Controller Design for Structured State-space Models via Contraction Theory
This work addresses control design for nonlinear systems, offering a scalable method with potential applications in domains like robotics or autonomous systems, but it appears incremental as it builds on existing SSM frameworks.
The paper tackles the problem of designing output feedback controllers for nonlinear systems using Structured State-space Models (SSMs) as surrogate models, establishing controllability and observability analysis, scalable control design via LMIs with contraction theory, and a separation principle, demonstrated through a numerical example.
This paper presents an indirect data-driven output feedback controller synthesis for nonlinear systems, leveraging Structured State-space Models (SSMs) as surrogate models. SSMs have emerged as a compelling alternative in modelling time-series data and dynamical systems. They can capture long-term dependencies while maintaining linear computational complexity with respect to the sequence length, in comparison to the quadratic complexity of Transformer-based architectures. The contributions of this work are threefold. We provide the first analysis of controllability and observability of SSMs, which leads to scalable control design via Linear Matrix Inequalities (LMIs) that leverage contraction theory. Moreover, a separation principle for SSMs is established, enabling the independent design of observers and state-feedback controllers while preserving the exponential stability of the closed-loop system. The effectiveness of the proposed framework is demonstrated through a numerical example, showcasing nonlinear system identification and the synthesis of an output feedback controller.