• 제어로봇시스템학회:학술대회논문집
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• 2001.10a
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• pp.108.3-108
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• 2001

In this work, we consider a real time optimal control problem of mechanical systems with restrictions for actuators i.e. input restrictions and constraints for the movable area i.e. state constraints. First, we formulate an optimal control problem which evaluates the cost function for a finite time horizon with input restrictions and state constraints of a wheeled vehicle as an example of mechanical systems. In this problem, the differentiability of the cost function is not required and this implies that the problem cannot be solved analytically. Therefore, in this work, we use an optimization method to solve the optimal control problem and a new real time optimization method is proposed to solve the problem. In this method, we provide a parameter that indicates the ...

• Journal of applied mathematics & informatics
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• v.7 no.3
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• pp.787-800
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• 2000

In this paper we consider an optimal control system described by n-dimensional heat equation with a thermal source. Thus problem is to find an optimal control which puts the system in a finite time T, into a stationary regime and to minimize a general objective function. Here we assume there is no constraints on control. This problem is reduced to a moment problem. We modify the moment problem into one consisting of the minimization of a positive linear functional over a set of Radon measures and we show that there is an optimal measure corresponding to the optimal control. The above optimal measure approximated by a finite combination of atomic measures. This construction gives rise to a finite dimensional linear programming problem, where its solution can be used to determine the optimal combination of atomic measures. Then by using the solution of the above linear programming problem we find a piecewise-constant optimal control function which is an approximate control for the original optimal control problem. Finally we obtain piecewise-constant optimal control for two examples of heat equations with a thermal source in one-dimensional.

• Transactions on Control, Automation and Systems Engineering
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• v.1 no.1
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• pp.16-20
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• 1999

Like the usual systems, the industrial robot manipulator has some constraints for motion. Usually we hope that the manipulators move fast to accomplish the given task. The problem can be formulated as the time-optimal control problem under the constraints such as the limits of velocity, acceleration and jerk. But it is very difficult to obtain the exact solution of the time-optimal control problem. This paper solves this problem in two steps. In the first step, we find the minimum time trajectories by optimizing cubic polynomial joint trajectories under the physical constraints using the modified evolution strategy. In the second step, the controller is optimized for robot manipulator to track precisely the optimized trajectory found in the previous step. Experimental results for SCARA type manipulator show that the proposed method is very useful.

• Journal of applied mathematics & informatics
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• v.20 no.1_2
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• pp.293-303
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• 2006

This paper describes a numerical scheme for optimal control of a time-dependent linear system to a moving final state. Discretization of the corresponding differential equations gives rise to a linear algebraic system. Defining some binary variables, we approximate the original problem by a mixed integer linear programming (MILP) problem. Numerical examples show that the resulting method is highly efficient.

• Journal of the Korean Society for Precision Engineering
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• v.12 no.5
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• pp.57-68
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• 1995

A general procedure for the numerical solution of coupled, nonlinear, differential two-point boundary-value problems, solutions of which are crucial to the controller design, has been developed and demonstrated. A fixed-end-points, free-terminal-time, optimal-control problem, which is derived from Pontryagin's Maximum Principle, is solved by an extension of Davidenko's method, a differential form of Newton's method, for algebraic root finding. By a discretization process like finite differences, the differential equations are converted to a nonlinear algebraic system. Davidenko's method reconverts this into a pseudo-time-dependent set of implicitly coupled ODEs suitable for solution by modern, high-performance solvers. Another important advantage of Davidenko's method related to the time-optimal problem is that the terminal time can be computed by treating this unkown as an additional variable and sup- plying the Hamiltonian at the terminal time as an additional equation. Davidenko's method uas used to produce optimal trajectories of a single-degree-of-freedom problem. This numerical method provides switching times for open-loop control, minimized terminal time and optimal input torque sequences. This numerical technique could easily be adapted to the multi-point boundary-value problems.

• ICROS
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• v.1 no.1
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• pp.16-16
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• 1995

Like the usual systems, the industrial robot manipulator has some constraints for motion. Usually we hope that the manipulators move fast to accomplish the given task. The problem can be formulated as the time-optimal control problem under the constraints such as the limits of velocity, acceleration and jerk. But it is very difficult to obtain the exact solution of the time-optimal control problem. This paper solves this problem in two steps. In the first step, we find the minimum time trajectories by optimizing cubic polynomial joint trajectories under the physical constraints using the modified evolution strategy. In the second step, the controller is optimized for robot manipulator to track precisely the optimized trajectory found in the previous step. Experimental results for SCARA type manipulator show that the proposed method is very useful.

• Journal of the Korea Institute of Military Science and Technology
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• v.11 no.3
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• pp.5-12
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• 2008

This paper presents the features of an impact angle constrained open-loop optimal trajectory which is given by a function of initial conditions and optimal guidance gains. Using missile motion described by linearized kinematic equations and a proper form of performance index, an inverse optimal problem is suggested to investigate the gains related to the performance index. The flight trajectory and time-to-go can be shaped in terms of the optimal guidance gains. The results are evaluated by 3-DOF simulation.

• 제어로봇시스템학회:학술대회논문집
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• 1996.10a
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• pp.263-266
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• 1996

A method to determine an optimal temperature trajectory that guarantees polymer products having controlled molecular weight distribution and desired values of molecular weight is presented. The coordinate transformation method and the optimal control theory are applied to a batch PMMA polymerization system to calculate the optimal temperature trajectory. Coordinate transformation method converts the original fixed-end-point, free-end-time problem to a free-end-point, fixed-end-time problem. The idea is that by making the reactor temperature track the optimal temperature trajectory one may be able to produce polymer products having the prespecified physical property in a minimum time. The on-line control experiments with the PID control algorithm have been conducted to establish the validity of the scheme proposed in this study. The experimental results show that prespecified polymer product could be obtained with tracking the calculated optimal temperature trajectory.

• 제어로봇시스템학회:학술대회논문집
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• 1996.10b
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• pp.1169-1172
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• 1996

A time-optimal control law for quick, strongly nonlinear systems has been developed and demonstrated. This procedure involves the utilization of neural networks as state feedback controllers that learn the time-optimal control actions by means of an iterative minimization of both the final time and the final state error for the known and unknown systems with constrained inputs and/or states. The nature of neural networks as a parallel processor would circumvent the problem of "curse of dimensionality". The control law has been demonstrated for a velocity input type motor identified by a genetic algorithm called GENOCOP.

• 제어로봇시스템학회:학술대회논문집
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• 1991.10a
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• pp.147-151
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• 1991

In this paper a time-optimal path planning scheme for the multiple robot manipulators will be proposed by using hopfield neural network. The time-optimal path planning, which can allow multiple robot system to perform the demanded tasks with a minimum execution time and collision avoidance, may be of consequence to improve the productivity. But most of the methods proposed till now suffers from a significant computational burden and thus limits the on-line application. One way to avoid such a difficulty is to rearrange the problem as MTSP(Multiple Travelling Salesmen Problem) and then apply the Hopfield network technique, which can allow the parallel computation, to the minimum time problem. This paper proposes an approach for solving the time-optimal path planning of the multiple robots by using Hopfield neural network. The effectiveness of the proposed method is demonstrated by computer simulation.