Assessing optimality and robustness for the control of dynamical systems

Demiralp M., Rabitz H.

PHYSICAL REVIEW E, vol.61, no.3, pp.2569-2578, 2000 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 61 Issue: 3
  • Publication Date: 2000
  • Doi Number: 10.1103/physreve.61.2569
  • Title of Journal : PHYSICAL REVIEW E
  • Page Numbers: pp.2569-2578

Abstract

This work presents a general framework for assessing the quality and robustness of control over a deterministic system described by a state vector x(t) under external manipulation via a control vector u(t). The control process is expressed in terms of a cost functional, including the physical objective, penalties, and constraints. The notions of optimality and robustness are expressed in terms of the sign and the magnitude of the cost functional curvature with respect to the controls. Both issues may be assessed from the eigenvalues of the stability operator S whose kernel K(t,tau) is determined by <(delta u(t))over bar>/<(delta u(tau))over bar> for t(0)1) will lead to a loss of local optimality. A simple illustrative example is given from a linear dynamical system, and a bound for the eigenvalue spectrum of the stability operator is presented. The bound is employed to qualitatively analyze control optimality and robustness behavior. A second example of a nonlinear quartic anharmonic oscillator is also presented for stability and robustness analysis. In this case it is proved that the control system kernel is negative definite, implying full stability but only marginal robustness.