Resilient State Estimation for Nonlinear Discrete-Time Systems via Input and State Interval Observer Synthesis

TL;DR

This paper proposes a novel resilient interval observer for nonlinear discrete-time systems that can detect and estimate states and unknown inputs even under sensor and actuator attacks, ensuring stability and optimality.

Contribution

It introduces a new observer design using mixed-monotone decomposition and affine outer-approximation, with synthesis methods for stability and optimality under attack conditions.

Findings

Observer guarantees containment of true states and inputs.

Semi-definite programs enable stable and optimal gain synthesis.

The method effectively detects and estimates in attacked nonlinear systems.

Abstract

This paper addresses the problem of resilient state estimation and attack reconstruction for bounded-error nonlinear discrete-time systems with nonlinear observations/ constraints, where both sensors and actuators can be compromised by false data injection attack signals/unknown inputs. By leveraging mixed-monotone decomposition of nonlinear functions, as well as affine parallel outer-approximation of the observation functions, along with introducing auxiliary states to cancel out the effect of the attacks/unknown inputs, our proposed observer recursively computes interval estimates that by construction, contain the true states and unknown inputs of the system. Moreover, we provide several semi-definite programs to synthesize observer gains to ensure input-to-state stability of the proposed observer and optimality of the design in the sense of minimum $\mathcal{H}_{\infty}$ gain.