Distributions and Direct Parametrization for Stable Stochastic State-Space Models

2025-03-18

IEEE Control Systems Letters

AI Summary

This work addresses the challenge of ensuring external stability for continuous-time stochastic state-space models (SSSMs). We propose the first explicit, stability-parameterized formulation grounded in the Stochastic Bounded Real Lemma (SBRL), directly embedding stability constraints into the model parameter space to induce an almost-surely stable probabilistic prior. Consequently, posterior predictive distributions—obtained via sampling-based Bayesian inference—are inherently stable. Unlike implicit stabilization techniques, our approach provides a differentiable, explicit, and constraint-consistent parameterization for SSSMs driven by stochastic differential equations, enabling stable modeling with rigorous uncertainty quantification and well-calibrated predictions. Simulation results demonstrate that the method achieves high predictive accuracy while guaranteeing 100% stable sample trajectories and producing statistically calibrated confidence intervals.

Technology Category

• Reasoning under Uncertainty: Relational Probabilistic Models
• Machine Learning: Probabilistic Circuits and Graphical Models
• Intelligent Robots: State Estimation

Application Category

• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• User Modeling, Personalization and Recommendation: User modeling and simulation for interactive and conversational systems
• Search and Retrieval-Augmented AI: Large language models for search

Abstract

We present a direct parametrization for continuous-time stochastic state-space models that ensures external stability via the stochastic bounded-real lemma. Our formulation facilitates the construction of probabilistic priors that enforce almost-sure stability which are suitable for sampling-based Bayesian inference methods. We validate our work with a simulation example and demonstrate its ability to yield stable predictions with uncertainty quantification.

Problem

• Ensuring external stability in stochastic state-space models
• Constructing probabilistic priors for almost-sure stability enforcement
• Enabling stable predictions with uncertainty quantification capabilities

Innovation

• Direct parametrization ensuring external stability via stochastic bounded-real lemma
• Probabilistic priors enforcing almost-sure stability for Bayesian inference
• Validated stable predictions with uncertainty quantification in simulations