Adversarial Observability and Performance Trade-offs in Optimal Control

TL;DR

This paper presents a method to design feedback controllers that reduce the observability of adversarial sensors in linear systems while maintaining desired performance levels, using semidefinite programming techniques.

Contribution

It introduces a novel framework for balancing observability reduction and control performance through theoretical bounds and optimization formulations.

Findings

Theoretical bounds on observability metrics under performance constraints.

Semidefinite programming formulations for observability and inverse observability optimization.

Simulation results demonstrating effective observability reduction with minimal performance loss.

Abstract

We develop a feedback controller that minimizes the observability of a set of adversarial sensors of a linear system, while adhering to strict closed-loop performance constraints. We quantify the effectiveness of adversarial sensors using the trace of their observability Gramian and its inverse, capturing both average observability and the least observable state directions of the system. We derive theoretical lower bounds on these metrics under performance constraints, characterizing the fundamental limits of observability reduction as a function of the performance trade-off. Finally, we show that the performance-constrained optimization of the Gramian's trace can be formulated as a one-shot semidefinite program, while we address the optimization of its inverse through sequential semidefinite programming. Simulations on an aircraft show how the proposed scheme yields controllers that deteriorate adversarial observability while having near-optimal performance.