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Algorithmic Feedback Synthesis for Robust Strong Invariance of Continuous Control Systems
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DOI：10.1109/tac.2026.3670765.png)
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Abstract
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This article presents a numerically viable technique for synthesizing feedback to ensure robust positive invariance of <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">given</i> compact sets for nonlinear control systems. The search for a suitable feedback is posed as a linear approximation problem in the functional analytic sense, and the verification of the so-called “cone conditions” for robust positive invariance is employed to achieve the ensuing approximation. This verification turns out to be equivalent to solving a compact family of convex inequalities on a compact domain, and an algorithmic procedure based on convex semi-infinite programming is deployed and charged with this task.The technique is entirely offline and applies to noisy continuous nonlinear control-affine systems without special algebraic structure, and does not even require the analytical expressions of the various vector fields as long as they can be evaluated at will. Numerical examples are included to illustrate our results.
Keywords:
Algorithmic synthesis
robust optimization
robust positive invariance
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7
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1.3W
Citations:
6.7W
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