Backstepping controller design for nonlinear stochastic systems under a risk-sensitive cost criterion

Zigang Pan, Tamer Başar

Research output: Contribution to journalArticlepeer-review

Abstract

This paper develops a methodology for recursive construction of optimal and near-optimal controllers for strict-feedback stochastic nonlinear systems under a risk-sensitive cost function criterion. The design procedure follows the integrator backstepping methodology, and the controllers obtained guarantee any desired achievable level of long-term average cost for a given risk-sensitivity parameter θ. Furthermore, they lead to closed-loop system trajectories that are bounded in probability, and in some cases asymptotically stable in the large. These results also generalize to nonlinear systems with strongly stabilizable zero dynamics. A numerical example included in the paper illustrates the analytical results.

Original languageEnglish (US)
Pages (from-to)957-995
Number of pages39
JournalSIAM Journal on Control and Optimization
Volume37
Issue number3
DOIs
StatePublished - Jan 1 1999

ASJC Scopus subject areas

  • Control and Optimization
  • Applied Mathematics

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