Optimal Feedback Production for a Supply Chain

2005 ◽  
pp. 50-66
Author(s):  
K. Wong ◽  
H. W.J. Lee ◽  
Chi Kin Chan
Keyword(s):  
Optimal Control ◽  
Supply Chain ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Objective Function ◽  
Production Rate ◽  
Infinite Horizon ◽  
Time Interval ◽  
Control Parameterization ◽  
Demand Rate

In this chapter, we modeled the dynamics of a supply chain considered by several authors. An infinite-horizon, time-delayed, optimal control problem was thus obtained. By approximating the time interval [0, ¥] by [0, Tf ], we obtained an approximated problem (P(Tf )) which could be easily solved by the control parameterization method. Moreover, we could show that the objective function of the approximated problem converged to that of the original problem as Tf ® ¥. Several examples have been solved to illustrate the efficiency of our method. In these examples, some important results relating the production rate to demand rate have been developed.

scholarly journals Intrinsic Optimal Control for Mechanical Systems on Lie Group

2017 ◽  
Vol 2017 ◽  
pp. 1-8
Author(s):  
Chao Liu ◽  
Shengjing Tang ◽  
Jie Guo
Keyword(s):  
Optimal Control ◽  
Analytical Solution ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Lie Group ◽  
Control Method ◽  
Geodesic Distance ◽  
Infinite Horizon ◽  
Mechanical Systems ◽  
Programming Approach

The intrinsic infinite horizon optimal control problem of mechanical systems on Lie group is investigated. The geometric optimal control problem is built on the intrinsic coordinate-free model, which is provided with Levi-Civita connection. In order to obtain an analytical solution of the optimal problem in the geometric viewpoint, a simplified nominal system on Lie group with an extra feedback loop is presented. With geodesic distance and Riemann metric on Lie group integrated into the cost function, a dynamic programming approach is employed and an analytical solution of the optimal problem on Lie group is obtained via the Hamilton-Jacobi-Bellman equation. For a special case on SO(3), the intrinsic optimal control method is used for a quadrotor rotation control problem and simulation results are provided to show the control performance.

METHOD TO SOLVE THE NONLINEAR INFINITE HORIZON OPTIMAL CONTROL PROBLEM WITH APPLICATION TO THE TRACK CONTROL OF A MOBILE ROBOT

2007 ◽  
Vol 17 (10) ◽  
pp. 3607-3611 ◽  
Author(s):  
THOMAS HOLZHÜTER ◽  
THOMAS KLINKER
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Mobile Robot ◽  
Control Problem ◽  
Infinite Horizon ◽  
Nonlinear Controller ◽  
Linear Quadratic ◽  
Lagrange Equations ◽  
Globally Asymptotically Stable ◽  
Low Dimensional

We present a numerical method to solve the infinite time horizon optimal control problem for low dimensional nonlinear systems. Starting from the linear-quadratic approximation close to the origin, the extremal field is efficiently calculated by solving the Euler–Lagrange equations backward in time. The resulting controller is given numerically on an interpolation grid. We use the method to obtain the optimal track controller for a mobile robot. The result is a globally asymptotically stable nonlinear controller, obtained without any specific insight into the system dynamics.

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