Stabilizing Optimal Density Control of Nonlinear Agents with Multiplicative Noise
- Resource Type
- Conference
- Authors
- Bakshi, Kaivalya; Theodorou, Evangelos A.; Grover, Piyush
- Source
- 2020 59th IEEE Conference on Decision and Control (CDC) Decision and Control (CDC), 2020 59th IEEE Conference on. :3054-3059 Dec, 2020
- Subject
- Robotics and Control Systems
Stability analysis
Optimal control
Steady-state
Statistics
Sociology
Mathematical model
Nonlinear dynamical systems
- Language
- ISSN
- 2576-2370
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 large populations 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.