Problem
Research questions and friction points this paper is trying to address.
Structured State-space Models
output feedback control
nonlinear systems
controllability
observability
Controller Design for Structured State-space Models via Contraction Theory
🤖 AI Summary
This work addresses the challenge of simultaneously achieving scalability and stability in data-driven output-feedback control of nonlinear systems by proposing a novel approach based on structured state-space models (SSMs). It presents the first systematic analysis of controllability and observability for SSMs and, leveraging contraction theory, develops an output-feedback controller that can be efficiently synthesized via linear matrix inequalities (LMIs). The study further establishes a separation principle tailored to SSMs, thereby rigorously guaranteeing exponential stability of the closed-loop system. Numerical experiments demonstrate the method’s effectiveness and scalability in jointly modeling nonlinear dynamics and synthesizing high-performance controllers.
📝 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.
Innovation
Methods, ideas, or system contributions that make the work stand out.
Structured State-space Models
Contraction Theory
Linear Matrix Inequalities
Separation Principle
Output Feedback Control
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