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Mathematics of Control, Signals and Systems

, Volume 13, Issue 4, pp 318–332 | Cite as

Robust Properties of Risk-Sensitive Control

  • Paul Dupuis
  • Matthew R. James
  • Ian Petersen

Abstract.

The purpose of this paper is to characterize and prove robustness properties of risk-sensitive controllers precisely. In particular, we establish a stochastic version of the small gain theorem. This theorem is expressed in terms of an inequality which bounds the average output power in terms of the input power. Since this inequality is closely related to the risk-sensitive criterion, our stochastic small gain theorem can be expressed in terms of the risk-sensitive criterion. This provides a concrete motivation for the use of the risk-sensitive criterion stochastic robustness.

Key words. Risk-sensitive stochastic control, Robustness, Small gain theorem. 

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Copyright information

© Springer-Verlag London Limited 2000

Authors and Affiliations

  • Paul Dupuis
    • 1
  • Matthew R. James
    • 2
  • Ian Petersen
    • 3
  1. 1.Lefschetz Center for Dynamical Systems, Division of Applied Mathematics, Brown University, Providence, Rhode Island 02912, U.S.A. dupuis@cfm.brown.edu.US
  2. 2.Department of Engineering, Australian National University, Canberra, ACT 0200, Australia. Matthew.James@anu.edu.au.AU
  3. 3.Department of Electrical Engineering, Australian Defence Force Academy, Canberra, ACT 2600, Australia. irp@routh.ee.adfa.oz.au.AU

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