Exploiting Over-Approximation Errors as Preview Information for Nonlinear Control
This work provides a new theoretical framework for nonlinear constrained control, offering a method to leverage approximation errors rather than treating them as disturbances.
The paper proposes exploiting over-approximation errors as input-dependent preview information for nonlinear control, enabling the formulation of informed policies and efficient computation of valid inputs via fixed-point equations.
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.