Controller Design for Structured State-space Models via Contraction Theory

TL;DR

This paper develops a scalable, contraction theory-based control design for structured state-space models, enabling independent observer and controller synthesis with proven stability.

Contribution

It provides the first controllability and observability analysis of SSMs, and introduces a control design framework using LMIs and a separation principle.

Findings

Controlled nonlinear systems using SSMs with stability guarantees

Demonstrated nonlinear system identification and output feedback control

Proved exponential stability of the closed-loop system

Abstract

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.