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From a Single Trajectory to Safety Controller Synthesis of Discrete-Time Nonlinear Polynomial Systems
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This work is concerned with developing a data-driven approach for learning control barrier certificates (CBCs) and associated safety controllers for discrete-time nonlinear polynomial systems with unknown mathematical models, guaranteeing system safety over an infinite time horizon. The proposed approach leverages measured data acquired through an input-output observation, referred to as a single trajectory, collected over a specified time horizon. By fulfilling a certain rank condition, which ensures the unknown system is persistently excited by the collected data, we design a CBC and its corresponding safety controller directly from the finite-length observed data, without explicitly identifying the unknown dynamical system. This is achieved through proposing a data-based sum-of-squares optimization (SOS) program to systematically design CBCs and their safety controllers. We validate our data-driven approach over two physical case studies including a jet engine and a Lorenz system, demonstrating the efficacy of our proposed method.
Forward citations
Cited by 4 Pith papers
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Learning k-Inductive Control Barrier Certificates for Unknown Nonlinear Dynamics Beyond Polynomials
A single trajectory of input-state data is enough to synthesize k-inductive safety certificates and controllers for unknown discrete-time nonlinear systems, including nonpolynomial ones.
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Learning Robust Safety Controllers for Uncertain Input-Affine Polynomial Systems
A single observed trajectory plus a known disturbance bound is enough to synthesize a robust safety certificate and controller for unknown input-affine polynomial systems.
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Abstraction-based Control of Unknown Continuous-Space Models with Just Two Trajectories
A two-trajectory data-driven method constructs a symbolic abstraction and a formal alternating simulation certificate, enabling controller refinement for unknown polynomial systems.
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Towards Mitigating Sim2Real Gaps: A Formal Quantitative Approach
The simulation gap between a nominal model and a high-fidelity simulator is quantified as a state and input dependent bound via convex optimization and Lipschitz constants, then used for symbolic controller synthesis.
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