A Method for Solving a Class of Optimal Control Problem of Boolean Networks on Infinite Horizon

2019 ◽  
Vol 08 (02) ◽  
pp. 309-319
Author(s):  
荧 周
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Infinite Horizon ◽  
Boolean Networks

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.

scholarly journals Stochastic optimal control problem with infinite horizon driven by G-Brownian motion

2018 ◽  
Vol 24 (2) ◽  
pp. 873-899 ◽  
Author(s):  
Mingshang Hu ◽  
Falei Wang
Keyword(s):  
Optimal Control ◽  
Brownian Motion ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Stochastic Optimal Control ◽  
Value Function ◽  
Infinite Horizon ◽  
Dynamic Programming Principle ◽  
Stochastic Optimal Control Problem ◽  
The Value Function

The present paper considers a stochastic optimal control problem, in which the cost function is defined through a backward stochastic differential equation with infinite horizon driven by G-Brownian motion. Then we study the regularities of the value function and establish the dynamic programming principle. Moreover, we prove that the value function is the unique viscosity solution of the related Hamilton−Jacobi−Bellman−Isaacs (HJBI) equation.

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