Neural State-Space MPC for Dual-Uncertainty Control
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Solution Overview
Problem
Current state-space models struggle to simultaneously capture both aleatoric and epistemic uncertainties inherent to real-world technical systems, which is crucial for robust predictive control, especially in safety-critical applications.
Innovation Solution
The integration of neural networks with state-space models to stochastically represent technical systems, encapsulating uncertainties in both hidden states and neural network parameters. This is achieved by using an augmented state that combines the system's latent state with the weights of the neural networks, and approximating the transition and observation functions, as well as the filtering distribution, using normal density functions.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If traditional state-space models are used to represent technical systems, then the model structure is simple and computationally efficient, but the model cannot simultaneously capture both aleatoric and epistemic uncertainties
Solution Approach 1:
The patent combines neural networks with state-space models to create a hybrid model that captures both aleatoric and epistemic uncertainties. The neural network component learns complex system behaviors and uncertainties from data, while the state-space model provides a structured framework for representing system dynamics and uncertainty propagation, achieving comprehensive uncertainty characterization without excessive complexity
Solution Approach 2:
The patent creates a composite modeling approach by integrating two different modeling paradigms: traditional state-space modeling and modern neural network techniques. This composite model leverages the strengths of both approaches - the interpretability and uncertainty formalism of state-space models and the data-driven flexibility of neural networks - to achieve reliable uncertainty capture
2Reliability
If sampling-based approaches are used to capture uncertainties, then both aleatoric and epistemic uncertainties can be represented, but computational complexity increases significantly
Solution Approach 1:
The patent replaces computationally intensive sampling-based uncertainty propagation with an analytical approach using normal density functions. By assuming normal distributions for the filtering distribution and using closed-form moment propagation through the neural network, the model achieves accurate uncertainty representation without the computational burden of Monte Carlo sampling or other sampling-based methods
Data Source
AI summary
A state-space model which includes one or more neural networks. The state-space model is configured to stochastically model a technical system by modelling uncertainties both in latent states of the technical system and in weights of the one or more neural networks. Thereby, the state-space model may be able to capture both aleatoric uncertainty (inherent unpredictability in observations) and epistemic uncertainty (uncertainty in the model's parameters or weights. During the training and during subsequent use for model-predictive control, moment matching across neural network layers is used, which may ensure that the model's predictions are consistent and close to real system behavior.