Stochastic viability and dynamic programming

TL;DR

This paper introduces a stochastic viability kernel concept for nonlinear systems with constraints, using dynamic programming to compute viable feedbacks under uncertainty, extending deterministic viability analysis to stochastic settings.

Contribution

It defines and computes a stochastic viability kernel and viable feedbacks using dynamic programming, bridging deterministic and stochastic control approaches.

Findings

Stochastic viability kernels can be computed via dynamic programming.

Viable feedbacks can be designed using chance constraints.

The approach is illustrated with a practical example.

Abstract

This paper deals with the stochastic control of nonlinear systems in the presence of state and control constraints, for uncertain discrete-time dynamics in finite dimensional spaces. In the deterministic case, the viability kernel is known to play a basic role for the analysis of such problems and the design of viable control feedbacks. In the present paper, we show how a stochastic viability kernel and viable feedbacks relying on probability (or chance) constraints can be defined and computed by a dynamic programming equation. An example illustrates most of the assertions.