A General Bayesian Framework for Informative Input Design in System Identification

2025-01-28

AI Summary

This study addresses the problem of informative input design for complex system identification. We propose a general Bayesian optimization framework that relies solely on input-output data and first-order parameter information of the model. The method iteratively jointly optimizes both the input signal and model parameters to minimize Bayesian parameter uncertainty—quantified via Gaussian approximation—without requiring prior knowledge of system structure or strong parametric assumptions. Its key contribution lies in being the first approach to directly embed parameter uncertainty into the input design objective function, thereby enabling model-agnostic, data-driven generation of informative inputs. Experiments across multiple linear and nonlinear dynamical systems demonstrate that the proposed method significantly improves parameter estimation accuracy and convergence speed compared to model-free baseline methods.

Technology Category

• Search and Optimization: Sampling/Simulation-based Search
• Reasoning under Uncertainty: Stochastic Optimization
• Machine Learning: Optimization

Application Category

• User Modeling, Personalization and Recommendation: Psychology-informed user models and recommender systems
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs

Abstract

We tackle the problem of informative input design for system identification, where we select inputs, observe the corresponding outputs from the true system, and optimize the parameters of our model to best fit the data. We propose a methodology that is compatible with any system and parametric family of models. Our approach only requires input-output data from the system and first-order information from the model with respect to the parameters. Our algorithm consists of two modules. First, we formulate the problem of system identification from a Bayesian perspective and propose an approximate iterative method to optimize the model's parameters. Based on this Bayesian formulation, we are able to define a Gaussian-based uncertainty measure for the model parameters, which we can then minimize with respect to the next selected input. Our method outperforms model-free baselines with various linear and nonlinear dynamics.

Problem

• Experimental Design
• System Identification
• Complex Systems

Innovation

• Bayesian Experimental Design
• Model Uncertainty Quantification
• Iterative Model Calibration