• Journal of Institute of Control, Robotics and Systems
• /
• v.21 no.5
• /
• pp.434-441
• /
• 2015

In this paper, we propose an inverse optimal distributed protocol for the formation and velocity consensus of nonholonomic mobile robots. The communication among mobile robots is described by a simple undirected graph, and the mobile robots' kinematics are considered. The group of mobile robots driven by the proposed protocols asymptotically achieves the desired formation and group velocity in an inverse optimal fashion. The design of the protocols is based on dynamic feedback linearization and the proposed linear quadratic (LQ) inverse optimal second-order consensus protocol. A numerical simulation is given to verify the effectiveness of the proposed scheme.

• 제어로봇시스템학회:학술대회논문집
• /
• 1994.10a
• /
• pp.628-633
• /
• 1994

A new Riemannian geometric model for the controlled plant is proposed by imbedding the control vector space in the state space, so as to reduce the dimension of the model. This geometric model is derived by replacing the orthogonal straight coordinate axes on the state space of a linear system with the curvilinear coordinate axes. Therefore the integral manifold of the geometric model becomes homeomorphic to that of fictitious linear system. For the lower dimensional Riemannian geometric model, a nonlinear optimal regulator with a quadratic form performance index which contains the Riemannian metric tensor is designed. Since the integral manifold of the nonlinear regulator is determined to be homeomorphic to that of the linear regulator, it is expected that the basic properties of the linear regulator such as feedback structure, stability and robustness are to be reflected in those of the nonlinear regulator. To apply the above regulator theory to a real nonlinear plant, it is discussed how to distort the curvilinear coordinate axes on which a nonlinear plant behaves as a linear system. Consequently, a partial differential equation with respect to the homeomorphism is derived. Finally, the computational algorithm for the nonlinear optimal regulator is discussed and a numerical example is shown.

• Bulletin of the Korean Mathematical Society
• /
• v.57 no.2
• /
• pp.311-330
• /
• 2020

This paper investigates infinite horizon optimal control problems driven by a class of backward stochastic delay differential equations in Hilbert spaces. We first obtain a prior estimate for the solutions of state equations, by which the existence and uniqueness results are proved. Meanwhile, necessary and sufficient conditions for optimal control problems on an infinite horizon are derived by introducing time-advanced stochastic differential equations as adjoint equations. Finally, the theoretical results are applied to a linear-quadratic control problem.

• Nuclear Engineering and Technology
• /
• v.21 no.2
• /
• pp.99-110
• /
• 1989

The optimal control of xenon concentration in a nuclear reactor is posed as a linear quadratic regulator problem with state feedback control. Since it is not possible to measure the state variables such as xenon and iodine concentrations directly, implementation of the optimal state feedback control law requires estimation of the unmeasurable state variables. The estimation method used is based on the Luenberger observer. The set of the reactor kinetics equations is a stiff system. This singularly perturbed system arises from the interaction of slow dynamic modes (iodine and xenon concentrations) and fast dynamic modes (neutron flux, fuel and coolant temperatures). The singular perturbation technique is used to overcome this stiffness problem. The observer-based controller of the original system is effected by separate design of the observer and controller of the reduced subsystem and the fast subsystem. In particular, since in the reactor kinetics control problem analyzed in the study the fast mode dies out quickly, we need only design the observer for the reduced slow subsystem. The results of the test problems demonstrated that the state feedback control of the xenon oscillation can be accomplished efficiently and without sacrificing accuracy by using the observer combined with the singular perturbation method.

• Proceedings of the Korea Committee for Ocean Resources and Engineering Conference
• /
• 2003.05a
• /
• pp.57-62
• /
• 2003

This paper describes the design and simulation of a multivariable optimal control system for the combined speed, heading and depth control of a Semi-Autonomous Underwater Vehicle (SAUV) developed in Korea Ocean Research and Development Institute (KRODI). The SAUV is a test-bed for the evaluation of the navigation and manipulator technologies developed for a mine disposal vehicle (MDV) in military use and for a light working underwater vehicle in scientific use. The vehicle was designed to control its cruising speed, heading and depth with 4 horizontal thrusters installed at the rear of the hull. Therefore, the decoupled control methods are limited to apply to the SAUV because the thrust forces are highly coupled with the surging, yawing, and pitching motion of the vehicle. The multivariable Linear Quadratic (LQ) control method is chosen to control steering and diving in variable speed motion automatically. A series of simulation is carried out with fully nonlinear six degree of freedom dynamic model to validate the controller.

