Correct-by-Design Control Synthesis of Stochastic Multi-agent Systems: a Robust Tensor-based Solution

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.