Correct-by-Design Control Synthesis of Stochastic Multi-agent Systems: a Robust Tensor-based Solution
It addresses the scalability problem in stochastic multi-agent control for temporal logic specifications, offering a method with probabilistic guarantees.
The paper tackles the verification and control of discrete-time stochastic systems with continuous spaces, proposing an abstraction-based framework that uses robust dynamic programming and tensor decomposition to provide scalable control strategies with provable lower bounds on temporal-logic satisfaction.
Discrete-time stochastic systems with continuous spaces are hard to verify and control, even with MDP abstractions due to the curse of dimensionality. We propose an abstraction-based framework with robust dynamic programming mappings that deliver control strategies with provable lower bounds on temporal-logic satisfaction, quantified via approximate stochastic simulation relations. Exploiting decoupled dynamics, we reveal a Canonical Polyadic Decomposition tensor structure in value functions that makes dynamic programming scalable. The proposed method provides correct-by-design probabilistic guarantees for temporal logic specifications. We validate our results on continuous-state linear stochastic systems.