Exploiting Over-Approximation Errors as Preview Information for Nonlinear Control
By: Antoine Aspeel, Antoine Girard, Thiago Alves Lima
Potential Business Impact:
Makes robots smarter by using mistakes as clues.
We study the control of nonlinear constrained systems via over-approximations. Our key observation is that the over-approximation error, rather than being an unknown disturbance, can be exploited as input-dependent preview information. This leads to the notion of informed policies, which depend on both the state and the error. We formulate the concretization problem -recovering a valid input for the true system from a preview-based policy- as a fixed-point equation. Existence of solutions follows from the Brouwer fixed-point theorem, while efficient computation is enabled through closed-form, linear, or convex programs for input-affine systems, and through an iterative method based on the Banach fixed-point theorem for nonlinear systems.
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