Learning Stable and Robust Linear Parameter-Varying State-Space Models
This work addresses the need for stable and robust models in control systems, particularly for convex analysis and controller design, but it is incremental as it builds on existing LPV-SS frameworks with specific parameterizations.
The paper tackles the problem of learning stable and robust linear parameter-varying state-space models by introducing two direct parameterizations that guarantee stability or bounded Lipschitz constants during training, enabling unconstrained optimization and demonstrating effectiveness on an LPV identification problem.
This paper presents two direct parameterizations of stable and robust linear parameter-varying state-space (LPV-SS) models. The model parametrizations guarantee a priori that for all parameter values during training, the allowed models are stable in the contraction sense or have their Lipschitz constant bounded by a user-defined value $γ$. Furthermore, since the parametrizations are direct, the models can be trained using unconstrained optimization. The fact that the trained models are of the LPV-SS class makes them useful for, e.g., further convex analysis or controller design. The effectiveness of the approach is demonstrated on an LPV identification problem.