A Tractable Fault Detection and Isolation Approach for Nonlinear Systems with Probabilistic Performance

This article presents a novel perspective along with a scalable methodology to design a fault detection and isolation (FDI) filter for high dimensional nonlinear systems. Previous approaches on FDI problems are either confined to linear systems or they are only applicable to low dimensional dynamics with specific structures. In contrast, shifting attention from the system dynamics to the disturbance inputs, we propose a relaxed design perspective to train a linear residual generator given some statistical information about the disturbance patterns. That is, we propose an optimization-based approach to robustify the filter with respect to finitely many signatures of the nonlinearity. We then invoke recent results in randomized optimization to provide theoretical guarantees for the performance of the proposed filer. Finally, motivated by a cyber-physical attack emanating from the vulnerabilities introduced by the interaction between IT infrastructure and power system, we deploy the developed theoretical results to detect such an intrusion before the functionality of the power system is disrupted

A note on the expected probability of constraint violation in sampled convex programs

In this note we derive an exact expression for the expected probability V of constraint violation in a sampled convex program (see [1], [2] for definitions and an introduction to this topic): V = expected number of support constraints/1 + number of constraints. This result (Theorem 1) is obtained using a simple technique based on cardinality count. In the note, we also use a Chernoff bounding technique on the upper tail violation probability expression derived in to obtain one of the tightest available explicit bounds on the sample complexity of sampled convex programs (Proposition 3