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H2-H∞ Control of Discrete Time Nonlinear Systems Using the SDRE Approach

[+] Author Affiliations
Xin Wang, Edwin E. Yaz, Susan C. Schneider

Marquette University, Milwaukee, WI

Yvonne I. Yaz

Milwaukee School of Engineering, Milwaukee, WI

Paper No. DSCC2011-5935, pp. 565-572; 8 pages
doi:10.1115/DSCC2011-5935
From:
  • ASME 2011 Dynamic Systems and Control Conference and Bath/ASME Symposium on Fluid Power and Motion Control
  • ASME 2011 Dynamic Systems and Control Conference and Bath/ASME Symposium on Fluid Power and Motion Control, Volume 1
  • Arlington, Virginia, USA, October 31–November 2, 2011
  • Conference Sponsors: Dynamic Systems and Control Division
  • ISBN: 978-0-7918-5475-4
  • Copyright © 2011 by ASME

abstract

A novel H2 –H∞ State Dependent Riccati Equation control approach is presented for providing a generalized control framework to discrete time nonlinear system. By solving a generalized Riccati Equation at each time step, the nonlinear state feedback control solution is found to satisfy mixed performance criteria guaranteeing quadratic optimality with inherent stability property in combination with H∞ type of disturbance attenuation. Two numerical techniques to compute the solution of the resulting Riccati equation are presented: The first one is based on finding the steady state solution of the difference equation at every step and the second one is based on finding the minimum solution of a linear matrix inequality. The effectiveness of the proposed techniques is demonstrated by simulations involving the control of an inverted pendulum on a cart, a benchmark mechanical system.

Copyright © 2011 by ASME

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