2 research outputs found
A Novel Distance Matric: Generalized Relative Entropy
Information entropy and its extension, which are important generalization of
entropy, have been applied in many research domains today. In this paper, a
novel generalized relative entropy is constructed to avoid some defects of
traditional relative entropy. We presented the structure of generalized
relative entropy after the discussion of defects in relative entropy. Moreover,
some properties of the provided generalized relative entropy is presented and
proved. The provided generalized relative entropy is proved to have a finite
range and is a finite distance metric.Comment: 7page
Stabilizing Optimal Density Control of Nonlinear Agents with Multiplicative Noise
Control of continuous time dynamics with multiplicative noise is a classic
topic in stochastic optimal control. This work addresses the problem of
designing infinite horizon optimal controls with stability guarantees for
\textit{a single agent or large population systems} of identical,
non-cooperative and non-networked agents, with multi-dimensional and nonlinear
stochastic dynamics excited by multiplicative noise. For agent dynamics
belonging to the class of reversible diffusion processes, we provide
constraints on the state and control cost functions which guarantee stability
of the closed-loop system under the action of the individual optimal controls.
A condition relating the state-dependent control cost and volatility is
introduced to prove the stability of the equilibrium density. This condition is
a special case of the constraint required to use the path integral Feynman-Kac
formula for computing the control. We investigate the connection between the
stabilizing optimal control and the path integral formalism, leading us to a
control law formulation expressed exclusively in terms of the desired
equilibrium density.Comment: 6 pages, 0 figures, IEEE Conference on Decision and Control 2020
(accepted