H-like control for nonlinear stochastic systems

N. Berman, U. Shaked

Research output: Contribution to journalArticlepeer-review

Abstract

In this paper we develop a H∞-type theory, from the dissipation point of view, for a large class of time-continuous stochastic nonlinear systems. In particular, we introduce the notion of stochastic dissipative systems analogously to the familiar notion of dissipation associated with deterministic systems and utilize it as a basis for the development of our theory. Having discussed certain properties of stochastic dissipative systems, we consider time-varying nonlinear systems for which we establish a connection between what is called the L2-gain property and the solution to a certain Hamilton-Jacobi inequality (HJI), that may be viewed as a bounded real lemma for stochastic nonlinear systems. The time-invariant case with infinite horizon is also considered, where for this case we synthesize a worst case-based stabilizing controller. Stability in this case is taken to be in the mean-square sense. In the stationary case, the problem of robust state feedback control is considered in the case of norm-bounded uncertainties. A solution is then derived in terms of linear matrix inequalities.

Original languageEnglish
Pages (from-to)247-257
Number of pages11
JournalSystems and Control Letters
Volume55
Issue number3
DOIs
StatePublished - Mar 2006

Keywords

  • Disturbance attenuation
  • H-infinity
  • Linear matrix inequalities
  • Nonlinear systems
  • Stochastic systems

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