Simple cell mapping method for multi-objective optimal feedback control design

This paper presents a study of the multi-objective optimal design of a sliding mode control for an under-actuated nonlinear system with the parallel simple cell mapping method. The multi-objective optimal design of the sliding mode control involves six design parameters and five objective functions. The parallel simple cell mapping method finds the Pareto set and Pareto front efficiently. The parallel computing is done on a graphics processing unit. Numerical simulations and experiments are done on a rotary flexible arm system. The results show that the proposed multi-objective designs are quite effective.

Download Full-text

Multi-Objective Optimal Design and Validation of Sliding Mode Control

Volume 8: 27th Conference on Mechanical Vibration and Noise ◽

10.1115/detc2015-46908 ◽

2015 ◽

Cited By ~ 1

Author(s):

Zhi-Chang Qin ◽

Fu-Rui Xiong ◽

Qian Ding ◽

Carlos Hernández ◽

Jesús Fernandez ◽

...

Keyword(s):

Optimal Design ◽

Mapping Method ◽

Simple Cell ◽

Design Parameters ◽

Processing Unit ◽

Cell Mapping ◽

Slide Mode Control ◽

Multi Objective ◽

Mode Control ◽

Simple Cell Mapping

This paper presents a study of multi-objective optimal design of a slide mode control for an under-actuated nonlinear system with the parallel simple cell mapping method. The multi-objective optimal design of the slide mode control involves 6 design parameters and 5 objective functions. The parallel simple cell mapping method finds the Pareto set and Pareto front efficiently. The parallel computing is done on a graphic processing unit (GPU). Numerical simulations and experiments are done on a rotary flexible arm system. The results show that the proposed multi-objective designs are quite effective.

Download Full-text

An Improved Method for Estimating the Domain of Attraction of Passive Biped Walker

Discrete Dynamics in Nature and Society ◽

10.1155/2019/2868543 ◽

2019 ◽

Vol 2019 ◽

pp. 1-11 ◽

Cited By ~ 1

Author(s):

Yu Wang ◽

Heng Cao ◽

JinLin Jiang

Keyword(s):

Domain Of Attraction ◽

Mapping Method ◽

Simple Cell ◽

Iteration Algorithm ◽

Poincaré Mapping ◽

Cell Mapping ◽

Improved Method ◽

Stable Domain ◽

Simple Cell Mapping ◽

Poincare Mapping

An indicator of a passive biped walker’s global stability is its domain of attraction, which is usually estimated by the simple cell mapping method. It needs to calculate a large number of cells’ Poincare mapping result in the estimating process. However, the Poincare mapping is usually computationally expensive and time-consuming due to the complex dynamical equation of the passive biped walker. How to estimate the domain of attraction efficiently and reliably is a problem to be solved. Based on the simple cell mapping method, an improved method is proposed to solve it. The proposed method uses the multiple iteration algorithm to calculate a stable domain of attraction and effectively decreases the total number of Poincare mappings. Through the simulation of the simplest passive biped walker, the improved method can obtain the same domain of attraction as that calculated using the simple cell mapping method and reduce calculation time significantly. Furthermore, this improved method not only proposes a way of rapid estimating the domain of attraction, but also provides a feasible tool for selecting the domain of interest and its discretization level.

Download Full-text

Robust optimal feedback control design for uncertain systems based on artificial neural network approximation of the Bellman’s value function

Neurocomputing ◽

10.1016/j.neucom.2020.06.085 ◽

2020 ◽

Vol 413 ◽

pp. 134-144 ◽

Cited By ~ 2

Author(s):

Mariana Ballesteros ◽

Isaac Chairez ◽

Alexander Poznyak

Keyword(s):

Neural Network ◽

Artificial Neural Network ◽

Feedback Control ◽

Uncertain Systems ◽

Value Function ◽

Control Design ◽

Optimal Feedback Control ◽

Optimal Feedback ◽

Artificial Neural

Download Full-text

Parallel simple cell mapping for multi-objective optimization

Engineering Optimization ◽

10.1080/0305215x.2016.1145215 ◽

2016 ◽

Vol 48 (11) ◽

pp. 1845-1868 ◽

Cited By ~ 7

Author(s):

Jesús Fernández ◽

Oliver Schütze ◽

Carlos Hernández ◽

Jian-Qiao Sun ◽

Fu-Rui Xiong

Keyword(s):

Simple Cell ◽

Multi Objective Optimization ◽

Cell Mapping ◽

Multi Objective ◽

Simple Cell Mapping

Download Full-text

Multi-Objective Optimal Control Design With the Simple Cell Mapping Method

Volume 4B: Dynamics, Vibration and Control ◽

10.1115/imece2013-65506 ◽

2013 ◽

Cited By ~ 2

Author(s):

Yousef Sardahi ◽

Yousef Naranjani ◽

Wei Liang ◽

Jian-Qiao Sun ◽

Carlos Hernandez ◽

...

Keyword(s):

Optimal Control ◽

Optimization Problems ◽

Control Design ◽

Optimal Solutions ◽

Multi Objective Optimization ◽

Cell Mapping ◽

Multi Objective ◽

Simple Cell Mapping ◽

Pareto Sets ◽

Single Objective

Controls are often designed to meet different and conflicting goals. Consider the well-known LQR optimal control. The performance index contains a response measure and a control penalty, which are conflicting requirements. Proper linear or nonlinear combinations of the conflicting objective functions have led to single objective optimization problems. However, such a single objective optimization is dependent on the combination algorithm, and only provides a narrow window of all possible optimal solutions that a system may have. Multi-objective optimization provides a set of optimal solutions, known as Pareto set. There have been many studies of search algorithms for Pareto sets of multi-objective optimization problems for complex dynamical systems. Recently, the simple cell mapping (SCM) method due to C.S. Hsu has been found to be a highly effective tool to compute Pareto sets. This paper applies the SCM method to several control design problems of linear and nonlinear dynamical systems. The results of the work are very exciting to report.

Download Full-text