Implications of dissipativity, inverse optimal control, and stability margins for nonlinear stochastic feedback regulators

Wassim M. Haddad, Xu Jin

Research output: Contribution to journalArticlepeer-review

4 Scopus citations


In this paper, we derive stability margins for optimal and inverse optimal stochastic feedback regulators. Specifically, gain, sector, and disk margin guarantees are obtained for nonlinear stochastic dynamical systems controlled by nonlinear optimal and inverse optimal Hamilton-Jacobi-Bellman controllers that minimize a nonlinear-nonquadratic performance criterion with cross-weighting terms. Furthermore, using the newly developed notion of stochastic dissipativity, we derive a return difference inequality to provide connections between stochastic dissipativity and optimality of nonlinear controllers for stochastic dynamical systems. In particular, using extended Kalman-Yakubovich-Popov conditions characterizing stochastic dissipativity, we show that our optimal feedback control law satisfies a return difference inequality predicated on the infinitesimal generator of a controlled Markov diffusion process if and only if the controller is stochastically dissipative with respect to a specific quadratic supply rate.

Original languageEnglish
Pages (from-to)5499-5519
Number of pages21
JournalInternational Journal of Robust and Nonlinear Control
Issue number16
StatePublished - Nov 10 2019

Bibliographical note

Funding Information:
This work was supported in part by the Air Force Office of Scientific Research under grant FA9550-16-1-0100.

Publisher Copyright:
© 2019 John Wiley & Sons, Ltd.


  • controlled Markov diffusion processes
  • disk margins
  • inverse optimality
  • stochastic control
  • stochastic dissipativity

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Chemical Engineering (all)
  • Biomedical Engineering
  • Aerospace Engineering
  • Mechanical Engineering
  • Industrial and Manufacturing Engineering
  • Electrical and Electronic Engineering


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