INFINITE-HORIZON OPTIMAL CONTROL BASED ON CONTINUOUS-TIME CONTINUOUS-STATE HOPFIELD NEURAL NETWORKS

2006 ◽  
Vol 04 (04) ◽  
pp. 707-719
Author(s):  
MING-AI LI ◽  
NAI-GONG YU ◽  
JUN-FEI QIAO ◽  
XIAO-GANG RUAN
Keyword(s):  
Optimal Control ◽  
Continuous Time ◽  
Control Method ◽  
Infinite Horizon ◽  
Hopfield Neural Network ◽  
Time Varying ◽  
Optimization Strategy ◽  
Linear Quadratic ◽  
Continuous State ◽  
Optimization Control

An optimal control method based on continuous-time continuous-state Hopfield neural network (CTCSHNN) is proposed for time-varying multivariable systems. The equivalence is built theoretically between receding-horizon linear quadratic (LQ) performance index and energy function of CTCSHNN, and the CTCSHNN is constructed to solve the above LQ optimization control problems. Moreover, the rolling optimization strategy is adopted to form closed-loop control structure that includes CTCSHNN so, the dynamic infinite-horizon optimization control is realized for multivariable time-varying systems. As an example, a second order time-varying system is simulated. Simulation results show the effectiveness and feasibility of the proposed method.

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.

scholarly journals Decentralized Reinforcement Learning Robust Optimal Tracking Control for Time Varying Constrained Reconfigurable Modular Robot Based on ACI andQ-Function

2013 ◽  
Vol 2013 ◽  
pp. 1-16 ◽  
Author(s):  
Bo Dong ◽  
Yuanchun Li
Keyword(s):  
Optimal Control ◽  
Reinforcement Learning ◽  
Control Theory ◽  
Continuous Time ◽  
Tracking Control ◽  
Control Policy ◽  
Time Varying ◽  
Optimal Tracking ◽  
Tracking Controller ◽  
Global Uncertainty

A novel decentralized reinforcement learning robust optimal tracking control theory for time varying constrained reconfigurable modular robots based on action-critic-identifier (ACI) and state-action value function (Q-function) has been presented to solve the problem of the continuous time nonlinear optimal control policy for strongly coupled uncertainty robotic system. The dynamics of time varying constrained reconfigurable modular robot is described as a synthesis of interconnected subsystem, and continuous time state equation andQ-function have been designed in this paper. Combining with ACI and RBF network, the global uncertainty of the subsystem and the HJB (Hamilton-Jacobi-Bellman) equation have been estimated, where critic-NN and action-NN are used to approximate the optimalQ-function and the optimal control policy, and the identifier is adopted to identify the global uncertainty as well as RBF-NN which is used to update the weights of ACI-NN. On this basis, a novel decentralized robust optimal tracking controller of the subsystem is proposed, so that the subsystem can track the desired trajectory and the tracking error can converge to zero in a finite time. The stability of ACI and the robust optimal tracking controller are confirmed by Lyapunov theory. Finally, comparative simulation examples are presented to illustrate the effectiveness of the proposed ACI and decentralized control theory.

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