Plant and Controller Optimization in the Context of Chaotic Dynamical Systems

Abstract

This paper presents a gradient-based framework for plant and controller design of chaotic dynamical systems. The proposed approach uses a least-squares-shadowing method 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.

Feedback control of chaotic systems using multiple shooting shadowing and application to Kuramoto–Sivashinsky equation

“…Thus, we can compare the control kernels produced by the shadowing and LQR approaches. We note that very few attempts have been made to solve an optimization problem using LSS before [25,26], and none have considered the computation of the feedback matrix.…”