Guaranteed Privacy-Preserving <i>H</i> _∞-Optimal Interval Observer Design for Nonlinear Discrete-Time Systems

We propose a novel guaranteed privacy-preserving (GP) interval observer design for perturbed nonlinear discrete-time bounded-error systems. Unlike stochastic differential privacy, guaranteed privacy offers strict bounds on the proximity between the ranges of two sets of estimated data. Our approach relies on synthesizing an interval observer for a perturbed nonlinear bounded-error system. The design procedure incorporates a bounded noise perturbation factor computation and observer gains synthesis based on solving tractable semi-definite programs. Consequently, the observer simultaneously provides GP and stable interval-valued estimates for the desired variable. We demonstrate the optimality of our design by minimizing the H∞ norm of the observer error system. Further, we assess the accuracy of our proposed mechanism by quantifying the loss incurred when considering GP specifications. Simulations illustrate the outperformance of the proposed approach to differential privacy.