can be viewed on a computer monitor by graphics and the taught works can be interfaced with a computer and controllers.

• Smart Structures and Systems
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• v.19 no.1
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• pp.21-31
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• 2017

To control the stochastic vibration of a vibration-sensitive instrument supported on a beam, the beam is designed as a sandwich structure with magneto-rheological visco-elastomer (MRVE) core. The MRVE has dynamic properties such as stiffness and damping adjustable by applied magnetic fields. To achieve better vibration control effectiveness, the optimal bounded parametric control for the MRVE sandwich beam with supported mass under stochastic and deterministic support motion excitations is proposed, and the stochastic and shock vibration suppression capability of the optimally controlled beam with multi-mode coupling is studied. The dynamic behavior of MRVE core is described by the visco-elastic Kelvin-Voigt model with a controllable parameter dependent on applied magnetic fields, and the parameter is considered as an active bounded control. The partial differential equations for horizontal and vertical coupling motions of the sandwich beam are obtained and converted into the multi-mode coupling vibration equations with the bounded nonlinear parametric control according to the Galerkin method. The vibration equations and corresponding performance index construct the optimal bounded parametric control problem. Then the dynamical programming equation for the control problem is derived based on the dynamical programming principle. The optimal bounded parametric control law is obtained by solving the programming equation with the bounded control constraint. The controlled vibration responses of the MRVE sandwich beam under stochastic and shock excitations are obtained by substituting the optimal bounded control into the vibration equations and solving them. The further remarkable vibration suppression capability of the optimal bounded control compared with the passive control and the influence of the control parameters on the stochastic vibration suppression effectiveness are illustrated with numerical results. The proposed optimal bounded parametric control strategy is applicable to smart visco-elastic composite structures under deterministic and stochastic excitations for improving vibration control effectiveness.

• International Journal of Control, Automation, and Systems
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• v.6 no.3
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• pp.401-412
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• 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 Astronomy and Space Sciences
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• v.20 no.1
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• pp.63-82
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• 2003

Using the Schwarzschild's linear programming technique, we obtained the general solutions of the collisionless Bolzmann equation describing the spherical galaxy in dynamical equilibrium. From this calculation we have confirmed the existence of isotropic spherical galaxies obeying a de Vaucouleurs'law which includes a dark halo. The flattening profile of the velocity dispersion curve seen in the elliptical galaxies can be explained as the increase of mass to light ratio in this dark matter. The space density distribution of this dark matter shows that the core radius of the dark matter is smaller than the effective radius of the galaxy.

• Structural Engineering and Mechanics
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• v.31 no.5
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• pp.621-624
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• 2009

The time delay in active and semi-active controls is an important research subject. Many researches on the time-delay control for deterministic systems have been made (Hu and Wang 2002, Yang et al. 1990, Abdel-Mooty and Roorda 1991, Pu 1998, Cai and Huang 2002), while the study on that for stochastic systems is very limited. The effects of the time delay on the control of nonlinear systems under Gaussian white noise excitations have been studied by Bilello et al. (2002). The controlled linear systems with deterministic and random time delay subjected to Gaussian white noise excitations have been treated by Grigoriu (1997). Recently, a stochastic averaging method for quasi-integrable Hamiltonian systems with time delay has been proposed (Liu and Zhu 2007). In the present paper, a stochastic optimal time-delay control method for stochastically excited nonlinear structural systems is proposed based on the stochastic averaging method for quasi Hamiltonian systems with time delay and the stochastic dynamical programming principle. An example of stochastically excited and controlled hysteretic column is given to illustrate the proposed control method.

• Journal of applied mathematics & informatics
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• v.23 no.1_2
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• pp.215-228
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• 2007

By using the variational calculus of fractional order, one derives a Hamilton-Jacobi equation and a Lagrangian variational approach to the optimal control of one-dimensional fractional dynamics with fractional cost function. It is shown that these two methods are equivalent, as a result of the Lagrange's characteristics method (a new approach) for solving non linear fractional partial differential equations. The key of this results is the fractional Taylor's series $f(x+h)=E_{\alpha}(h^{\alpha}D^{\alpha})f(x)$ where $E_{\alpha}(.)$ is the Mittag-Leffler function.

• Journal of the Korean Society for Aeronautical & Space Sciences
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• v.45 no.5
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• pp.437-446
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• 2017

An integrated flight simulation program for multicopter drones is presented. The program includes rigid body dynamics, propeller thrust, battery energy, control, and air. Using this program, users can monitor and analyze the states of drones along flight trajectories. As a programming language, Modelica has been chosen, that specializes in simulation program development. Modelica enables users to develop simulation programs efficiently due to acausal and object oriented properties. For missions including horizontal and vertical maneuvers, many dynamical states of drones have been analyzed with simulation results.