Definition

Standard Observability - A system is observable if you can determine its complete internal state by observing its outputs over a finite time period. This means you have enough sensor measurements to figure out exactly what's happening within the system.

Sparse Observability - A system is sparse observable if you can determine its internal state even when a limited number of sensors are compromised or unavailable. It implies a degree of resilience – the ability to reconstruct the system state even with partial information.

In terms of a number of sensors $s$ , a system is said to be $s$-sparse observable if it remains observable even with the failure or attack of up to $s$ sensors.

Importance

Sensor Failure - In real-world systems, sensors can malfunction or become unreliable. Sparse observability guarantees that you can still estimate the system's state, crucial for maintaining control and safety.

Cybersecurity - With an increase in cyberattacks on control systems, sensors can be compromised and feed false information. Sparse observability allows for the detection of such attacks and makes the system more robust to them.

Cost Reduction - In some applications, deploying a large number of sensors can be expensive. Sparse observability helps determine the minimum number of sensors needed for reliable state estimation.

Mitigation

Sensor Placement - Strategically placing sensors within the system can improve sparse observability.

State Estimation with Redundant Information - Combining measurements from multiple sensors and using estimation algorithms helps reconstruct the system state even with missing information.

Attack Detection and Isolation - Algorithms can be designed to detect if sensors have been compromised and isolate them, keeping the system safe.