Linear optimal control of continuous time chaotic systems

Kaveh Merat; Jafar Abbaszadeh Chekan; Hassan Salarieh; Aria Alasty

doi:10.1016/j.isatra.2014.01.003

Linear optimal control of continuous time chaotic systems

ISA Trans. 2014 Jul;53(4):1209-15. doi: 10.1016/j.isatra.2014.01.003. Epub 2014 Apr 13.

Authors

Kaveh Merat¹, Jafar Abbaszadeh Chekan¹, Hassan Salarieh², Aria Alasty¹

Affiliations

¹ Department of Mechanical Engineering, Sharif University of Technology, P.O. Box 11155-9567, Tehran, Iran.
² Department of Mechanical Engineering, Sharif University of Technology, P.O. Box 11155-9567, Tehran, Iran. Electronic address: salarieh@sharif.edu.

PMID: 24736189
DOI: 10.1016/j.isatra.2014.01.003

Abstract

In this research study, chaos control of continuous time systems has been performed by using dynamic programming technique. In the first step by crossing the response orbits with a selected Poincare section and subsequently applying linear regression method, the continuous time system is converted to a discrete type. Then, by solving the Riccati equation a sub-optimal algorithm has been devised for the obtained discrete chaotic systems. In the next step, by implementing the acquired algorithm on the quantized continuous time system, the chaos has been suppressed in the Rossler and AFM systems as some case studies.

Keywords: AFM system; Chaos; Continuous time system; Optimal control; Rossler system.