• 제어로봇시스템학회:학술대회논문집
• /
• 1991.10a
• /
• pp.395-400
• /
• 1991

In spinning satellite, a gyrotorquer generates a control torquer along two orthogonal axes normal to the spin axis of the vehicle. Matrix Fraction Description(MFD) are used to obtain minimal realization of the transfer matrix relating the attitude angles and the rate of rotation of the gimbals of gyrotorquer. In this paper, the Linear Quadratic Gaussian with Loop Transfer Recovery and H.meihodologies are used to design controller for spinning satellite.

• 제어로봇시스템학회:학술대회논문집
• /
• 1992.10b
• /
• pp.225-228
• /
• 1992

The purpose of this project is the presentation of new method for selection of a scalar control of linear time-periodic system. The approach has been proposed by Radziszewski and Zaleski [4] and utilizes the quadratic form of Lyapunov function. The system under consideration is assigned either in closed-loop state or in modal variables as in Calico, Wiesel [1]. The case of scalar control is considered, the gain matrix being assumed to be at worst periodic with the system period T, each element being represented by a Fourier series. As the optimal gain matrix we consider the matrix ensuring the minimum value of the larger real part of the two Poincare exponents of the system. The method, based on two-step optimization procedure, allows to find the approximate optimal gain matrix. At present state of art determination of the gain matrix for this case has been done by systematic numerical search procedure, at each step of which the Floquet solution must be found.

• Journal of Magnetics
• /
• v.17 no.4
• /
• pp.275-279
• /
• 2012

The linear actuator has the inherent drawback of air gap variation because its linear motion is usually guided by the springs, which destabilizes the dynamic performance. In order to design the linear actuator to be insensitive to air gap, this paper describes the robust design of the air compressor driving linear actuator using Taguchi method. The orthogonal arrays are constructed with selected control factors and noise factor for minimum experiment. The control factors are thickness of inner magnet, height of upper yoke, thickness of outer magnet and thickness of lower yoke while noise factor is airgap. The finite element analysis using commercial electromagnetic analysis program "MAXWELL" are performed instead of experiment. ANOVA are performed to investigate the effects of design factors. In result, the optimal robust linear actuator which is insensitive to air gap variation is designed.

• Journal of Advanced Marine Engineering and Technology
• /
• v.23 no.5
• /
• pp.630-636
• /
• 1999

In this paper in optimal modulation controller for position control and anti-sway of container crane systems is designed by a recursive algorithm that determines the state weighting matrix Q of a linear quadratic performance. The optimal modulation controller is based on optimal control. The basic feature of the recursive algorithm is the reduction of the number of iterations as well as minimization of the calculations involved So in order to obtain a mathematical model which rep-resents the equation of motion of the trolley and load Lagrange equation is used. The optimal modulation controller has been verified and simulated to show that it is robust when a load dis-turbance is applied and a reference is changed.

• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• v.19 no.3
• /
• pp.217-234
• /
• 2015

In this tutorial the theoretical background of LQ optimal guidance is reviewed, starting from calculus of variations. LQ optimal control is then introduced and applied to missile guidance to obtain the basic form of LQ optimal guidance laws. Extension of LQ optimal guidance methodology for handling weighted cost function, dynamic lag associated with the missile dynamics and the autopilot, constrained impact angle, and constrained impact time is also described with a brief discussion on the asymptotic properties of the optimal guidance laws. Furthermore, an introduction to polynomial guidance and generalized impactangle-control guidance, which are closed related with LQ optimal guidance, is provided to demonstrate the current status of missile guidance techniques.