Plant and Controller Optimization in the Context of Chaotic Dynamical Systems

This paper presents a gradient-based framework for plant and controller design of chaotic dynamical systems. The proposed approach uses a least-squares-shadowingmethod to perform the sensitivity analysis of the chaotic system and a first-order optimization algorithm to carry out the optimization process. Two different optimization strategies are examined. The first is a sequential approach, where the plant and control optimization problems are solved in series. The second is a simultaneous approach, where a single optimization problem is solved that considers both the plant and control disciplines at once. The two optimization strategies are applied to a simplified flow-control problem consisting of N potential vortices trapped inside a rectangular domain and controlled by one or more control vortices.

[1]  Panos Y. Papalambros,et al.  An Investigation into Modeling and Solution Strategies for Optimal Design and Control , 2000 .

[2]  Anil V. Rao,et al.  ( Preprint ) AAS 09-334 A SURVEY OF NUMERICAL METHODS FOR OPTIMAL CONTROL , 2009 .

[3]  M. Allen,et al.  Sensitivity analysis of the climate of a chaotic system , 2000 .

[4]  R. Haftka,et al.  An approach to structure/control simultaneous optimization for large flexible spacecraft , 1987 .

[5]  S. Pilyugin.  Shadowing in dynamical systems , 1999 .

[6]  Sandeep Gupta,et al.  An Integrated Control/Structure Design Method using Multi-objective Optimization , 1991 .

[7]  Yurii Nesterov,et al.  First-order methods of smooth convex optimization with inexact oracle , 2013, Mathematical Programming.

[8]  K. Grigoriadis,et al.  Integrated design of structural and control systems with a homotopy like iterative method , 2005, ACC.

[9]  Panos Y. Papalambros,et al.  Combined Optimal Design and Control With Application to an , 2002 .

[10]  J. Humphrey,et al.  Analytical prediction of two-dimensional potential flow due to fixed vortices in a rectangular domain , 1984 .

[11]  A. Galip Ulsoy,et al.  On the coupling between the plant and controller optimization problems , 2001, Proceedings of the 2001 American Control Conference. (Cat. No.01CH37148).

[12]  Jaroslaw Sobieszczanski-Sobieski,et al.  Multidisciplinary aerospace design optimization - Survey of recent developments , 1996 .

[13]  Qiqi Wang,et al.  Least Squares Shadowing sensitivity analysis of chaotic limit cycle oscillations , 2012, J. Comput. Phys..

[14]  Itsuro Kajiwara,et al.  Integrated Design of Aerodynamics and Control System for Micro Air Vehicles , 2000 .

[15]  Qiqi Wang,et al.  Forward and adjoint sensitivity computation of chaotic dynamical systems , 2012, J. Comput. Phys..

[16]  A. K. Dhingra,et al.  Multiobjective design of actively controlled structures using a hybrid optimization method , 1995 .

[17]  Jianhua Zhang,et al.  Active-Passive Hybrid Optimization of Rotor Blades With Trailing Edge Flaps , 2000 .