Implications of dissipativity, inverse optimal control, and stability margins for nonlinear stochastic feedback regulators
Abstract
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.
Document Details
- Document Type
- Pub Defense Publication
- Publication Date
- Jul 19, 2019
- Source ID
- 10.1002/rnc.4678
Entities
People
- Wassim M. Haddad
- Xu Jin
Organizations
- Air Force Office of Scientific Research
- Georgia Tech