Dissipativity, inverse optimal control, and stability margins for nonlinear discrete-time 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 discrete-time nonlinear stochastic dynamical systems controlled by nonlinear optimal and inverse optimal controllers that minimise a nonlinear-nonquadratic performance criterion. 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 discrete-time stochastic dynamical systems. In particular, using extended Kalman-Yakubovich-Popov conditions characterising stochastic dissipativity we show that our optimal feedback control law satisfies a return difference inequality predicated on a difference operator of a controlled Markov dispersion process and is stochastically dissipative with respect to a specific quadratic supply rate.

KEYWORDS:

• Stochastic dissipativity
• controlled Markov chains
• Kalman-Yakubovic-Popov conditions
• inverse optimality
• gain
• sensor
• and disk margins

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was supported in part by the Air Force Office of Scientific Research under Grant FA9550-20-1-0038.