• The Transactions of The Korean Institute of Electrical Engineers
• /
• v.61 no.3
• /
• pp.451-458
• /
• 2012

This paper addresses the problem that policy iteration (PI) for continuous-time (CT) systems requires explorations of the state space which is known as persistency of excitation in adaptive control community, and as a result, proposes a PI scheme explorized by an additional probing signal to solve the addressed problem. The proposed PI method efficiently finds in online fashion the related CT linear quadratic (LQ) optimal control without knowing the system matrix A, and guarantees the stability and convergence to the LQ optimal control, which is proven in this paper in the presence of the probing signal. A design method for the probing signal is also presented to balance the exploration of the state space and the control performance. Finally, several simulation results are provided to verify the effectiveness of the proposed explorized PI method.

• Korean Journal of Mathematics
• /
• v.23 no.2
• /
• pp.293-312
• /
• 2015

We deal with a boundary control problem for the vorticity minimization, in which the ow is governed by the time-dependent two dimensional incompressible Navier-Stokes equations. We derive a mathematical formulation and a process for an appropriate control along the portion of the boundary to minimize the vorticity motion due to the ow in the fluid domain. After showing the existence of an optimal solution, we derive the optimality system for which optimal solutions may be determined. The differentiability of the state solution in regard to the control parameter shall be conjunct with the necessary conditions for the optimal solutions.

• Journal of the Korean Society for Precision Engineering
• /
• v.21 no.7
• /
• pp.76-82
• /
• 2004

The solutions of neighboring optimal control are typically obtained using the sweep method or transition matrices. Due to the numerical integration, however, the gain matrix can become infinite as time go to final one in the transition matrices, and the Riccati solution can become infinite when the final time free. To overcome these disadvantages, this paper proposes the pseudospectral Legendre method which is to first discreteize the linear boundary value problem using the global orthogonal polynomial, then transforms into an algebraic equations. Because this method is not necessary to take any integration of transition matrix or Riccati equation, it can be usefully used in real-time operation. Finally, its performance is verified by the numerical example for the space vehicle's orbit transfer.

• The Transactions of the Korean Institute of Electrical Engineers D
• /
• v.54 no.6
• /
• pp.359-365
• /
• 2005

This paper presents an reduced-order near-optimal controller for the congestion control of Available Bit Rate (ABR) service in Asynchronous Transfer Mode (ATM) networks. We introduce the model, of a class of ABR traffic, that can be controlled using a Explicit Rate feedback for congestion control in ATM networks. Since there are great computational complexities in the class of optimal control problem for the ABR model, the near-optimal controller via reduced-order technique is applied to this model. It is implemented by the help of weakly coupling and singular perturbation theory, and we use bilinear transformation because of its computational convenience. Since the bilinear transformation can convert discrete Riccati equation into continuous Riccati equation, the design problems of optimal congestion control can be reduced. Using weakly coupling and singular perturbation theory, the computation time of Riccati equations can be saved, moreover the real-time congestion control for ATM networks can be possible.

• Honam Mathematical Journal
• /
• v.8 no.1
• /
• pp.21-49
• /
• 1986

A class of singular quadratic control problem is considered. The state is governed by a higher order system of ordinary linear differential equations and very general nonstandard boundary conditions. These conditions in many important cases reduce to standard boundary conditions and because of the conditions the usual controllability condition is not needed. In the special case where the coefficient matrix of the control variable in the cost functional is a time-independent singular matrix, the corresponding optimal control law as well as the optimal controller are computed. The method of investigation is based on the theory of least-squares solutions of multi-valued operator equations.

• 제어로봇시스템학회:학술대회논문집
• /
• 1993.10a
• /
• pp.293-298
• /
• 1993

In this paper, methods for computing the time-optimal motion of a robotic manipulator are presented that considers the nonlinear manipulator dynamics, actuator constraints, joint limits, and obstacles. The optimization problem can be reduced to a search for the time-optimal path in the n-dimensional position space. These paths are further optimized with a local path optimization to yield a global optimal solution. Time-optimal motion of a robot with an articulated arm is presented as an example.

• Nuclear Engineering and Technology
• /
• v.35 no.5
• /
• pp.399-411
• /
• 2003

A model predictive control method is applied to design an automatic controller for thermal power control in a reactor core. The basic concept of the model predictive control is to solve an optimization problem for a finite future at current time and to implement as the current control input only the first optimal control input among the solutions of the finite time steps. At the next time step, the second optimal control input is not implemented and the procedure to solve the optimization problem is then repeated. The objectives of the proposed model predictive controller are to minimize the difference between the output and the desired output and the variation of the control rod position. The nonlinear PWR plant model (a nonlinear point kinetics equation with six delayed neutron groups and the lumped thermal-hydraulic balance equations) is used to verify the proposed controller of reactor power. And a controller design model used for designing the model predictive controller is obtained by applying a parameter estimation algorithm at an initial stage. From results of numerical simulation to check the controllability of the proposed controller at the $5\%/min$ ramp increase or decrease of a desired load and its $10\%$ step increase or decrease which are design requirements, the performances of this controller are proved to be excellent.

• Bulletin of the Korean Mathematical Society
• /
• v.14 no.1
• /
• pp.43-50
• /
• 1977

• Journal of applied mathematics & informatics
• /
• v.15 no.1_2
• /
• pp.127-146
• /
• 2004

In this paper we consider a heat flow in an inhomogeneous. body without internal source. There exists special initial and boundary conditions in this system and we intend to find a convenient coefficient of heat conduction for this body so that body cool off as much as possible after definite time. We consider this problem in a general form as an optimal control problem which coefficient of heat conduction is optimal function. Then we replace this problem by another in which we seek to minimize a linear form over a subset of the product of two measures space defined by linear equalities. Then we construct an approximately optimal control.

• Journal of Biosystems Engineering
• /
• v.23 no.2
• /
• pp.115-124
• /
• 1998

Over- and under-application of pesticides to crops have recently become main concerns regarding the environment conservation, product cost and firmer's safety. Thus, a uniform and optimal application method of pesticides was needed. The objective of study was to evaluate flow compensating characteristics of a variable flow control system for a boom sprayer using a laboratory setup. At the most variable conditions, the control system was acceptable with the flowrate control strategy. However, the sprayer control system became unstably fluctuating at the long execution time with small tolerance because of the constant valve on-time. This problem was solved by employing a variable on-time control. The optimal values for the damping ratio and the execution time were 2 and 1.0 sec, respectively, with the tolerances less than 3%. The performance of the control system at the optimal conditions were the response time of 3.8sec and the absolute steady-state error of 0.5% with the stable RCV and ROS ( < 1.0).